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Inflation: Its Causes, Effects, and Social Costs

Reading: Chapter 5, Mankiw.

Tasneem Raihan

Department of Economics

University of California, Riverside

MACROECONOMICS

N. Gregory Mankiw

PowerPoint ® Slides by Ron Cronovich

Fall 2014 update

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CHAPTER 5 Inflation

IN THIS CHAPTER, YOU WILL LEARN:

The macroeconomic effects of monetary policy

The classical theory of inflation

causes

effects

social costs

“Classical” – assumes prices are flexible & markets clear

Applies to the long run

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CHAPTER 5 Inflation

Money: Definition

Money is the stock of assets that can be readily used to make transactions.

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CHAPTER 5 Inflation

Money: Types

1. Fiat money

has no intrinsic value

example: the paper currency we use

2. Commodity money

has intrinsic value

examples: gold coins, cigarettes in P.O.W. camps

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CHAPTER 5 Inflation

NOW YOU TRY Discussion Question

Which of these are money?

a. Currency

b. Checks

c. Deposits in checking accounts (“demand deposits”)

d. Credit cards

e. Certificates of deposit (“time deposits”)

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CHAPTER 5 Inflation

Answers:

a - yes

b - no, not the checks themselves, but the funds in checking accounts are money.

c - yes (see b)

d - no, credit cards are a means of deferring payment.

e - CDs are a store of value, and they are measured in money units. They are not readily spendable, though.

For each item listed, which of the functions of money it serves?

The money supply and monetary policy definitions

The money supply is the quantity of money available in the economy.

Monetary policy is the control over the money supply.

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CHAPTER 5 Inflation

Again, this is mostly review.

Money supply measures, June 2014

9,952

M1 + small time deposits, savings deposits, money market mutual funds, money market deposit accounts

2,270

C + demand deposits, travelers’ checks, other checkable deposits

1,214

Currency

amount ($ billions)

assets included

symbol

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CHAPTER 5 Inflation

The most important thing that students should get from this slide is the following:

Each successive measure of the money supply is BIGGER and LESS LIQUID than the one it follows. I.e.,

checking account deposits (in M1 but not C) are less liquid than currency.

Money market deposit account and savings account balances (in M2 but not M1) are less liquid than demand deposits.

Whether you require your students to learn the definitions of every component of each monetary aggregate is up to you. Most professors agree that students should learn the definitions of M1, M2, demand deposits, and time deposits. Some professors feel that, since the quantity of information students can learn in a semester is finite, it is not worthwhile to require students to learn such terms as “repurchase agreements.” However, you might orally state the definitions of such terms to help students better understand the nature of the monetary aggregates.

Source: Federal Reserve Board, H.6 release.

http://www.federalreserve.gov/releases/h6/current/h6.htm

Figures are seasonally adjusted.

Banks’ role in the monetary system

The money supply equals currency plus demand (checking account) deposits:

M = C + D

Since the money supply includes demand deposits, the fractional reserve banking system and household behavior play important roles.

Read chapter 4 to revise what you learnt in Introductory Macroeconomics course.

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CHAPTER 5 Inflation

The central bank and monetary control

Monetary policy is conducted by a country’s central bank.

The U.S.’ central bank is called the Federal Reserve (“the Fed”).

To control the money supply, the Fed uses open market operations, the purchase and sale of government bonds.

The Federal Reserve Building Washington, DC

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CHAPTER 5 Inflation

Again, this is mostly review.

U.S. inflation and its trend, 1960–2014

% change in GDP deflator

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CHAPTER 5 Inflation

Over the short run, the inflation rate can be volatile. In later chapters, we will learn about the forces that affect inflation in the short run. In this chapter, we focus on…

Source: Federal Reserve Bank of St. Louis

http://research.stlouisfed.org/fred2/

GDPDEF (percent change from year ago)

GDP Deflator 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001. 75 2002 2002.25 2002.5 2002.75 2003 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 1.2242400000000001E-2 1.44698E-2 1.53545E-2 1.3934800000000001E-2 1.1986399999999999E-2 1.10878E-2 1.04569E-2 1.1122999999999999E-2 1.4778899999999999E-2 1.3947299999999999E-2 1.3214500000000001E-2 1.29046E-2 9.2534000000000002E-3 9.7652999999999993E-3 9.4280000000000006E-3 1.3888899999999999E-2 1.46385E-2 1.53902E-2 1.7382700000000001E-2 1.46771E-2 1.6635E-2 1.8331699999999999E-2 1.80038E-2 1.9540200000000001E-2 2.1059499999999998E-2 2.53432E-2 3.2114200000000002E-2 3.4995999999999999E-2 3.3039899999999997E-2 2.9718999999999999E-2 2.9221899999999999E-2 3.11192E-2 3.7632899999999997E-2 4.2958499999999997E-2 4.3012799999999997E-2 4.60864E-2 4.5588799999999999E-2 4.8084399999999999E-2 5.2679200000000002E-2 5. 1502699999999998E-2 5.53839E-2 5.6422100000000003E-2 4.9742300000000003E-2 4.9658599999999997E-2 5.0637700000000001E-2 4.98206E-2 5.2090999999999998E-2 4.7107299999999998E-2 4.7480700000000001E-2 4.0070700000000001E-2 3.9671699999999997E-2 4.4949500000000003E-2 4.1187000000000001E-2 5.1104799999999999E-2 6.1314599999999997E-2 6.8271600000000002E-2 7.6086600000000004E-2 8.4950399999999995E-2 9.5699699999999999E-2 0.10656019999999999 0.1108587 0.1011195 8.9399999999999993E-2 7.6464199999999996E-2 6.3497899999999996E-2 5.9046500000000002E-2 5.3803400000000001E-2 5.4203099999999997E-2 6.0453E-2 6.4246800000000007E-2 6.2797699999999998E-2 6.6802500000000001E-2 6.4504800000000001E-2 6.8855100000000002E-2 7.3536000000000004E-2 7.2681800000000005E-2 7.6081999999999997E-2 8.2696599999999995E-2 8.80 48899999999999E-2 8.70475E-2 9.0410699999999997E-2 8.8003300000000007E-2 8.9275599999999997E-2 9.7335900000000003E-2 0.10200679999999999 9.8244899999999996E-2 9.2713900000000002E-2 8.2652799999999998E-2 7.0205100000000006E-2 6.3053700000000004E-2 5.9434899999999999E-2 5.1739599999999997E-2 4.60852E-2 4.1121999999999999E-2 3.6964799999999999E-2 3.3380600000000003E-2 3.8065000000000002E-2 3.9358299999999999E-2 3.7148899999999999E-2 3.6158000000000003E-2 3.4520099999999998E-2 3.1559299999999998E-2 2.75461E-2 2.7702000000000001E-2 2.1591200000000001E-2 2.1192900000000001E-2 2.2790600000000001E-2 2.29643E-2 2.7283200000000001E-2 2.77132E-2 2.99321E-2 3.08808E-2 2.9738199999999999E-2 3.35214E-2 3.7042699999999998E-2 3.6975399999999999E-2 4.0185899999999997E-2 4.0636400000000003 E-2 3.5778900000000002E-2 3.4788800000000002E-2 3.5548499999999997E-2 3.7378099999999997E-2 4.0083000000000001E-2 4.15547E-2 4.01877E-2 3.5559E-2 3.4106400000000002E-2 3.18137E-2 2.6044899999999999E-2 2.5082799999999999E-2 2.1894500000000001E-2 2.1768200000000001E-2 2.2684800000000001E-2 2.2022199999999999E-2 2.1985500000000002E-2 2.1796599999999999E-2 2.10358E-2 2.0267299999999999E-2 2.1627199999999999E-2 2.1280899999999998E-2 2.1774999999999999E-2 2.1433299999999999E-2 2.0171399999999999E-2 2.0092800000000001E-2 2.0138699999999999E-2 1.95339E-2 1.7975100000000001E-2 1.8431800000000002E-2 1.9124200000000001E-2 1.75931E-2 1.7921900000000001E-2 1.6067399999999999E-2 1.1240200000000001E-2 1.13089E-2 1.1647100000000001E-2 1.0969400000000001E-2 1.37679E-2 1.4906000000000001E-2 1.48025E-2 1.5316099999999999E-2 1.8860499999999999E-2 2.0432700000000002E-2 2.2770599999999998E-2 2.45347E-2 2.3340900000000001E-2 2.51001E-2 2.21738E-2 1.9956000000000002E-2 1.66678E-2 1.4327299999999999E-2 1.55137E-2 1.8217299999999999E-2 2.1713699999999999E-2 2.01163E-2 2.1372200000000001E-2 2.0711799999999999E-2 2.24496E-2 2.80872E-2 2.9808000000000001E-2 3.2230200000000001E-2 3.27572E-2 3.0969400000000001E-2 3.4061099999999997E-2 3.5024600000000003E-2 3.3196299999999998E-2 3.5308800000000001E-2 3.2511100000000001E-2 2.8469299999999999E-2 3.2580499999999998E-2 3.0598E-2 2.6310199999999999E-2 2.6606299999999999E-2 1.9192600000000001E-2 1.8458700000000001E-2 2.1871100000000001E-2 1.8875200000000002E-2 1.5806000000000001E-2 9.2236999999999996E-3 2.1573999999999999E-3 3.5668000000000002E-3 4.4870999999999999E-3 1.0620900000000001E-2 1.5459499999999999E-2 1.7690999999999998E-2 1.82066E-2 2.0246E-2 2.20079E-2 1.8119199999999999E-2 1.9033999999999999E-2 1.6970499999999999E-2 1.58418E-2 1.8153300000000001E-2 1.7393599999999999E-2 1.44057E-2 1.41131E-2 1.44794E-2 1.34866E-2

% change from 12 mos. earlier

U.S. inflation and its trend, 1960–2014

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CHAPTER 5 Inflation

…the long-run trend behavior of inflation. We will learn a simple theory of inflation over the long run and see that its predictions are very consistent with U.S. and international data.

Note about the graph:

The long-run trend line was produced in Excel, type polynomial order 3.

GDP Deflator 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001.75 2002 2002.25 2002.5 2002.75 2003 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 1.2242400000000001E-2 1.44698E-2 1.53545E-2 1.3934800000000001E-2 1.1986399999999999E-2 1.10878E-2 1.04569E-2 1.1122999999999999E-2 1.4778899999999999E-2 1.3947299999999999E-2 1.3214500000000001E-2 1.29046E-2 9.2534000000000002E-3 9.7652999999999993E-3 9.4280000000000006E-3 1.3888899999999999E-2 1.46385E-2 1.53902E-2 1.7382700000000001E-2 1.46771E-2 1.6635E-2 1.8331699999999999E-2 1.80038E-2 1.9540200000000001E-2 2.1059499999999998E-2 2.53432E-2 3.2114200000000002E-2 3.4995999999999999E-2 3.3039899999999997E-2 2.9718999999999999E-2 2.9221899999999999E-2 3.11192E-2 3.7632899999999997E-2 4.2958499999999997E-2 4.3012799999999997E-2 4.60864E-2 4.5588799999999999E-2 4.8084399999999999E-2 5.2679200000000002E-2 5.1502699999999998E-2 5.53839E-2 5.6422100000000003E-2 4.9742300000000003E-2 4.9658599999999997E-2 5.0637700000000001E-2 4.98206E-2 5.2090999999999998E-2 4.7107299999999998E-2 4.7480700000000001E-2 4.0070700000000001E-2 3.9671699999999997E-2 4.4949500000000003E-2 4.1187000000000001E-2 5.1104799999999999E-2 6.1314599999999997E-2 6.8271600000000002E-2 7.6086600000000004E-2 8.4950399999999995E-2 9.5699699999999999E-2 0.10656019999999999 0.1108587 0.1011195 8.9399999999999993E-2 7.6464199999999996E-2 6.3497899999999996E-2 5.9046500000000002E-2 5.3803400000000001E-2 5.4203099999999997E-2 6.0453E-2 6.4246800000000007E-2 6.2797699999999998E-2 6.6802500000000001E-2 6.4504800000000001E-2 6.8855100000000002E-2 7.3536000000000004E-2 7.2681800000000005E-2 7.6081999999999997E-2 8.2696599999999995E-2 8.8048899999999999E-2 8.70475E-2 9.0410699999999997E-2 8.8003300000000007E-2 8.9275599999999997E-2 9.7335900000000003E-2 0.10200679999999999 9.8244899999999996E-2 9.2713900000000002E-2 8.2652799999999998E-2 7.0205100000000006E-2 6.3053700000000004E-2 5.9434899999999999E-2 5.1739599999999997E-2 4.60852E-2 4.1121999999999999E-2 3.6964799999999999E-2 3.3380600000000003E-2 3.8065000000000002E-2 3.9358299999999999E-2 3.7148899999999999E-2 3.6158000000000003E-2 3.4520099999999998E-2 3.1559299999999998E-2 2.75461E-2 2.7702000000000001E-2 2.1591200000000001E-2 2.1192900000000001E-2 2.2790600000000001E-2 2.29643E-2 2.7283200000000001E-2 2.77132E-2 2.99321E-2 3.08808E-2 2.9738199999999999E-2 3.35214E-2 3.7042699999999998E-2 3.6975399999999999E-2 4.0185899999999997E-2 4.0636400000000003E-2 3.5778900000000002E-2 3.4788800000000002E-2 3.5548499999999997E-2 3.7378099999999997E-2 4.0083000000000001E-2 4.15547E-2 4.01877E-2 3.5559E-2 3.4106400000000002E-2 3.18137E-2 2.6044899999999999E-2 2.5082799999999999E-2 2.1894500000000001E-2 2.1768200000000001E-2 2.2684800000000001E-2 2.2022199999999999E-2 2.1985500000000002E-2 2.1796599999999999E-2 2.10358E-2 2.0267299999999999E-2 2.1627199999999999E-2 2.1280899999999998E-2 2.1774999999999999E-2 2.1433299999999999E-2 2.0171399999999999E-2 2.0092800000000001E-2 2.0138699999999999E-2 1.95339E-2 1.7975100000000001E-2 1.8431800000000002E-2 1.9124200000000001E-2 1.75931E-2 1.7921900000000001E-2 1.6067399999999999E-2 1.1240200000000001E-2 1.13089E-2 1.1647100000000001E-2 1.0969400000000001E-2 1.37679E-2 1.4906000000000001E-2 1.48025E-2 1.5316099999999999E-2 1.8860499999999999E-2 2.0432700000000002E-2 2.2770599999999998E-2 2.45347E-2 2.3340900000000001E-2 2.51001E-2 2.21738E-2 1.9956000000000002E-2 1.66678E-2 1.4327299999999999E-2 1.55137E-2 1.8217299999999999E-2 2.1713699999999999E-2 2.01163E-2 2.1372200000000001E-2 2.0711799999999999E-2 2.24496E-2 2.80872E-2 2.9808000000000001E-2 3.2230200000000001E-2 3.27572E-2 3.0969400000000001E-2 3.4061099999999997E-2 3.5024600000000003E-2 3.3196299999999998E-2 3.5308800000000001E-2 3.2511100000000001E-2 2.8469299999999999E-2 3.2580499999999998E-2 3.0598E-2 2.6310199999999999E-2 2.6606299999999999E-2 1.9192600000000001E-2 1.8458700000000001E-2 2.1871100000000001E-2 1.8875200000000002E-2 1.5806000000000001E-2 9.2236999999999996E-3 2.1573999999999999E-3 3.5668000000000002E-3 4.4870999999999999E-3 1.0620900000000001E-2 1.5459499999999999E-2 1.7690999999999998E-2 1.82066E-2 2.0246E-2 2.20079E-2 1.8119199999999999E-2 1.9033999999999999E-2 1.6970499999999999E-2 1.58418E-2 1.8153300000000001E-2 1.7393599999999999E-2 1.44057E-2 1.41131E-2 1.44794E-2 1.34866E-2

% change from 12 mos. earlier

The quantity theory of money

A simple theory linking the inflation rate to the growth rate of the money supply.

Begins with the concept of quantity equation

M × V = P × T

M= quantity of money, V= velocity of money, T= no. of transactions/year, P= price of a typical transaction

So right hand side is the value of all transactions.

This identity is based on the insight that people hold money for transaction purposes i.e. to buy goods and services

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CHAPTER 5 Inflation

Velocity

basic concept: the rate at which money circulates

definition: the number of times a dollar bill changes hands in a given time period

Example: 60 loaves of bread are sold/year

So, T=60, Assume Price, P= $0.5/loaf

Total number of dollars exchanged= 60*0.5= $30/year

But assume that money supply, M= $10

So velocity of money, V= PT/M= $30 per year/$10= 3 times per year.

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CHAPTER 5 Inflation

That is, for $30 of transactions per year to occur with $10 of money, each dollar must change hands 3 times per year.

From Transactions to Income

Economists use a slightly different version of this equation

The quantity equation becomes M × V = P × Y

Replace T with Y. Dollar value of transactions is roughly proportional to the dollar value of output.

Right hand side is the dollar value of output i.e. nominal GDP. P = GDP deflator, Y = Real output.

In 2012, GDP was about $15, 829 billion and the M2 money stock averaged $10, 476 billion. Therefore, M2 velocity was about 1.7.

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CHAPTER 5 Inflation

What’s the difference between nominal GDP and the value of transactions?

Answer: nominal GDP includes the value of purchases of final goods; total transactions also includes the value of intermediate goods and used goods.

Even though they are different, they are highly correlated. Also, our models focus on GDP, and there’s lots of great data on GDP. So from this point on, we’ll use the income version of velocity.

Money demand and the quantity equation

M/P = real money balances, the purchasing power of the money supply.

A simple money demand function: (M/P )d = k Y where k = how much money people wish to hold for each dollar of income. (k is exogenous)

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CHAPTER 5 Inflation

Illustrating real money balances using a simple example:

An economy produces only bread. Price= $0.50 and M= $10, M/P= 20 loaves of bread. That means, at current prices, the stock of money in the economy is able to buy 20 loaves.

Money demand and the quantity equation

money demand: (M/P )d = k Y

=> M × (1/k) = P × Y

quantity equation: M × V = P × Y

The connection between them: k = 1/V

When people hold lots of money relative to their incomes (k is large), money changes hands infrequently (V is small).

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CHAPTER 5 Inflation

Back to the quantity theory of money

starts with quantity equation

assumes V is constant & exogenous:

Then, quantity equation becomes:

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CHAPTER 5 Inflation

The quantity theory of money, cont.

How the price level is determined:

With V constant, the money supply determines nominal GDP (P × Y ).

Real GDP is determined by the economy’s supplies of K and L and the production function.

The price level is P = (nominal GDP)/(real GDP).

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CHAPTER 5 Inflation

It’s worthwhile to underscore the order (logical order, though not necessarily chronological order) in which variables are determined in this model:

First, real GDP is already determined outside this model (real GDP is determined by the model from Chapter 3, which was completely independent of the money supply or velocity or other nominal variables).

Second, the quantity theory of money determines nominal GDP.

Third, the values of nominal GDP (PY) and real GDP (Y) together determine P

(as a ratio of PY to Y).

If, on an exam or homework problem, students forget the logical order in which endogenous variables are determined—or on a more fundamental level, forget which variables are endogenous and which are exogenous—then they are much less likely to earn the high grades that most of them desire.

[Note the similarity between the way P is determined and the definition of the GDP deflator from Chapter 2.]

The quantity theory of money, cont.

Recall from Chapter 2: The growth rate of a product equals the sum of the growth rates.

The quantity equation in growth rates:

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CHAPTER 5 Inflation

The quantity theory of money, cont.

π (Greek letter pi ) denotes the inflation rate:

The result from the preceding slide:

Solve this result for π:

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CHAPTER 5 Inflation

The quantity theory of money, cont.

Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions.

Money growth in excess of this amount leads to inflation.

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CHAPTER 5 Inflation

The text on this slide is an intuitive way to understand the equation.

For students that are more comfortable with concrete numerical examples:

Suppose real GDP is growing by 3% per year over the long run. Thus, production, income, and spending are all growing by 3%. This means that the volume of transactions will be growing as well.

The central bank can achieve zero inflation (on average over the long run) simply by setting the growth rate of the money supply at 3%, in which case exactly enough new money is being supplied to facilitate the growth in transactions.

The quantity theory of money, cont.

ΔY/Y depends on growth in the factors of production and on technological progress (all of which we take as given, for now).

Hence, the quantity theory predicts a one-for-one relation between changes in the money growth rate and changes in the inflation rate.

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CHAPTER 5 Inflation

Note: the theory doesn’t predict that the inflation rate will equal the money growth rate. It predicts that a change in the money growth rate will cause an equal change in the inflation rate.

Confronting the quantity theory with data

The quantity theory of money implies:

1. Countries with higher money growth rates should have higher inflation rates.

2. The long-run trend in a country’s inflation rate should be similar to the long-run trend in the country’s money growth rate.

Are the data consistent with these implications?

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CHAPTER 5 Inflation

International data on inflation and money growth

Inflation rate (percent)

Money supply growth (percent)

China

Iraq

Turkey

Belarus

Zambia

U.S.

Mexico

Malta

Cyprus

Serbia

Suriname

Russia

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CHAPTER 5 Inflation

Figure 5-2, p.108

Each variable is measured as an annual average over the period 2000-2010.

The strong positive correlation is evidence for the quantity theory of money.

Source:

Money Supply Data - www.imf.org > Data > International Financial Statistics (IFS)

Inflation Data - www.imf.org > Data > World Economic Outlook

33.377971773021613 8.2449974960931183 14.29818564991132 7.9738888866701938 20.659189031542201 25.65284596506244 41.833193033535217 5.8810722353787916 16.618299883625589 17.346509947151219 45.836667102845489 8.9460559957681216 27.91235096154923 20.16141511568895 21.66476 8289530279 16.01473573770372 19.27444528669562 19.96294980173651 28.377604154066539 10.636909865134569 10.51428896358785 17.842917735342251 12.6047109111075 8.8566876518306401 19.303571339664959 -1.3514437602506999 8.6329908802473785 6.1867196670466704 7.3337782724083702 18.53452932219113 13.45127827714856 4.1558916852556607 15.2986508244731 16.38754284686209 -1.248368718068982 25.496050040686551 16.080969220197289 7.3592460330412361 15.054147317671619 10.65488618756625 13.432738084495551 13.72126367980465 10.05454477148503 23.723233727065089 13.044991914496659 30.592004856045559 8.6035126892024927 2.110886444903648 11.535881697714901 39.863945462962342 13.47011227910297 8.5854604121110665 12.202306260702271 26.70195611939026 17.651776624205361 11.79848502456732 14.52534185984768 18.758315475749889 16.817842568707832 28.253870611537089 11.143119876728999 -5.3039065873282372 12.26984175061911 27.75590234546042 33.36937796849471 10.858830571425971 24.885917810911572 19.638422544482211 14.371673676546971 5.7942143294855759 13.03905709319732 28.115657526873871 8.1806918001872546 18.070469471584719 14.52448524772938 17.71209062953081 10.243639527530769 24.82232144910272 25.434645082077779 36.353660962303493 10.53580145664848 25.98476290004022 13.13320731676254 19.897524091432292 6.4027835297653768 25.037405592917729 8.0645106191808331 -3.9288137491320412 -1.6354943956790691 19.24194789280125 12.9311193777976 9.4469240642699148 11.214357776494889 8.1697631990814426 6.164277188249101 26 .682483200625839 43.761207547600847 13.06961279141902 6.9126401107536504 5.2283300706534259 19.04354513664169 10.537225942139649 1.7166157155642541 36.866795791727448 20.44966647454061 36.216282426341188 6.0277867504305762 16.002878732890562 36.156478894690643 34.283397185087523 27.294534998580101 11.251250000000001 2.7676363636363641 3.0975454545454539 1.906363636363636 8.7645454545454538 3.916363636363636 7.0614545454545468 2.1725454545454541 1.6113636363636361 5.9040909090909066 34.552 2.5584545454545449 4.8307272727272696 2.824272727272727 8.5653636363636405 6.7293636363636402 6.4067272727272719 10.63636363636364 4.7847272727272676 1.9954545454545449 3.3210000000000002 2.0016363636363632 5.9029999999999996 4.2205454545454444 10.427272727272721 2.6422727272727271 2.6662727272727271 2.144727272727275 2.1460909090909088 12.46036363636364 7.5111818181818144 3.3303636363636362 18.341363636363621 4.1824545454545454 10.62127272727272 6.3879090909090896 17.696090909090909 2.9180909090909091 6.7406363636363631 5.9409999999999998 14.0189090909091 7.9148181818181822 6.0108181818181814 6.1344545454545436 8.111727272727272 20.657833333333329 11.16209090909091 -0.30327272727272703 3.81309090909091 9.1490000000000009 8.1063636363636373 3.1010909090909098 3.400727272727273 8.5543636363636377 5.1894545454545451 2.665909090909091 6.9454545454545462 9.5984545454545458 2.887909090909091 14.28727272727272 2.1409090909090911 2.471545454545454 5.1199999999999974 11.56063636363637 9.1027272727272752 1.8301818181818199 10.795090909090909 7.1599999999999966 5.9094545454545457 2.6487272727272742 8.1283636363636216 12.459545454545459 2.1132727272727281 2.6370909090909089 7.9671818181818068 7.9309090909090907 3.425636363636364 4.9614545454545453 15.4379090909091 13.323454545454551 5.1909090909090896 15.89 2.3877272727272731 21.46672727272718 8.2040000000000006 8.6266363636363632 1.6087272727272719 4.841636363636364 4.6135454545454433 8.3872727272727179 5.9592727272727304 10.603 3.1890000000000001 2.8455454545454542 2.6629090909090909 9.0521818181818201 17.74009090909091 7.1513636363636399 1.8582727272727271 0.92990909090909102 6.3460909090909086 7.6500909090909008 6.6716363636363631 21.83127272727274 6.4815454545454543 12.824818181818181 2.4851818181818182 8.4075454545454544 2.879454545454545 21.632636363636362 16.49218181818182

U.S. inflation and money growth, 1960–2014

M2 growth rate

inflation rate

‹#›

CHAPTER 5 Inflation

source:

Federal Reserve Bank of St. Louis

http://research.stlouisfed.org/fred2/

M2SL (percent change from year ago, quarterly aggregation method average)

GDPDEF (percent change from year ago)

Money Stock 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001.75 2002 2002.25 2002.5 2002.75 20 03 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 3.7873499999999997E-2 3.0811399999999999E-2 3.5123300000000003E-2 4.6448999999999997E-2 5.8922000000000002E-2 6.9744299999999995E-2 6.8841799999999995E-2 7.2048899999999999E-2 7.5561199999999995E-2 7.8547000000000006E-2 7.6923099999999994E-2 7.9808000000000004E-2 8.1422700000000001E-2 8.2038E-2 8.7301599999999993E-2 8.6412900000000001E-2 8.0456600000000003E-2 7.5551999999999994E-2 7.7945799999999996E-2 7.9028100000000004E-2 8.2767300000000002E-2 8.2117200000000001E-2 7.8839199999999998E-2 8.03508E-2 7.9461000000000004E-2 7.4742900000000001E-2 6.0300399999999997E-2 4.8047399999999997E-2 4.4984900000000001E-2 5.7209700000000002E-2 7.9492599999999997E-2 9.1480000000000006E-2 9.2275999999999997E-2 8.4489999999999996E-2 7.61849E-2 7.8442700000000004E-2 7.8446199999999994E-2 7.0116899999999996E-2 5.6596899999999999E-2 4.1437000000000002E-2 2.7627200000000001E-2 2.5654400000000001E-2 4.2197699999999998E-2 6.0963099999999999E-2 9.1203000000000006E-2 0.1255704 0.1335316 0.1337518 0.1314517 0.1168168 0.1208631 0.1277683 0.12072769999999999 0.11132019999999999 9.0270600000000006E-2 6.8731100000000003E-2 6.33301E-2 5.86741E-2 5.5237399999999999E-2 5.7715000000000002E-2 5.82861E-2 8.4104700000000004E-2 0.11158849999999999 0.1213808 0.13539499999999999 0.12806999999999999 0.1173718 0.13048660000000001 0.13291629999999999 0.1295085 0.12561439999999999 0.1087491 9.23456E-2 8.35539E-2 7.8926099999999999E-2 7.6770699999999997E-2 7.2561799999999996E-2 7.7874499999999999E-2 8.3195900000000003E-2 7.9170000000000004E-2 8.2155000000000006E-2 7.2814799999999999E-2 7.96430000000000 05E-2 8.6452600000000004E-2 8.5968900000000001E-2 9.9035999999999999E-2 8.5752700000000001E-2 9.0555399999999994E-2 9.6501500000000004E-2 9.0412099999999995E-2 8.931E-2 8.5798100000000002E-2 0.1202521 0.1250069 0.1240381 0.11929620000000001 8.3735199999999996E-2 7.9334000000000002E-2 7.6555899999999996E-2 8.0776500000000001E-2 8.9779800000000007E-2 8.5707800000000001E-2 9.4308400000000001E-2 8.6392700000000003E-2 7.0347099999999996E-2 7.9526899999999998E-2 8.3561800000000006E-2 9.1539599999999999E-2 9.2545500000000003E-2 7.3552199999999998E-2 5.3853999999999999E-2 4.2670300000000001E-2 4.4480800000000001E-2 5.5603600000000003E-2 5.8770799999999998E-2 5.6018100000000001E-2 4.3526700000000002E-2 3.0778199999999999E-2 4.0920600000000001E-2 5.2006400000000001E-2 6.1265300000000002E-2 6.2734100000000001E-2 5.40092E-2 4.1525800000000002E-2 3.9208899999999998E-2 4.2316300000000001E-2 3.50455E-2 3.0561000000000001E-2 2.69281E-2 1.6065800000000002E-2 1.32932E-2 1.7263899999999999E-2 5.6863E-3 9.4517000000000004E-3 1.3148200000000001E-2 1.20929E-2 1.7958600000000002E-2 1.6101299999999999E-2 1.1961400000000001E-2 5.6855999999999999E-3 4.0867000000000004E-3 1.08512E-2 2.8029599999999998E-2 3.8282700000000003E-2 4.9729099999999998E-2 5.2480600000000002E-2 4.4009699999999999E-2 4.6019900000000002E-2 4.63084E-2 4.5573500000000003E-2 5.2232000000000001E-2 5.62029E-2 6.23434E-2 7.0038699999999995E-2 7.0978600000000003E-2 8.1932400000000002E-2 8.0989500000000006E-2 7.6692999999999997E-2 7.4790099999999998E-2 6.1715300000000001E-2 5.9969099999999997E-2 6.2292800000000002E-2 5.9014400000000002E-2 6.0545300000000003E-2 7.15832E-2 8.0210900000000002E-2 9.1424400000000003E-2 9.9926100000000004E-2 9.0248900000000007E-2 7.2049000000000002E-2 6.8261699999999995E-2 6.6296999999999995E-2 6.4886700000000005E-2 7.7822299999999997E-2 7.9771900000000007E-2 5.6694599999999998E-2 4.8284500000000001E-2 4.95489E-2 3.9927200000000003E-2 5.5110899999999997E-2 5.2849599999999997E-2 3.8002800000000003E-2 4.0654500000000003E-2 4.1208000000000002E-2 4.8729099999999997E-2 5.2474899999999998E-2 5.2297499999999997E-2 5.61228E-2 5.7600999999999999E-2 6.4061800000000002E-2 6.5193699999999993E-2 5.9766899999999998E-2 6.4106499999999997E-2 6.4262E-2 6.0916999999999999E-2 8.3253599999999997E-2 9.6848900000000002E-2 9.0410000000000004E-2 8.0790799999999996E-2 5.3355699999999999E-2 2.02863E-2 1.90192E-2 2.63374E-2 3.3221500000000001E-2 4.6492100000000001E-2 5.4985699999999998E-2 9.3044799999999997E-2 9.6962999999999994E-2 0.101535 9.6342300000000006E-2 7.0486800000000002E-2 7.5445700000000004E-2 7.3414900000000005E-2 7.0513000000000006E-2 6.5895099999999998E-2 6.0864599999999998E-2 5.9869600000000002E-2 GDP Deflator 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001.75 2002 2002.25 200 2.5 2002.75 2003 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 1.2242400000000001E-2 1.44698E-2 1.53545E-2 1.3934800000000001E-2 1.1986399999999999E-2 1.10878E-2 1.04569E-2 1.1122999999999999E-2 1.4778899999999999E-2 1.3947299999999999E-2 1.3214500000000001E-2 1.29046E-2 9.2534000000000002E-3 9.7652999999999993E-3 9.4280000000000006E-3 1.3888899999999999E-2 1.46385E-2 1.53902E-2 1.7382700000000001E-2 1.46771E-2 1.6635E-2 1.8331699999999999E-2 1.80038E-2 1.9540200000000001E-2 2.1059499999999998E-2 2.53432E-2 3.2114200000000002E-2 3.4995999999999999E-2 3.3039899999999997E-2 2.9718999999999999E-2 2.9221899999999999E-2 3.11192E-2 3.7632899999999997E-2 4.2958499999999997E-2 4.3012799999999997E-2 4.60864E-2 4.5588799999999999E-2 4.8084399999999999E-2 5.2679200000000002E-2 5.1502699999999998E-2 5.53839E-2 5.6422100000000003E-2 4.9742300000000003E-2 4.9658599999999997E-2 5.0637700000000001E-2 4.98206E-2 5.2090999999999998E-2 4.7107299999999998E-2 4.7480700000000001E-2 4.0070700000000001E-2 3.9671699999999997E-2 4.4949500000000003E-2 4.1187000000000001E-2 5.1104799999999999E-2 6.1314599999999997E-2 6.8271600000000002E-2 7.6086600000000004E-2 8.4950399999999995E-2 9.5699699999999999E-2 0.10656019999999999 0.1108587 0.1011195 8.9399999999999993E-2 7.6464199999999996E-2 6.3497899999999996E-2 5.9046500000000002E-2 5.3803400000000001E-2 5.4203099999999997E-2 6.0453E-2 6.4246800000000007E-2 6.2797699999999998E-2 6.6802500000000001E-2 6.4504800000000001E-2 6.8855100000000002E-2 7.3536000000000004E-2 7.2681800000000005E-2 7.6081999999999997E-2 8.2696599999999995E-2 8.8048899999999999E-2 8.70475E-2 9.0410699999999997E-2 8.8003300000000007E-2 8.9275599999999997E-2 9.7335900000000003E-2 0.10200679999999999 9.8244899999999996E-2 9.2713900000000002E-2 8.2652799999999998E-2 7.0205100000000006E-2 6.3053700000000004E-2 5.9434899999999999E-2 5.1739599999999997E-2 4.60852E-2 4.1121999999999999E-2 3.6964799999999999E-2 3.3380600000000003E-2 3.8065000000000002E-2 3.9358299999999999E-2 3.7148899999999999E-2 3.6158000000000003E-2 3.4520099999999998E-2 3.1559299999999998E-2 2.75461E-2 2.7702000000000001E-2 2.1591200000000001E-2 2.1192900000000001E-2 2.2790600000000001E-2 2.29643E-2 2.7283200000000001E-2 2.77132E-2 2.99321E-2 3.08808E-2 2.9738199999999999E-2 3.35214E-2 3.7042699999999998E-2 3.6975399999999999E-2 4.0185899999999997E-2 4.0636400000000003E-2 3.5778900000000002E-2 3.4788800000000002E-2 3.5548499999999997E-2 3.7378099999999997E-2 4.0083000000000001E-2 4.15547E-2 4.01877E-2 3.5559E-2 3.4106400000000002E-2 3.18137E-2 2.6044899999999999E-2 2.5082799999999999E-2 2.1894500000000001E-2 2.1768200000000001E-2 2.2684800000000001E-2 2.2022199999999999E-2 2.1985500000000002E-2 2.1796599999999999E-2 2.10358E-2 2.0267299999999999E-2 2.1627199999999999E-2 2.1280899999999998E-2 2.1774999999999999E-2 2.1433299999999999E-2 2.0171399999999999E-2 2.0092800000000001E-2 2.0138699999999999E-2 1.95339E-2 1.7975100000000001E-2 1.8431800000000002E-2 1.9124200000000001E-2 1.75931E-2 1.7921900000000001E-2 1.6067399999999999E-2 1.1240200000000001E-2 1.13089E-2 1.1647100000000001E-2 1.0969400000000001E-2 1.37679E-2 1.4906000000000001E-2 1.48025E-2 1.5316099999999999E-2 1.8860499999999999E-2 2.0432700000000002E-2 2.2770599999999998E-2 2.45347E-2 2.3340900000000001E-2 2.51001E-2 2.21738E-2 1.9956000000000002E-2 1.66678E-2 1.4327299999999999E-2 1.55137E-2 1.8217299999999999E-2 2.1713699999999999E-2 2.01163E-2 2.1372200000000001E-2 2.0711799999999999E-2 2.24496E-2 2.80872E-2 2.9808000000000001E-2 3.2230200000000001E-2 3.27572E-2 3.0969400000000001E-2 3.4061099999999997E-2 3.5024600000000003E-2 3.3196299999999998E-2 3.5308800000000001E-2 3.2511100000000001E-2 2.8469299999999999E-2 3.2580499999999998E-2 3.0598E-2 2.6310199999999999E-2 2.6606299999999999E-2 1.9192600000000001E-2 1.8458700000000001E-2 2.1871100000000001E-2 1.8875200000000002E-2 1.5806000000000001E-2 9.2236999999999996E-3 2.1573999999999999E-3 3.5668000000000002E-3 4.4870999999999999E-3 1.0620900000000001E-2 1.5459499999999999E-2 1.7690999999999998E-2 1.82066E-2 2.0246E-2 2.20079E-2 1.8119199999999999E-2 1.9033999999999999E-2 1.6970499999999999E-2 1.58418E-2 1.8153300000000001E-2 1.7393599999999999E-2 1.44057E-2 1.41131E-2 1.44794E-2 1.34866E-2

% change from 12 mos. earlier

U.S. inflation and money growth, 1960–2014

Inflation and money growth have the same long-run trends, as the quantity theory predicts.

‹#›

CHAPTER 5 Inflation

The quantity theory of money is intended to explain the long-run relation of inflation and money growth, not the short-run relation. In the long run, inflation and money growth are positively related, as the theory predicts.

(In the short run, however, inflation and money growth appear highly negatively correlated! One possible reason is that the causality is reversed in the short run: when inflation rises – or is expected to rise – the Fed cuts back on money growth. If the economy slumps and inflation falls, the Fed increases money growth. It might be appropriate to discuss this when covering the chapters on short-run fluctuations.)

source:

Federal Reserve Bank of St. Louis

http://research.stlouisfed.org/fred2/

M2SL (percent change from year ago, quarterly aggregation method average)

GDPDEF (percent change from year ago)

Money Stock 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001.75 2002 2002.25 2002.5 2002.75 2003 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 3.7873499999999997E-2 3.0811399999999999E-2 3.5123300000000003E-2 4.6448999999999997E-2 5.8922000000000002E-2 6.9744299999999995E-2 6.8841799999999995E-2 7.2048899999999999E-2 7.5561199999999995E-2 7.8547000000000006E-2 7.6923099999999994E-2 7.9808000000000004E-2 8.1422700000000001E-2 8.2038E-2 8.7301599999999993E-2 8.6412900000000001E-2 8.0456600000000003E-2 7.5551999999999994E-2 7.7945799999999996E-2 7.9028100000000004E-2 8.2767300000000002E-2 8.2117200000000001E-2 7.8839199999999998E-2 8.03508E-2 7.9461000000000004E-2 7.4742900000000001E-2 6.0300399999999997E-2 4.8047399999999997E-2 4.4984900000000001E-2 5.7209700000000002E-2 7.9492599999999997E-2 9.1480000000000006E-2 9.2275999999999997E-2 8.4489999999999996E-2 7.61849E-2 7.8442700000000004E-2 7.8446199999999994E-2 7.0116899999999996E-2 5.6596899999999999E-2 4.1437000000000002E-2 2.7627200000000001E-2 2.5654400000000001E-2 4.2197699999999998E-2 6.0963099999999999E-2 9.1203000000000006E-2 0.1255704 0.1335316 0.1337518 0.1314517 0.1168168 0.1208631 0.1277683 0.12072769999999999 0.11132019999999999 9.0270600000000006E-2 6.8731100000000003E-2 6.33301E-2 5.86741E-2 5.5237399999999999E-2 5.7715000000000002E-2 5.82861E-2 8.4104700000000004E-2 0.11158849999999999 0.1213808 0.13539499999999999 0.12806999999999999 0.1173718 0.13048660000000001 0.13291629999999999 0.1295085 0.12561439999999999 0.1087491 9.23456E-2 8.35539E-2 7.8926099999999999E-2 7.6770699999999997E-2 7.2561799999999996E-2 7.7874499999999999E-2 8.3195900000000003E-2 7.9170000000000004E-2 8.2155000000000006E-2 7.2814799999999999E-2 7.9643000000000005E-2 8.6452600000000004E-2 8.5968900000000001E-2 9.9035999999999999E-2 8.5752700000000001E-2 9.0555399999999994E-2 9.6501500000000004E-2 9.0412099999999995E-2 8.931E-2 8.5798100000000002E-2 0.1202521 0.1250069 0.1240381 0.11929620000000001 8.3735199999999996E-2 7.9334000000000002E-2 7.6555899999999996E-2 8.0776500000000001E-2 8.9779800000000007E-2 8.5707800000000001E-2 9.4308400000000001E-2 8.6392700000000003E-2 7.0347099999999996E-2 7.9526899999999998E-2 8.3561800000000006E-2 9.1539599999999999E-2 9.2545500000000003E-2 7.3552199999999998E-2 5.385399999 9999999E-2 4.2670300000000001E-2 4.4480800000000001E-2 5.5603600000000003E-2 5.8770799999999998E-2 5.6018100000000001E-2 4.3526700000000002E-2 3.0778199999999999E-2 4.0920600000000001E-2 5.2006400000000001E-2 6.1265300000000002E-2 6.2734100000000001E-2 5.40092E-2 4.1525800000000002E-2 3.9208899999999998E-2 4.2316300000000001E-2 3.50455E-2 3.0561000000000001E-2 2.69281E-2 1.6065800000000002E-2 1.32932E-2 1.7263899999999999E-2 5.6863E-3 9.4517000000000004E-3 1.3148200000000001E-2 1.20929E-2 1.7958600000000002E-2 1.6101299999999999E-2 1.1961400000000001E-2 5.6855999999999999E-3 4.0867000000000004E-3 1.08512E-2 2.8029599999999998E-2 3.8282700000000003E-2 4.9729099999999998E-2 5.2480600000000002E-2 4.4009699999999999E-2 4.6019900000000002E-2 4.63084E-2 4.5 573500000000003E-2 5.2232000000000001E-2 5.62029E-2 6.23434E-2 7.0038699999999995E-2 7.0978600000000003E-2 8.1932400000000002E-2 8.0989500000000006E-2 7.6692999999999997E-2 7.4790099999999998E-2 6.1715300000000001E-2 5.9969099999999997E-2 6.2292800000000002E-2 5.9014400000000002E-2 6.0545300000000003E-2 7.15832E-2 8.0210900000000002E-2 9.1424400000000003E-2 9.9926100000000004E-2 9.0248900000000007E-2 7.2049000000000002E-2 6.8261699999999995E-2 6.6296999999999995E-2 6.4886700000000005E-2 7.7822299999999997E-2 7.9771900000000007E-2 5.6694599999999998E-2 4.8284500000000001E-2 4.95489E-2 3.9927200000000003E-2 5.5110899999999997E-2 5.2849599999999997E-2 3.8002800000000003E-2 4.0654500000000003E-2 4.1208000000000002E-2 4.8729099999999997E-2 5.2474899999999998E-2 5.2297499999999997E-2 5.612 28E-2 5.7600999999999999E-2 6.4061800000000002E-2 6.5193699999999993E-2 5.9766899999999998E-2 6.4106499999999997E-2 6.4262E-2 6.0916999999999999E-2 8.3253599999999997E-2 9.6848900000000002E-2 9.0410000000000004E-2 8.0790799999999996E-2 5.3355699999999999E-2 2.02863E-2 1.90192E-2 2.63374E-2 3.3221500000000001E-2 4.6492100000000001E-2 5.4985699999999998E-2 9.3044799999999997E-2 9.6962999999999994E-2 0.101535 9.6342300000000006E-2 7.0486800000000002E-2 7.5445700000000004E-2 7.3414900000000005E-2 7.0513000000000006E-2 6.5895099999999998E-2 6.0864599999999998E-2 5.9869600000000002E-2 GDP Deflator 1960 1960.25 1960.5 1960.75 1961 1961.25 1961.5 1961.75 1962 1962.25 1962.5 1962.75 1963 1963.25 1963.5 1963.75 1964 1964.25 1964.5 1964.75 1965 1965.25 1965.5 1965.75 1966 1966.25 1966.5 1966.75 1967 1967.25 1967.5 1967.75 1968 1968.25 1968.5 1968.75 1969 1969.25 1969.5 1969.75 1970 1970.25 1970.5 1970.75 1971 1971.25 1971.5 1971.75 1972 1972.25 1972.5 1972.75 1973 1973.25 1973.5 1973.75 1974 1974.25 1974.5 1974.75 1975 1975.25 1975.5 1975.75 1976 1976.25 1976.5 1976.75 1977 1977.25 1977.5 1977.75 1978 1978.25 1978.5 1978.75 1979 1979.25 1979.5 1979.75 1980 1980.25 1980.5 1980.75 1981 1981.25 1981.5 1981.75 1982 1982.25 1982.5 1982.75 1983 1983.25 1983.5 1983.75 1984 1984.25 1984.5 1984.75 1985 1985.25 1985.5 1985.75 1986 1986.25 1986.5 1986.75 1987 1987.25 1987.5 1987.75 1988 1988.25 1988.5 1988.75 1989 1989.25 1989.5 1989.75 1990 1990.25 1990.5 1990.75 1991 1991.25 1991.5 1991.75 1992 1992.25 1992.5 1992.75 1993 1993.25 1993.5 1993.75 1994 1994.25 1994.5 1994.75 1995 1995.25 1995.5 1995.75 1996 1996.25 1996.5 1996.75 1997 1997.25 1997.5 1997.75 1998 1998.25 1998.5 1998.75 1999 1999.25 1999.5 1999.75 2000 2000.25 2000.5 2000.75 2001 2001.25 2001.5 2001.75 2002 2002.25 2002.5 2002.75 2003 2003.25 2003.5 2003.75 2004 2004.25 2004.5 2004.75 2005 2005.25 2005.5 2005.75 2006 2006.25 2006.5 2006.75 2007 2007.25 2007.5 2007.75 2008 2008.25 2008.5 2008.75 2009 2009. 25 2009.5 2009.75 2010 2010.25 2010.5 2010.75 2011 2011.25 2011.5 2011.75 2012 2012.25 2012.5 2012.75 2013 2013.25 2013.5 2013.75 2014 1.2242400000000001E-2 1.44698E-2 1.53545E-2 1.3934800000000001E-2 1.1986399999999999E-2 1.10878E-2 1.04569E-2 1.1122999999999999E-2 1.4778899999999999E-2 1.3947299999999999E-2 1.3214500000000001E-2 1.29046E-2 9.2534000000000002E-3 9.7652999999999993E-3 9.4280000000000006E-3 1.3888899999999999E-2 1.46385E-2 1.53902E-2 1.7382700000000001E-2 1.46771E-2 1.6635E-2 1.8331699999999999E-2 1.80038E-2 1.9540200000000001E-2 2.1059499999999998E-2 2.53432E-2 3.2114200000000002E-2 3.4995999999999999E-2 3.3039899999999997E-2 2.9718999999999999E-2 2.9221899999999999E-2 3.11192E-2 3.7632899999999997E-2 4.2958499999999997E-2 4.3012799999999997E-2 4.60864E-2 4.5588799999999999E-2 4.8084399999999999E-2 5.2679200000000002E-2 5.1502699999999998E-2 5.53839E-2 5.6422100000000003E-2 4.9742300000000003E-2 4.9658599999999997E-2 5.0637700000000001E-2 4.98206E-2 5.2090999999999998E-2 4.7107299999999998E-2 4.7480700000000001E-2 4.0070700000000001E-2 3.9671699999999997E-2 4.4949500000000003E-2 4.1187000000000001E-2 5.1104799999999999E-2 6.1314599999999997E-2 6.8271600000000002E-2 7.6086600000000004E-2 8.4950399999999995E-2 9.5699699999999999E-2 0.10656019999999999 0.1108587 0.1011195 8.93 99999999999993E-2 7.6464199999999996E-2 6.3497899999999996E-2 5.9046500000000002E-2 5.3803400000000001E-2 5.4203099999999997E-2 6.0453E-2 6.4246800000000007E-2 6.2797699999999998E-2 6.6802500000000001E-2 6.4504800000000001E-2 6.8855100000000002E-2 7.3536000000000004E-2 7.2681800000000005E-2 7.6081999999999997E-2 8.2696599999999995E-2 8.8048899999999999E-2 8.70475E-2 9.0410699999999997E-2 8.8003300000000007E-2 8.9275599999999997E-2 9.7335900000000003E-2 0.10200679999999999 9.8244899999999996E-2 9.2713900000000002E-2 8.2652799999999998E-2 7.0205100000000006E-2 6.3053700000000004E-2 5.9434899999999999E-2 5.1739599999999997E-2 4.60852E-2 4.1121999999999999E-2 3.6964799999999999E-2 3.3380600000000003E-2 3.8065000000000002E-2 3.9358299999999999E-2 3.7148899999999999E-2 3.6158000000000003E-2 3.4520099999999998E-2 3.1559299999999998E-2 2.75461E-2 2.7702000000000001E-2 2.1591200000000001E-2 2.1192900000000001E-2 2.2790600000000001E-2 2.29643E-2 2.7283200000000001E-2 2.77132E-2 2.99321E-2 3.08808E-2 2.9738199999999999E-2 3.35214E-2 3.7042699999999998E-2 3.6975399999999999E-2 4.0185899999999997E-2 4.0636400000000003E-2 3.5778900000000002E-2 3.4788800000000002E-2 3.5548499999999997E-2 3.7378099999999997E-2 4.0083000000000001E-2 4.15547E-2 4.01877E-2 3.5559E-2 3.4106400000000002E-2 3.18137E-2 2.6044899999999999E-2 2.5082799999999999E-2 2.1894500000000001E-2 2.1768200000000001E-2 2.2684800000000001E-2 2.2022199999999999E-2 2.1985500000000002E-2 2.1796599999999999E-2 2.10358E-2 2.0267299999999999E-2 2.1627199999999999E-2 2.1280899999999998E-2 2.177 4999999999999E-2 2.1433299999999999E-2 2.0171399999999999E-2 2.0092800000000001E-2 2.0138699999999999E-2 1.95339E-2 1.7975100000000001E-2 1.8431800000000002E-2 1.9124200000000001E-2 1.75931E-2 1.7921900000000001E-2 1.6067399999999999E-2 1.1240200000000001E-2 1.13089E-2 1.1647100000000001E-2 1.0969400000000001E-2 1.37679E-2 1.4906000000000001E-2 1.48025E-2 1.5316099999999999E-2 1.8860499999999999E-2 2.0432700000000002E-2 2.2770599999999998E-2 2.45347E-2 2.3340900000000001E-2 2.51001E-2 2.21738E-2 1.9956000000000002E-2 1.66678E-2 1.4327299999999999E-2 1.55137E-2 1.8217299999999999E-2 2.1713699999999999E-2 2.01163E-2 2.1372200000000001E-2 2.0711799999999999E-2 2.24496E-2 2.80872E-2 2.9808000000000001E-2 3.2230200000000001E-2 3.27572E-2 3.0969400000000001E-2 3.4061099999999997E-2 3.5024600000000003E-2 3.3196299999999998E-2 3.5308800000000001E-2 3.2511100000000001E-2 2.8469299999999999E-2 3.2580499999999998E-2 3.0598E-2 2.6310199999999999E-2 2.6606299999999999E-2 1.9192600000000001E-2 1.8458700000000001E-2 2.1871100000000001E-2 1.8875200000000002E-2 1.5806000000000001E-2 9.2236999999999996E-3 2.1573999999999999E-3 3.5668000000000002E-3 4.4870999999999999E-3 1.0620900000000001E-2 1.5459499999999999E-2 1.7690999999999998E-2 1.82066E-2 2.0246E-2 2.20079E-2 1.8119199999999999E-2 1.9033999999999999E-2 1.6970499999999999E-2 1.58418E-2 1.8153300000000001E-2 1.7393599999999999E-2 1.44057E-2 1.41131E-2 1.44794E-2 1.34866E-2

% change from 12 mos. earlier

Seigniorage

To spend more without raising taxes or selling bonds, the govt can print money.

The “revenue” raised from printing money is called seigniorage (pronounced SEEN-your-idge).

The inflation tax: Printing money to raise revenue causes inflation. Inflation is like a tax on people who hold money.

‹#›

CHAPTER 5 Inflation

Introduction of abbreviation “govt” for “government”

It’s quicker and easier for students to write “govt” in their notes.

In the U.S., seigniorage accounts for only about 3% of total government revenue. In Italy and Greece, seigniorage has often been more than 10% of total revenue. In countries experiencing hyperinflation, seigniorage is often the government’s main source of revenue, and the need to print money to finance government expenditure is a primary cause of hyperinflation.

See Case Study on p.109 “Paying for the American Revolution.”

Inflation and interest rates

Nominal interest rate, i not adjusted for inflation

Real interest rate, r adjusted for inflation: r = i − π

‹#›

CHAPTER 5 Inflation

This slide will be very familiar to students who have recently taken an introductory course.

The Fisher effect

The Fisher equation: i = r + π

Savings and investment together determine r .

Hence, an increase in π causes an equal increase in i.

This one-for-one relationship is called the Fisher effect.

‹#›

CHAPTER 5 Inflation

Note that S and I are real variables. The factors that determine S and I do not include the money supply, velocity, inflation, or other nominal variables.

Hence, in the classical (long-run) theory covered here in Chapter 5, changes in money growth or inflation do not affect the real interest rate. This is why there’s a one-for-one relationship between changes in the inflation rate and changes in the nominal interest rate.

(Again, the Fisher effect does not imply that the nominal interest rate equals the inflation rate. It implies that changes in the nominal interest rate equal changes in the inflation rate, given a constant value of the real interest rate.)

U.S. inflation and nominal interest rates, 1960–2014

inflation rate

nominal interest rate

‹#›

CHAPTER 5 Inflation

The data are consistent with the Fisher effect: inflation and the nominal interest rate are very highly correlated.

That they are not perfectly correlated does not contradict the Fisher effect. Over time, the saving and investment curves (see Chapter 3) move around, changing the real interest rate, which, in turn, causes the nominal interest rate to change for a given value of inflation.

About the data:

The inflation rate is the percentage change in the CPI from 12 months earlier.

(CPIAUCSL, monthly, percent change from year ago)

The nominal interest rate is the 3-month Treasury bill rate in the secondary market (TB3MS, monthly)

Data obtained from http://research.stlouisfed.org/fred2/

CPI 1960 1960.083333333333 1960.166666666667 1960.25 1960.333333333333 1960.416666666667 1960.5 1960.583333333333 1960.666666666667 1960.75 1960.833333333333 1960.916666666667 1961 1961.0833333333301 1961 .1666666666699 1961.25 1961.3333333333301 1961.4166666666699 1961.5 1961.5833333333301 1961.6666666666699 1961.75 1961.8333333333301 1961.9166666666599 1962 1962.0833333333301 1962.1666666666599 1962.25 1962.3333333333301 1962.4166666666599 1962.5 1962.5833333333301 1962.6666666666599 1962.75 1962.8333333333301 1962.9166666666599 1963 1963.0833333333301 1963.1666666666599 1963.25 1963.3333333333301 1963.4166666666599 1963.5 1963.5833333333301 1963.6666666666599 1963.75 1963.8333333333301 1963.9166666666599 1964 1964.0833333333301 1964.1666666666599 1964.25 1964.3333333333301 1964.4166666666599 1964.5 1964.5833333333301 1964.6666666666599 1964.75 1964.8333333333301 1964.9166666666599 1965 1965.0833333333301 1965.1666666666599 1965.25 1965.3333333333301 1965.4166666666599 1965.49999999999 1965.5833333333301 1965.6666666666599 1965.74999999999 1965.8333333333301 1965.9166666666599 1965.99999999999 1966.0833333333301 1966.1666666666599 1966.24999999999 1966.3333333333301 1966.4166666666599 1966.49999999999 1966.5833333333301 1966.6666666666599 1966.74999999999 1966.8333333333301 1966.9166666666599 1966.99999999999 1967.0833333333301 1967.1666666666599 1967.24999999999 1967.3333333333301 1967.4166666666599 1967.49999999999 1967.5833333333301 1967.6666666666599 1967.74999999999 1967.8333333333301 1967.9166666666599 1967.99999999999 1968.0833333333301 1968.1666666666599 1968.24999999999 1968.3333333333301 1968.4166666666599 1968.49999999999 1968.5833333333301 1968.6666666666599 1968.74999999999 1968.8333333333301 1968.9166666666599 1968.99999999999 1969.0833333333301 1969.1666666666599 1969.24999999999 1969.3333333333201 1969.4166666666599 1969.49999999999 1969.5833333333201 1969.6666666666599 1969.74999999999 1969.8333333333201 1969.9166666666599 1969.99999999999 1970.0833333333201 1970.1666666666599 1970.24999999999 1970.3333333333201 1970.4166666666599 1970.49999999999 1970.5833333333201 1970.6666666666599 1970.74999999999 1970.8333333333201 1970.9166666666599 1970.99999999999 1971.0833333333201 1971.1666666666599 1971.24999999999 1971.3333333333201 1971.4166666666599 1971.49999999999 1971.5833333333201 1971.6666666666599 1971.74999999999 1971.8333333333201 1971.9166666666599 1971.99999999999 1972.0833333333201 1972.1666666666599 1972.24999999999 1972.3333333333201 1972.4166666666599 1972.49999999999 1972.5833333333201 1972.6666666666599 1972.74999999999 1972.8333333333201 1972.9166666666499 1972.99999999999 1973.0833333333201 1973.1666666666499 1973.24999999999 1973.3333333333201 1973.4166666666499 1973.49999999999 1973.5833333333201 1973.6666666666499 1973.74999999999 1973.8333333333201 1973.9166666666499 1973.99999999999 1974.0833333333201 1974.1666666666499 1974.24999999999 1974.3333333333201 1974.4166666666499 1974.49999999999 1974.5833333333201 1974.6666666666499 1974.74999999999 1974.8333333333201 1974.9166666666499 1974.99999999999 1975.0833333333201 1975.1666666666499 1975.24999999999 1975.3333333333201 1975.4166666666499 1975.49999999999 1975.5833333333201 1975.6666666666499 1975.74999999999 1975.8333333333201 1975.9166666666499 1975.99999999999 1976.0833333333201 1976.1666666666499 1976.24999999999 1976.3333333333201 1976.4166666666499 1976.49999999998 1976.5833333333201 1976.6666666666499 1976.74999999998 1976.8333333333201 1976.9166666666499 1976.99999999998 1977.0833333333201 1977.1666666666499 1977.24999999998 1977.3333333333201 1977.4166666666499 1977.49999999998 1977.5833333333201 1977.6666666666499 1977.74999999998 1977.8333333333201 1977.9166666666499 1977.99999999998 1978.0833333333201 1978.1666666666499 1978.24999999998 1978.3333333333201 1978.4166666666499 1978.49999999998 1978.5833333333201 1978.6666666666499 1978.74999999998 1978.8333333333201 1978.9166666666499 1978.99999999998 1979.0833333333201 1979.1666666666499 1979.24999999998 1979.3333333333201 1979.4166666666499 1979.49999999998 1979.5833333333201 1979.6666666666499 1979.74999999998 1979.8333333333201 1979.9166666666499 1979.99999999998 1980.0833333333201 1980.1666666666499 1980.24999999998 1980.3333333333101 1980.4166666666499 1980.49999999998 1980.5833333333101 1980.6666666666499 1980.74999999998 1980.8333333333101 1980.9166666666499 1980.99999999998 1981.0833333333101 1981.1666666666499 1981.24999999998 1981.3333333333101 1981.4166666666499 1981.49999999998 1981.5833333333101 1981.6666666666499 1981.74999999998 1981.8333333333101 1981.9166666666499 1981.99999999998 1982.0833333333101 1982.1666666666499 1982.24999999998 1982.3333333333101 1982.4166666666499 1982.49999999998 1982.5833333333101 1982.6666666666499 1982.74999999998 1982.8333333333101 1982.9166666666499 1982.99999999998 1983.0833333333101 1983.1666666666499 1983.24999999998 1983.3333333333101 1983.4166666666499 1983.49999999998 1983.5833333333101 1983.6666666666499 1983.74999999998 1983.8333333333101 1983.9166666666399 1983.99999999998 1984.0833333333101 1984.1666666666399 1984.24999999998 1984.3333333333101 1984.4166666666399 1984.49999999998 1984.5833333333101 1984.6666666666399 1984.74999999998 1984.833333333 3101 1984.9166666666399 1984.99999999998 1985.0833333333101 1985.1666666666399 1985.24999999998 1985.3333333333101 1985.4166666666399 1985.49999999998 1985.5833333333101 1985.6666666666399 1985.74999999998 1985.8333333333101 1985.9166666666399 1985.99999999998 1986.0833333333101 1986.1666666666399 1986.24999999998 1986.3333333333101 1986.4166666666399 1986.49999999998 1986.5833333333101 1986.6666666666399 1986.74999999998 1986.8333333333101 1986.9166666666399 1986.99999999998 1987.0833333333101 1987.1666666666399 1987.24999999998 1987.3333333333101 1987.4166666666399 1987.49999999997 1987.5833333333101 1987.6666666666399 1987.74999999997 1987.8333333333101 1987.9166666666399 1987.99999999997 1988.0833333333101 1988.166 6666666399 1988.24999999997 1988.3333333333101 1988.4166666666399 1988.49999999997 1988.5833333333101 1988.6666666666399 1988.74999999997 1988.8333333333101 1988.9166666666399 1988.99999999997 1989.0833333333101 1989.1666666666399 1989.24999999997 1989.3333333333101 1989.4166666666399 1989.49999999997 1989.5833333333101 1989.6666666666399 1989.74999999997 1989.8333333333101 1989.9166666666399 1989.99999999997 1990.0833333333101 1990.1666666666399 1990.24999999997 1990.3333333333101 1990.4166666666399 1990.49999999997 1990.5833333333101 1990.6666666666399 1990.74999999997 1990.8333333333101 1990.9166666666399 1990.99999999997 1991.0833333333101 1991.1666666666399 1991.24999999997 1991.3333333333001 1991.4166666666399 19 91.49999999997 1991.5833333333001 1991.6666666666399 1991.74999999997 1991.8333333333001 1991.9166666666399 1991.99999999997 1992.0833333333001 1992.1666666666399 1992.24999999997 1992.3333333333001 1992.4166666666399 1992.49999999997 1992.5833333333001 1992.6666666666399 1992.74999999997 1992.8333333333001 1992.9166666666399 1992.99999999997 1993.0833333333001 1993.1666666666399 1993.24999999997 1993.3333333333001 1993.4166666666399 1993.49999999997 1993.5833333333001 1993.6666666666399 1993.74999999997 1993.8333333333001 1993.9166666666399 1993.99999999997 1994.0833333333001 1994.1666666666399 1994.24999999997 1994.3333333333001 1994.4166666666399 1994.49999999997 1994.5833333333001 1994.6666666666399 1994.74999999997 1994.8333333333001 1994.9166666666299 1994.99999999997 1995.0833333333001 1995.1666666666299 1995.24999999997 1995.3333333333001 1995.4166666666299 1995.49999999997 1995.5833333333001 1995.6666666666299 1995.74999999997 1995.8333333333001 1995.9166666666299 1995.99999999997 1996.0833333333001 1996.1666666666299 1996.24999999997 1996.3333333333001 1996.4166666666299 1996.49999999997 1996.5833333333001 1996.6666666666299 1996.74999999997 1996.8333333333001 1996.9166666666299 1996.99999999997 1997.0833333333001 1997.1666666666299 1997.24999999997 1997.3333333333001 1997.4166666666299 1997.49999999997 1997.5833333333001 1997.6666666666299 1997.74999999997 1997.8333333333001 1997.9166666666299 1997.99999999997 1998.0833333333001 1998.1666666666299 1998.24999999997 1998.3333333333001 1998.4166666666299 1998.49999999996 1998.5833333333001 1998.6666666666299 1998.74999999996 1998.8333333333001 1998.9166666666299 1998.99999999996 1999.0833333333001 1999.1666666666299 1999.24999999996 1999.3333333333001 1999.4166666666299 1999.49999999996 1999.5833333333001 1999.6666666666299 1999.74999999996 1999.8333333333001 1999.9166666666299 1999.99999999996 2000.0833333333001 2000.1666666666299 2000.24999999996 2000.3333333333001 2000.4166666666299 2000.49999999996 2000.5833333333001 2000.6666666666299 2000.74999999996 2000.8333333333001 2000.9166666666299 2000.99999999996 2001.0833333333001 2001.1666666666299 2001.24999999996 2001.3333333333001 2001.4166666666299 2001.49999999996 2001.5833333333001 2001.6666666666299 2001.74999999996 2001.8333333333001 2001.9166666666299 2001.99999999996 2002.0833333333001 2002.1666666666299 2002.24999999996 2002.3333333332901 2002.4166666666299 2002.49999999996 2002.5833333332901 2002.6666666666299 2002.74999999996 2002.8333333332901 2002.9166666666299 2002.99999999996 2003.0833333332901 2003.1666666666299 2003.24999999996 2003.3333333332901 2003.4166666666299 2003.49999999996 2003.5833333332901 2003.6666666666299 2003.74999999996 2003.8333333332901 2003.9166666666299 2003.99999999996 2004.0833333332901 2004.1666666666299 2004.24999999996 2004.3333333332901 2004.4166666666299 2004.49999999996 2004.5833333332901 2004.6666666666299 2004.74999999996 2004.8333333332901 2004.9166666666299 2004.99999999996 2005.0833333332901 2005.1666666666299 2005.24999999996 2005.3333333332901 2005.4166666666299 2005.49999999996 2005.5833333332901 2005.6666666666299 2005.74999999996 2005.8333333332901 2005.9166666666199 2005.99999999996 2006.0833333332901 2006.1666666666199 2006.24999999996 2006.3333333332901 2006.4166666666199 2006.49999999996 2006.5833333332901 2006.6666666666199 2006.74999999996 2006.8333333332901 2006.9166666666199 2006.99999999996 2007.0833333332901 2007.1666666666199 2007.24999999996 2007.3333333332901 2007.4166666666199 2007.49999999996 2007.5833333332901 2007.6666666666199 2007.74999999996 2007.8333333332901 2007.9166666666199 2007.99999999996 2008.0833333332901 2008.1666666666199 2008.24999999996 2008.3333333332901 2008.4166666666199 2008.49999999996 2008.5833333332901 2008.6666666666199 2008.74999999996 2008.8333333332901 2008.9166666666199 2008.99999999996 2009.0833333332901 2009.1666666666199 2009.24999999996 2009.3333333332901 2009.4166666666199 2009.49999999995 2009.5833333332901 2009.6666666666199 2009.74999999995 2009.8333333332901 2009.9166666666199 2009.99999999995 2010.0833333332901 2010.1666666666199 2010.24999999995 2010.3333333332901 2010.4166666666199 2010.49999999995 2010.5833333332901 2010.6666666666199 2010.74999999995 2010.8333333332901 2010.9166666666199 2010.99999999995 2011.0833333332901 2011.1666666666199 2011.24999999995 2011.3333333332901 2011.416666666 6199 2011.49999999995 2011.5833333332901 2011.6666666666199 2011.74999999995 2011.8333333332901 2011.9166666666199 2011.99999999995 2012.0833333332901 2012.1666666666199 2012.24999999995 2012.3333333332901 2012.4166666666199 2012.49999999995 2012.5833333332901 2012.6666666666199 2012.74999999995 2012.8333333332901 2012.9166666666199 2012.99999999995 2013.0833333332901 2013.1666666666199 2013.24999999995 2013.3333333332801 2013.4166666666499 2013.49999999999 2013.5833333333301 2013.6666666666699 2013.75000000001 2013.8333333333501 2013.9166666666899 2014.00000000003 2014.0833333333701 2014.1666666667099 2014.25000000005 2014.3333333333901 1.24095E-2 1.41379E-2 1.51881E-2 1.9323699999999999E-2 1.8250700000000002E-2 1.7176199999999999E-2 1.3722099999999999E-2 1.47361E-2 1.23077E-2 1.3628599999999999E-2 1.46508E-2 1.36008E-2 1.6002700000000002E-2 1.4620899999999999E-2 1.4620899999999999E-2 9.1401E-3 9.1309000000000008E-3 7.7676000000000004E-3 1.25212E-2 1.1144899999999999E-2 1.24958E-2 7.7311000000000003E-3 6.7159000000000003E-3 6.7092000000000002E-3 6.7023999999999999E-3 9.0483000000000004E-3 1.1058999999999999E-2 1.3418299999999999E-2 1.34048E-2 1.2399500000000001E-2 1.00267E-2 1.1356E-2 1.46765E-2 1.33422E-2 1.33422E-2 1.23292E-2 1.33156E-2 1.22883E-2 1.12695E-2 8.9373999999999999E-3 8.9286000000000001E-3 1.32406E-2 1.55526E-2 1.5521800000000001E-2 9.8618999999999998E-3 1.21791E-2 1.3166600000000001E-2 1.6458199999999999E-2 1.6425800000000001E-2 1.41076E-2 1.4093700000000001E-2 1.54199E-2 1.54048E-2 1.30676E-2 1.07527E-2 9.7561000000000002E-3 1.17188E-2 1.20325E-2 1.3970099999999999E-2 1.19819E-2 1.0989000000000001E-2 1.19702E-2 1.19586E-2 1.38934E-2 1.6139400000000002E-2 1.9348600000000001E-2 1.80529E-2 1.6103099999999999E-2 1.7374500000000001E-2 1.7030799999999999E-2 1.7302100000000001E-2 1.9199999999999998E-2 1.91816E-2 2.5575400000000002E-2 2.7786600000000002E-2 2.86807E-2 2.7636600000000001E-2 2.43594E-2 2.75491E-2 3.4865300000000002E-2 3.5736900000000002E-2 3.7914700000000003E-2 3.55906E-2 3.3595E-2 3.1995000000000003E-2 2.86783E-2 2.5481699999999999E-2 2.54027E-2 2.31839E-2 2.84126E-2 2.9275800000000001E-2 2.60337E-2 2.59542E-2 2.5875200000000001E-2 3.1021900000000002E-2 3.2806799999999997E-2 3.6474199999999998E-2 3.6363600000000003E-2 3.9393900000000003E-2 3.9274900000000001E-2 4.2296100000000003E-2 4.2042000000000003E-2 4.4910199999999997E-2 4.4776099999999999E-2 4.4642899999999999E-2 4.7477699999999998E-2 4.4247799999999997E-2 4.7058799999999998E-2 4.6920799999999999E-2 4.6783600000000002E-2 5.24781E-2 5.52326E-2 5.5072500000000003E-2 5.4754999999999998E-2 5.4441299999999998E-2 5.4285699999999999E-2 5.6980099999999999E-2 5.6657199999999998E-2 5.9322E-2 5.8988800000000001E-2 6.1624600000000002E-2 6.4245800000000006E-2 6.0941799999999997E-2 6.0606100000000003E-2 6.0439600000000003E-2 6.0109299999999997E-2 5.7065200000000003E-2 5.6910599999999999E-2 5.6603800000000003E-2 5.6300299999999998E-2 5.6000000000000001E-2 5.57029E-2 5.2770400000000002E-2 4.7244099999999997E-2 4.4386399999999999E-2 4.1558400000000002E-2 4.4041499999999997E-2 4.3814400000000003E-2 4.3701799999999999E-2 4.3589700000000002E-2 4.08163E-2 3.8071099999999997E-2 3.5353500000000003E-2 3.2663299999999999E-2 3.2581499999999999E-2 3.7594000000000002E-2 3.5000000000000003E-2 3.4912699999999998E-2 3.2258099999999998E-2 2.9629599999999999E-2 2.9556700000000002E-2 2.9484E-2 3.1862700000000001E-2 3.1784800000000002E-2 3.4146299999999997E-2 3.4063299999999998E-2 3.6407799999999997E-2 3.8647300000000002E-2 4.8309199999999997E-2 5.3011999999999997E-2 5.5288499999999997E-2 5.9951999999999998E-2 5.7416300000000003E-2 7.3985700000000001E-2 7.3634199999999997E-2 8.0568699999999993E-2 8.2547200000000001E-2 8.94118E-2 9.6018699999999998E-2 0.1 0.1013825 0.1006865 0.1070615 0.10859729999999999 0.1153846 0.1088889 0.11946900000000001 0.1184211 0.1220044 0.1209503 0.1175214 0.1120507 0.1046025 0.10187110000000001 9.2592599999999997E-2 9.1836699999999993E-2 9.5334699999999994E-2 8.6172299999999993E-2 7.9051399999999994E-2 7.64706E-2 7.3786400000000002E-2 7.1290900000000004E-2 6.6921599999999998E-2 6.2737600000000004E-2 6.0606100000000003E-2 5.8490599999999997E-2 6.2146899999999998E-2 5.9813100000000001E-2 5.5555599999999997E-2 5.7195599999999999E-2 5.4945099999999997E-2 5.46448E-2 5.0632900000000002E-2 5.03597E-2 5.1971299999999998E-2 6.0822899999999999E-2 6.4285700000000001E-2 6.9518700000000003E-2 6.7375900000000002E-2 6.7019400000000007E-2 6.6666699999999995E-2 6.6317600000000004E-2 6.4236100000000004E-2 6.3903299999999996E-2 6.7125599999999994E-2 6.6780800000000001E-2 6.8143099999999998E-2 6.2394600000000001E-2 6.3758400000000007E-2 6.5000000000000002E-2 7.1428599999999995E-2 7.4380199999999994E-2 7.7302599999999999E-2 7.8559699999999996E-2 8.4828700000000007E-2 8.9285699999999996E-2 8.8709700000000002E-2 8.9887599999999998E-2 9.2504000000000003E-2 9.8412700000000006E-2 0.1025237 0.10485129999999999 0.10697669999999999 0.1107692 0.1145038 0.1183612 0.118797 0.1207154 0.12592590000000001 0.1325479 0.13868610000000001 0.14161850000000001 0.14592269999999999 0.14589240000000001 0.14425769999999999 0.14265929999999999 0.13150680000000001 0.12890090000000001 0.1276882 0.12632979999999999 0.12631580000000001 0.1235371 0.1179487 0.1139241 0.1061174 0.1013597 9.7919199999999998E-2 9.6969700000000006E-2 0.1077482 0.10817309999999999 0.1096544 0.1027155 9.5794400000000002E-2 8.9120400000000002E-2 8.2568799999999998E-2 7.6136400000000007E-2 6.8848800000000002E-2 6.6217700000000004E-2 6.9119299999999995E-2 7.1823200000000004E-2 6.5573800000000002E-2 5.9652900000000002E-2 4.94092E-2 5.0321200000000003E-2 4.4776099999999999E-2 3.8257199999999998E-2 3.70763E-2 3.48469E-2 3.5902900000000001E-2 0.04 3.4410799999999998E-2 2.4742299999999998E-2 2.3589700000000002E-2 2.4565E-2 2.76356E-2 2.7522899999999999E-2 3.16327E-2 3.7871000000000002E-2 4.2900899999999999E-2 4.6938800000000003E-2 4.89297E-2 4.55466E-2 4.3346799999999998E-2 4.3259600000000002E-2 4.3086199999999998E-2 4.2957000000000002E-2 4.2828699999999997E-2 4.2658700000000001E-2 4.1542999999999997E-2 4.0433900000000002E-2 3.5259499999999999E-2 3.6062400000000001E-2 3.7900900000000001E-2 3.5818000000000003E-2 3.5748799999999997E-2 3.6644200000000002E-2 3.4582099999999998E-2 3.3524900000000003E-2 3.2473700000000001E-2 3.23501E-2 3.5137700000000001E-2 3.7914700000000003E-2 3.9735100000000002E-2 3.1984899999999997E-2 2.1535599999999998E-2 1.58879E-2 1.6791E-2 1.76744E-2 1.6713100000000002E-2 1.57553E-2 1.75763E-2 1.56682E-2 1.2844E-2 1.18721E-2 1.3648800000000001E-2 1.91431E-2 2.84143E-2 3.6798499999999998E-2 3.6697199999999999E-2 3.7477099999999999E-2 3.9269400000000003E-2 4.2883200000000003E-2 4.2727300000000003E-2 4.3557199999999997E-2 4.5289900000000001E-2 4.33213E-2 4.1292599999999999E-2 3.9356000000000002E-2 3.8324400000000002E-2 3.9928999999999999E-2 3.9822999999999997E-2 3.9647599999999998E-2 4.1300499999999997E-2 4.1119900000000001E-2 4.1848299999999998E-2 4.2608699999999999E-2 4.2460999999999999E-2 4.41176E-2 4.4827600000000002E-2 4.6471600000000002E-2 4.8926999999999998E-2 5.0341299999999999E-2 5.2766E-2 5.1694900000000002E-2 5.0632900000000002E-2 4.6218500000000003E-2 4.4351500000000002E-2 4.5871599999999998E-2 4.6550300000000003E-2 4.6396E-2 5.1980199999999997E-2 5.2631600000000001E-2 5.2373200000000002E-2 4.7116199999999997E-2 4.3653999999999998E-2 4.67365E-2 4.8192800000000001E-2 5.7028099999999998E-2 6.1698700000000002E-2 6.3795900000000003E-2 6.1953899999999999E-2 6.2549499999999994E-2 5.6470600000000003E-2 5.3124999999999999E-2 4.8211499999999997E-2 4.8099299999999998E-2 5.03486E-2 4.69592E-2 4.36782E-2 3.7993899999999997E-2 3.3962300000000001E-2 2.8485799999999999E-2 3.0665700000000001E-2 2.9806300000000001E-2 2.6726099999999999E-2 2.81899E-2 3.18991E-2 3.1828299999999997E-2 3.0235999999999999E-2 3.01471E-2 3.1571200000000001E-2 3.0746699999999998E-2 2.9926999999999999E-2 3.2798800000000003E-2 3.1204599999999999E-2 2.9667099999999998E-2 3.2537999999999997E-2 3.2467500000000003E-2 3.0194100000000001E-2 3.1563800000000003E-2 3.2211900 000000002E-2 2.9978600000000001E-2 2.84698E-2 2.84091E-2 2.7640000000000001E-2 2.7522899999999999E-2 2.7445500000000001E-2 2.8109599999999998E-2 2.4509800000000002E-2 2.5157200000000001E-2 2.6517800000000001E-2 2.3643899999999999E-2 2.28849E-2 2.4948000000000001E-2 2.6989599999999999E-2 2.90055E-2 2.96552E-2 2.6098900000000001E-2 2.6027399999999999E-2 2.5974000000000001E-2 2.87081E-2 2.86299E-2 2.78722E-2 3.125E-2 3.11864E-2 3.0426000000000002E-2 2.8301900000000001E-2 2.61745E-2 2.5452099999999998E-2 2.7443100000000002E-2 2.6034700000000001E-2 2.5316499999999999E-2 2.7907000000000001E-2 2.7170300000000001E-2 2.8439200000000001E-2 2.83267E-2 2.8270900000000002E-2 2.8215199999999999E-2 2.8833600000000001E-2 2.8122999999999999E-2 3.0045700000000002E-2 3.0618900000000001E-2 3.2530900000000001E-2 3.3788199999999997E-2 3.0381399999999999E-2 3.0322600000000002E-2 2.7652699999999999E-2 2.4343400000000001E-2 2.2378499999999999E-2 2.23357E-2 2.1656100000000001E-2 2.2900799999999999E-2 2.2193999999999998E-2 2.0859699999999998E-2 1.89036E-2 1.6970499999999999E-2 1.6311200000000001E-2 1.4402E-2 1.37672E-2 1.4383999999999999E-2 1.6885600000000001E-2 1.62297E-2 1.74564E-2 1.6169200000000002E-2 1.4267999999999999E-2 1.4860699999999999E-2 1.4842299999999999E-2 1.6069199999999999E-2 1.66667E-2 1.66667E-2 1.7284000000000001E-2 2.28113E-2 2.09102E-2 1.9656E-2 2.1446099999999999E-2 2.2643799999999999E-2 2.6299699999999999E-2 2.56254E-2 2.6203500000000001E-2 2.6764E-2 2.7929599999999999E-2 3.2179699999999999E-2 3.7621399999999999E-2 3.0138600000000001E-2 3.13253E-2 3.7349399999999998E-2 3.5992799999999998E-2 3.3512899999999998E-2 3.4564999999999999E-2 3.4503300000000001E-2 3.4441800000000002E-2 3.43602E-2 3.7212000000000002E-2 3.5294100000000002E-2 2.98246E-2 3.2182599999999999E-2 3.5630799999999997E-2 3.1939599999999999E-2 2.7214800000000001E-2 2.7214800000000001E-2 2.5921699999999999E-2 2.12766E-2 1.8943700000000001E-2 1.6036700000000001E-2 1.1958999999999999E-2 1.13636E-2 1.3628599999999999E-2 1.64399E-2 1.2408300000000001E-2 1.0692200000000001E-2 1.46561E-2 1.74746E-2 1.516E-2 2.0270300000000002E-2 2.2535199999999998E-2 2.48027E-2 2.7574600000000001E-2 3.1460700000000001E-2 3.0252100000000001E-2 2.1751300000000001E-2 1.89415E-2 1.94878E-2 2.05556E-2 2.2160699999999998E-2 2.3783200000000001E-2 2.0419400000000001E-2 1.9283700000000001E-2 2.0351999999999999E-2 2.02629E-2 1.68845E-2 1.7400800000000001E-2 2.29258E-2 2.8977599999999999E-2 3.1676700000000002E-2 2.93958E-2 2.5474299999999998E-2 2.53917E-2 3.1909100000000003E-2 3.6216199999999997E-2 3.34232E-2 2.84487E-2 3.05303E-2 3.2068399999999997E-2 3.3617899999999999E-2 2.86929E-2 2.54103E-2 3.06716E-2 3.6469300000000003E-2 4.7418299999999997E-2 4.3500999999999998E-2 3.3385499999999999E-2 3.3385499999999999E-2 4.0187899999999999E-2 3.6382499999999998E-2 3.41792E-2 3.6138400000000001E-2 3.9772700000000001E-2 4.1817199999999999E-2 4.1046699999999998E-2 3.926570 0000000001E-2 2.0120699999999998E-2 1.4063300000000001E-2 1.9687E-2 2.52398E-2 2.07577E-2 2.4202600000000001E-2 2.7982E-2 2.5929199999999999E-2 2.7098899999999999E-2 2.6927699999999999E-2 2.3178899999999999E-2 1.8974499999999998E-2 2.83383E-2 3.6107E-2 4.3732699999999999E-2 4.1088100000000002E-2 4.2946999999999999E-2 4.1429599999999997E-2 3.9749E-2 3.9037599999999999E-2 4.08841E-2 4.9359699999999999E-2 5.4975099999999999E-2 5.3080200000000001E-2 4.9533199999999999E-2 3.7310599999999999E-2 1.0999200000000001E-2 -2.2230000000000001E-4 -1.0463E-3 6.3940000000000004E-4 -4.3336E-3 -6.0063E-3 -1.02691E-2 -1.22871E-2 -1.9615E-2 -1.48521E-2 -1.3692599999999999E-2 -2.3641000000000001E-3 1.8822200000000001E-2 2.8226399999999999E -2 2.6071899999999999E-2 2.12994E-2 2.2853999999999999E-2 2.17439E-2 1.98687E-2 1.18161E-2 1.3832000000000001E-2 1.19661E-2 1.12979E-2 1.1613E-2 1.06187E-2 1.42755E-2 1.6502800000000001E-2 2.0942599999999999E-2 2.6341E-2 3.0366199999999999E-2 3.46039E-2 3.5618799999999999E-2 3.63085E-2 3.7459899999999997E-2 3.8631499999999999E-2 3.53066E-2 3.4528499999999997E-2 3.02493E-2 2.97808E-2 2.8501100000000001E-2 2.5911099999999999E-2 2.28871E-2 1.7633099999999999E-2 1.70452E-2 1.43026E-2 1.6816299999999999E-2 1.9464100000000002E-2 2.1569000000000001E-2 1.7848300000000001E-2 1.7640300000000001E-2 1.6054200000000001E-2 1.9553999999999998E-2 1.4615400000000001E-2 1.10086E-2 1.4155600000000001E-2 1.7633599999999999E-2 1.9551599999999999E-2 1.5137899999999999E-2 1.14979E-2 9.1947999999999995E-3 1.2297199999999999E-2 1.51234E-2 1.56147E-2 1.1049099999999999E-2 1.5361400000000001E-2 1.96239E-2 2.13636E-2 Nominal Interest Rate 1960 1960.083333333333 1960.166666666667 1960.25 1960.333333333333 1960.416666666667 1960.5 1960.583333333333 1960.666666666667 1960.75 1960.833333333333 1960.916666666667 1961 1961.0833333333301 1961.1666666666699 1961.25 1961.3333333333301 1961.4166666666699 1961.5 1961.5833333333301 1961.6666666666699 1961.75 1961.8333333333301 1961.9166666666599 1962 1962.0833333333301 1962.1666666666599 1962.25 1962.3333333333301 1962.4166666666599 1962.5 1962.5833333333301 1962.6666666666599 1962.75 1962.8333333333301 1962.9166666666599 1963 1963.0833333333301 1963.1666666666599 1963.25 1963.3333333333301 1963.4166666666599 1963.5 1963.5833333333301 1963.6666666666599 1963.75 1963.8333333333301 1963.9166666666599 1964 1964.0833333333301 1964.1666666666599 1964.25 1964.3333333333301 1964.4166666666599 1964.5 1964.5833333333301 1964.6666666666599 1964.75 1964.8333333333301 1964.9166666666599 1965 1965.0833333333301 1965.1666666666599 1965.25 1965.3333333333301 1965.4166666666599 1965.49999999999 1965.5833333333301 1965.6666666666599 1965.74999999999 1965.8333333333301 1965.9166666666599 1965.99999999999 1966.0833333333301 1966.1666666666599 1966.24999999999 1966.3333333333301 1966.4166666666599 1966.49999999999 1966.5833333333301 1966.6666666666599 1966.74999999999 1966.8333333333301 1966.9166666666599 1966.99999999999 1967.0833333333301 1967.1666666666599 1967.24999999999 1967.3333333333301 1967.4166666666599 1967.49999999999 1967.5833333333301 1967.6666666666599 1967.74999999999 1967.8333333333301 1967.9166666666599 1967.99999999999 1968.0833333333301 1968.1666666666599 1968.24999999999 1968.3333333333301 1968.4166666666599 1968.49999999999 1968.5833333333301 1968.6666666666599 1968.74999999999 1968.8333333333301 1968.9166666666599 1968.99999999999 1969.0833333333301 1969.1666666666599 1969.24999999999 1969.3333333333201 1969.4166666666599 1969.49999999999 1969.5833333333201 1969.6666666666599 1969.74999999999 1969.8333333333201 1969.9166666666599 1969.99999999999 1970.0833333333201 1970.1666666666599 1970.24999999999 1970.3333333333201 1970.4166666666599 1970.49999999999 1970.5833333333201 1970.6666666666599 1970.74999999999 1970.8333333333201 1970.9166666666599 1970.99999999999 1971.0833333333201 1971.1666666666599 1971.24999999999 1971.3333333333201 1971.4166666666599 1971.49999999999 1971.5833333333201 1971.6666666666599 1971.74999999999 1971.8333333333201 1971.9166666666599 1971.99999999999 1972.0833333333201 1972.1666666666599 1972.24999999999 1972.3333333333201 1972.4166666666599 1972.49999999999 1972.5833333333201 1972.6666666666599 1972.74999999999 1972.8333333333201 1972.9166666666499 1972.99999999999 1973.0833333333201 1973.1666666666499 1973.24999999999 1973.3333333333201 1973.4166666666499 1973.49999999999 1973.5833333333201 1973.6666666666499 1973.74999999999 1973.8333333333201 1973.9166666666499 1973.99999999999 1974.0833333333201 1974.1666666666499 1974.24999999999 1974.3333333333201 1974.4166666666499 1974.49999999999 1974.5833333333201 1974.6666666666499 1974.74999999999 1974.8333333333201 1974.9166666666499 1974.99999999999 1975.0833333333201 1975.1666666666499 1975.24999999999 1975.3333333333201 1975.4166666666499 1975.49999999999 1975.5833333333201 1975.6666666666499 1975.74999999999 1975.8333333333201 1975.9166666666499 1975.99999999999 1976.0833333333201 1976.1666666666499 1976.24999999999 1976.3333333333201 1976.4166666666499 1976.49999999998 1976.5833333333201 1976.6666666666499 1976.74999999998 1976.8333333333201 1976.9166666666499 1976.99999999998 1977.0833333333201 1977.1666666666499 1977.24999999998 1977.3333333333201 1977.4166666666499 1977.49999999998 1977.5833333333201 1977.6666666666499 1977.74999999998 1977.8333333333201 1977.9166666666499 1977.99999999998 1978.0833333333201 1978.1666666666499 1978.24999999998 1978.3333333333201 1978.4166666666499 1978.49999999998 1978.5833333333201 1978.6666666666499 1978.74999999998 1978.8333333333201 1978.9166666666499 1978.99999999998 1979.0833333333201 1979.1666666666499 1979.24999999998 1979.3333333333201 1979.4166666666499 1979.49999999998 1979.5833333333201 1979.6666666666499 1979.74999999998 1979.8333333333201 1979.9166666666499 1979.99999999998 1980.0833333333201 1980.1666666666499 1980.24999999998 1980.3333333333101 1980.4166666666499 1980.49999999998 1980.5833333333101 1980.6666666666499 1980.74999999998 1980.8333333333101 1980.9166666666499 1980.99999999998 1981.0833333333101 1981.1666666666499 1981.24999999998 1981.3333333333101 1981.4166666666499 1981.49999999998 1981.5833333333101 1981.6666666666499 1981.74999999998 1981.8333333333101 1981.9166666666499 1981.99999999998 1982.0833333333101 1982.1666666666499 1982.24999999998 1982.3333333333101 1982.4166666666499 1982.49999999998 1982.5833333333101 1982.6666666666499 1982.74999999998 1982.8333333333101 1982.9166666666499 1982.99999999998 1983.0833333333101 1983.1666666666499 1983.24999999998 1983.3333333333101 1983.4166666666499 1983.49999999998 1983.5833333333101 1983.6666666666499 1983.74999999998 1983.8333333333101 1983.9166666666399 1983.99999999998 1984.0833333333101 1984.1666666666399 1984.24999999998 1984.3333333333101 1984.4166666666399 1984.49999999998 1984.5833333333101 1984.6666666666399 1984.74999999998 1984.8333333333101 1984.9166666666399 1984.99999999998 1985.0833333333101 1985.1666666666399 1985.24999999998 1985.3333333333101 1985.4166666666399 1985.49999999998 1985.5833333333101 1985.6666666666399 1985.74999999998 1985.8333333333101 1985.9166666666399 1985.99999999998 1986.0833333333101 1986.1666666666399 1986.24999999998 1986.3333333333101 1986.4166666666399 1986.49999999998 1986.5833333333101 1986.6666666666399 1986.74999999998 1986.8333333333101 1986.9166666666399 1986.99999999998 1987.0833333333101 1987.1666666666399 1987.24999999998 1987.3333333333101 1987.4166666666399 1987.49999999997 1987.5833333333101 1987.6666666666399 1987.74999999997 1987.8333333333101 1987.9166666666399 1987.99999999997 1988.0833333333101 1988.1666666666399 1988.24999999997 1988.3333333333101 1988.4166666666399 1988.49999999997 1988.583333333 3101 1988.6666666666399 1988.74999999997 1988.8333333333101 1988.9166666666399 1988.99999999997 1989.0833333333101 1989.1666666666399 1989.24999999997 1989.3333333333101 1989.4166666666399 1989.49999999997 1989.5833333333101 1989.6666666666399 1989.74999999997 1989.8333333333101 1989.9166666666399 1989.99999999997 1990.0833333333101 1990.1666666666399 1990.24999999997 1990.3333333333101 1990.4166666666399 1990.49999999997 1990.5833333333101 1990.6666666666399 1990.74999999997 1990.8333333333101 1990.9166666666399 1990.99999999997 1991.0833333333101 1991.1666666666399 1991.24999999997 1991.3333333333001 1991.4166666666399 1991.49999999997 1991.5833333333001 1991.6666666666399 1991.74999999997 1991.8333333333001 1991.916 6666666399 1991.99999999997 1992.0833333333001 1992.1666666666399 1992.24999999997 1992.3333333333001 1992.4166666666399 1992.49999999997 1992.5833333333001 1992.6666666666399 1992.74999999997 1992.8333333333001 1992.9166666666399 1992.99999999997 1993.0833333333001 1993.1666666666399 1993.24999999997 1993.3333333333001 1993.4166666666399 1993.49999999997 1993.5833333333001 1993.6666666666399 1993.74999999997 1993.8333333333001 1993.9166666666399 1993.99999999997 1994.0833333333001 1994.1666666666399 1994.24999999997 1994.3333333333001 1994.4166666666399 1994.49999999997 1994.5833333333001 1994.6666666666399 1994.74999999997 1994.8333333333001 1994.9166666666299 1994.99999999997 1995.0833333333001 1995.1666666666299 19 95.24999999997 1995.3333333333001 1995.4166666666299 1995.49999999997 1995.5833333333001 1995.6666666666299 1995.74999999997 1995.8333333333001 1995.9166666666299 1995.99999999997 1996.0833333333001 1996.1666666666299 1996.24999999997 1996.3333333333001 1996.4166666666299 1996.49999999997 1996.5833333333001 1996.6666666666299 1996.74999999997 1996.8333333333001 1996.9166666666299 1996.99999999997 1997.0833333333001 1997.1666666666299 1997.24999999997 1997.3333333333001 1997.4166666666299 1997.49999999997 1997.5833333333001 1997.6666666666299 1997.74999999997 1997.8333333333001 1997.9166666666299 1997.99999999997 1998.0833333333001 1998.1666666666299 1998.24999999997 1998.3333333333001 1998.4166666666299 1998.49999999996 1998.5833333333001 1998.6666666666299 1998.74999999996 1998.8333333333001 1998.9166666666299 1998.99999999996 1999.0833333333001 1999.1666666666299 1999.24999999996 1999.3333333333001 1999.4166666666299 1999.49999999996 1999.5833333333001 1999.6666666666299 1999.74999999996 1999.8333333333001 1999.9166666666299 1999.99999999996 2000.0833333333001 2000.1666666666299 2000.24999999996 2000.3333333333001 2000.4166666666299 2000.49999999996 2000.5833333333001 2000.6666666666299 2000.74999999996 2000.8333333333001 2000.9166666666299 2000.99999999996 2001.0833333333001 2001.1666666666299 2001.24999999996 2001.3333333333001 2001.4166666666299 2001.49999999996 2001.5833333333001 2001.6666666666299 2001.74999999996 2001.8333333333001 2001.9166666666299 2001.99999999996 2002.0833333333001 2002.1666666666299 2002.24999999996 2002.3333333332901 2002.4166666666299 2002.49999999996 2002.5833333332901 2002.6666666666299 2002.74999999996 2002.8333333332901 2002.9166666666299 2002.99999999996 2003.0833333332901 2003.1666666666299 2003.24999999996 2003.3333333332901 2003.4166666666299 2003.49999999996 2003.5833333332901 2003.6666666666299 2003.74999999996 2003.8333333332901 2003.9166666666299 2003.99999999996 2004.0833333332901 2004.1666666666299 2004.24999999996 2004.3333333332901 2004.4166666666299 2004.49999999996 2004.5833333332901 2004.6666666666299 2004.74999999996 2004.8333333332901 2004.9166666666299 2004.99999999996 2005.0833333332901 2005.1666666666299 2005.24999999996 2005.3333333332901 2005.4166666666299 2005.49999999996 2005.5833333332901 2005.6666666666299 2005.74999999996 2005.8333333332901 2005.9166666666199 2005.99999999996 2006.0833333332901 2006.1666666666199 2006.24999999996 2006.3333333332901 2006.4166666666199 2006.49999999996 2006.5833333332901 2006.6666666666199 2006.74999999996 2006.8333333332901 2006.9166666666199 2006.99999999996 2007.0833333332901 2007.1666666666199 2007.24999999996 2007.3333333332901 2007.4166666666199 2007.49999999996 2007.5833333332901 2007.6666666666199 2007.74999999996 2007.8333333332901 2007.9166666666199 2007.99999999996 2008.0833333332901 2008.1666666666199 2008.24999999996 2008.3333333332901 2008.4166666666199 2008.49999999996 2008.5833333332901 2008.6666666666199 2008.74999999996 2008.8333333332901 2008.9166666666199 2008.99999999996 2009.0833333332901 2009.1666666666199 2009.24999999996 2009.3333333332901 2009.4166666666199 2009.49999999995 2009.5833333332901 2009.6666666666199 2009.74999999995 2009.8333333332901 2009.9166666666199 2009.99999999995 2010.0833333332901 2010.1666666666199 2010.24999999995 2010.3333333332901 2010.4166666666199 2010.49999999995 2010.5833333332901 2010.6666666666199 2010.74999999995 2010.8333333332901 2010.9166666666199 2010.99999999995 2011.0833333332901 2011.1666666666199 2011.24999999995 2011.3333333332901 2011.4166666666199 2011.49999999995 2011.5833333332901 2011.6666666666199 2011.74999999995 2011.8333333332901 2011.9166666666199 2011.99999999995 2012.0833333332901 2012.1666666666199 2012.24999999995 2012.3333333332901 2012.4166666666199 2012.49999999995 2012.5833333332901 2012.6666666666199 2012.74999999995 2012.8333333332901 2012.9166666666199 2012.99999999995 2013.0833333332901 2013.1666666666199 2013.24999999995 2013.3333333332801 2013.4166666666499 2013.49999999999 2013.5833333333301 2013.6666666666699 2013.75000000001 2013.8333333333501 2013.9166666666899 2014.00000000003 2014.0833333333701 2014.1666666667099 2014.25000000005 2014.3333333333901 4.3499999999999997E-2 3.9600000000000003E-2 3.3099999999999997E-2 3.2300000000000002E-2 3.2899999999999999E-2 2.46E-2 2.3E-2 2.3E-2 2.4799999999999999E-2 2.3E-2 2.3699999999999999E-2 2.2499999999999999E-2 2.24E-2 2.4199999999999999E-2 2.3900000000000001E-2 2.29E-2 2.29E-2 2.3300000000000001E-2 2.24E-2 2.3900000000000001E-2 2.2800000000000001E-2 2.3E-2 2.4799999999999999E-2 2.5999999999999999E-2 2.7199999999999998E-2 2.7300000000000001E-2 2.7199999999999998E-2 2.7300000000000001E-2 2.69E-2 2.7300000000000001E-2 2.92E-2 2.8199999999999999E-2 2.7799999999999998E-2 2.7400000000000001E-2 2.8299999999999999E-2 2.87E-2 2.9100000000000001E-2 2.92E-2 2.8899999999999999E-2 2.9000000000000001E-2 2.93E-2 2.9899999999999999E-2 3.1800000000000002E-2 3.32E-2 3.3799999999999997E-2 3.4500000000000003E-2 3.5200000000000002E-2 3.5200000000000002E-2 3.520000 0000000002E-2 3.5299999999999998E-2 3.5400000000000001E-2 3.4700000000000002E-2 3.4799999999999998E-2 3.4799999999999998E-2 3.4599999999999999E-2 3.5000000000000003E-2 3.5299999999999998E-2 3.5700000000000003E-2 3.6400000000000002E-2 3.8399999999999997E-2 3.8100000000000002E-2 3.9300000000000002E-2 3.9300000000000002E-2 3.9300000000000002E-2 3.8899999999999997E-2 3.7999999999999999E-2 3.8399999999999997E-2 3.8399999999999997E-2 3.9199999999999999E-2 4.0300000000000002E-2 4.0899999999999999E-2 4.3799999999999999E-2 4.5900000000000003E-2 4.65E-2 4.5900000000000003E-2 4.6199999999999998E-2 4.6399999999999997E-2 4.4999999999999998E-2 4.8000000000000001E-2 4.9599999999999998E-2 5.3699999999999998E-2 5.3499999999999999E-2 5.3199999999999997E-2 4.9599999999999998E-2 4.7199999999999999E-2 4.5600000000000002E-2 4.2599999999999999 E-2 3.8399999999999997E-2 3.5999999999999997E-2 3.5400000000000001E-2 4.2099999999999999E-2 4.2700000000000002E-2 4.4200000000000003E-2 4.5600000000000002E-2 4.7300000000000002E-2 4.9700000000000001E-2 0.05 4.9799999999999997E-2 5.1700000000000003E-2 5.3800000000000001E-2 5.6599999999999998E-2 5.5199999999999999E-2 5.3100000000000001E-2 5.0900000000000001E-2 5.1900000000000002E-2 5.3499999999999999E-2 5.45E-2 5.96E-2 6.1400000000000003E-2 6.1199999999999997E-2 6.0199999999999997E-2 6.1100000000000002E-2 6.0400000000000002E-2 6.4399999999999999E-2 7.0000000000000007E-2 6.9800000000000001E-2 7.0900000000000005E-2 7.0000000000000007E-2 7.2400000000000006E-2 7.8200000000000006E-2 7.8700000000000006E-2 7.1300000000000002E-2 6.6299999999999998E-2 6.5100000000000005E-2 6.8400000000000002E-2 6.6799999999999998E-2 6.4500000000000002E-2 6.4100000000000004E-2 6.1199999999999997E-2 5.91E-2 5.28E-2 4.87E-2 4.4400000000000002E-2 3.6999999999999998E-2 3.3799999999999997E-2 3.8600000000000002E-2 4.1399999999999999E-2 4.7500000000000001E-2 5.3999999999999999E-2 4.9399999999999999E-2 4.6899999999999997E-2 4.4600000000000001E-2 4.2200000000000001E-2 4.0099999999999997E-2 3.3799999999999997E-2 3.2000000000000001E-2 3.73E-2 3.7100000000000001E-2 3.6900000000000002E-2 3.9100000000000003E-2 3.9800000000000002E-2 4.02E-2 4.6600000000000003E-2 4.7399999999999998E-2 4.7800000000000002E-2 5.0700000000000002E-2 5.4100000000000002E-2 5.6000000000000001E-2 6.0900000000000003E-2 6.2600000000000003E-2 6.3600000000000004E-2 7.1900000000000006E-2 8.0100000000000005E-2 8.66999 99999999999E-2 8.2900000000000001E-2 7.22E-2 7.8299999999999995E-2 7.4499999999999997E-2 7.7700000000000005E-2 7.1199999999999999E-2 7.9600000000000004E-2 8.3299999999999999E-2 8.2299999999999998E-2 7.9000000000000001E-2 7.5499999999999998E-2 8.9599999999999999E-2 8.0600000000000005E-2 7.46E-2 7.4700000000000003E-2 7.1499999999999994E-2 6.2600000000000003E-2 5.5E-2 5.4899999999999997E-2 5.6099999999999997E-2 5.2299999999999999E-2 5.3400000000000003E-2 6.13E-2 6.4399999999999999E-2 6.4199999999999993E-2 5.96E-2 5.4800000000000001E-2 5.4399999999999997E-2 4.87E-2 4.8800000000000003E-2 0.05 4.8599999999999997E-2 5.1999999999999998E-2 5.4100000000000002E-2 5.2299999999999999E-2 5.1400000000000001E-2 5.0799999999999998E-2 4.9200000000000001E-2 4.7500000000 000001E-2 4.3499999999999997E-2 4.6199999999999998E-2 4.6699999999999998E-2 4.5999999999999999E-2 4.5400000000000003E-2 4.9599999999999998E-2 5.0200000000000002E-2 5.1900000000000002E-2 5.4899999999999997E-2 5.8099999999999999E-2 6.1600000000000002E-2 6.0999999999999999E-2 6.0699999999999997E-2 6.4399999999999999E-2 6.4500000000000002E-2 6.2899999999999998E-2 6.2899999999999998E-2 6.4100000000000004E-2 6.7299999999999999E-2 7.0099999999999996E-2 7.0800000000000002E-2 7.85E-2 7.9899999999999999E-2 8.6400000000000005E-2 9.0800000000000006E-2 9.35E-2 9.3200000000000005E-2 9.4799999999999995E-2 9.4600000000000004E-2 9.6100000000000005E-2 9.06E-2 9.2399999999999996E-2 9.5200000000000007E-2 0.1026 0.11700000000000001 0.1179 0.12039999999999999 0.12 0.128599 99999999999 0.152 0.13200000000000001 8.5800000000000001E-2 7.0699999999999999E-2 8.0600000000000005E-2 9.1300000000000006E-2 0.1027 0.1162 0.13730000000000001 0.15490000000000001 0.1502 0.1479 0.1336 0.13689999999999999 0.16300000000000001 0.14729999999999999 0.14949999999999999 0.15509999999999999 0.14699999999999999 0.13539999999999999 0.1086 0.1085 0.12280000000000001 0.1348 0.1268 0.127 0.12089999999999999 0.12470000000000001 0.1135 8.6800000000000002E-2 7.9200000000000007E-2 7.7100000000000002E-2 8.0699999999999994E-2 7.9399999999999998E-2 7.8600000000000003E-2 8.1100000000000005E-2 8.3500000000000005E-2 8.2100000000000006E-2 8.1900000000000001E-2 8.7900000000000006E-2 9.080000000 0000006E-2 9.3399999999999997E-2 0.09 8.6400000000000005E-2 8.7599999999999997E-2 0.09 8.8999999999999996E-2 9.0899999999999995E-2 9.5200000000000007E-2 9.69E-2 9.8299999999999998E-2 9.8699999999999996E-2 0.1012 0.1047 0.1037 9.74E-2 8.6099999999999996E-2 8.0600000000000005E-2 7.7600000000000002E-2 8.2699999999999996E-2 8.5199999999999998E-2 7.9500000000000001E-2 7.4800000000000005E-2 6.9500000000000006E-2 7.0800000000000002E-2 7.1400000000000005E-2 7.0999999999999994E-2 7.1599999999999997E-2 7.2400000000000006E-2 7.0999999999999994E-2 7.0699999999999999E-2 7.0599999999999996E-2 6.5600000000000006E-2 6.0600000000000001E-2 6.1499999999999999E-2 6.2100000000000002E-2 5.8299999999999998E-2 5.5300000000000002E-2 5.21E-2 5.1799999999999999E-2 5.3499999999999999E-2 5.5300000000000002E-2 5.4300000000000001E-2 5.5899999999999998E-2 5.5899999999999998E-2 5.6399999999999999E-2 5.6599999999999998E-2 5.67E-2 5.6899999999999999E-2 6.0400000000000002E-2 6.4000000000000001E-2 6.13E-2 5.6899999999999999E-2 5.7700000000000001E-2 5.8099999999999999E-2 5.6599999999999998E-2 5.7000000000000002E-2 5.91E-2 6.2600000000000003E-2 6.4600000000000005E-2 6.7299999999999999E-2 7.0599999999999996E-2 7.2400000000000006E-2 7.3499999999999996E-2 7.7600000000000002E-2 8.0699999999999994E-2 8.2699999999999996E-2 8.5300000000000001E-2 8.8200000000000001E-2 8.6499999999999994E-2 8.43E-2 8.1500000000000003E-2 7.8799999999999995E-2 7.9000000000000001E-2 7.7499999999999999E-2 7.6399999999999996E-2 7.6899999999999996E-2 7.6300000000000007E-2 7.6399999999999996E-2 7.7399999999999997E-2 7.9000000000000001E-2 7.7700000000000005E-2 7.7399999999999997E-2 7.7299999999999994E-2 7.6200000000000004E-2 7.4499999999999997E-2 7.3599999999999999E-2 7.17E-2 7.0599999999999996E-2 6.7400000000000002E-2 6.2199999999999998E-2 5.9400000000000001E-2 5.91E-2 5.6500000000000002E-2 5.4600000000000003E-2 5.57E-2 5.5800000000000002E-2 5.33E-2 5.2200000000000003E-2 4.99E-2 4.5600000000000002E-2 4.07E-2 3.7999999999999999E-2 3.8399999999999997E-2 4.0399999999999998E-2 3.7499999999999999E-2 3.6299999999999999E-2 3.6600000000000001E-2 3.2099999999999997E-2 3.1300000000000001E-2 2.9100000000000001E-2 2.86E-2 3.1300000000000001E-2 3.2199999999999999E-2 0.03 2.93E-2 2.9499999999999998E-2 2.87E-2 2.9600000000000001E-2 3.0700000000000002E-2 3.04E-2 3.0200000000000001E-2 2.9499999999999998E-2 3.0200000000000001E-2 3.1E-2 3.0599999999999999E-2 2.98E-2 3.2500000000000001E-2 3.5000000000000003E-2 3.6799999999999999E-2 4.1399999999999999E-2 4.1399999999999999E-2 4.3299999999999998E-2 4.48E-2 4.6199999999999998E-2 4.9500000000000002E-2 5.2900000000000003E-2 5.6000000000000001E-2 5.7099999999999998E-2 5.7700000000000001E-2 5.7299999999999997E-2 5.6500000000000002E-2 5.67E-2 5.4699999999999999E-2 5.4199999999999998E-2 5.3999999999999999E-2 5.28E-2 5.28E-2 5.3600000000000002E-2 5.1400000000000001E-2 0.05 4.8300000000000003E-2 4.9599999999999998E-2 4.9500000000000002E-2 5.0200000000000002E-2 5.0900000000000001E-2 5.1499999999999997E-2 5.05 00000000000003E-2 5.0900000000000001E-2 4.99E-2 5.0299999999999997E-2 4.9099999999999998E-2 5.0299999999999997E-2 5.0099999999999999E-2 5.1400000000000001E-2 5.16E-2 5.0500000000000003E-2 4.9299999999999997E-2 5.0500000000000003E-2 5.1400000000000001E-2 4.9500000000000002E-2 4.9700000000000001E-2 5.1400000000000001E-2 5.16E-2 5.04E-2 5.0900000000000001E-2 5.0299999999999997E-2 4.9500000000000002E-2 0.05 4.9799999999999997E-2 4.9599999999999998E-2 4.9000000000000002E-2 4.6100000000000002E-2 3.9600000000000003E-2 4.41E-2 4.3900000000000002E-2 4.3400000000000001E-2 4.4400000000000002E-2 4.4400000000000002E-2 4.2900000000000001E-2 4.4999999999999998E-2 4.5699999999999998E-2 4.5499999999999999E-2 4.7199999999999999E-2 4.6800000000000001E-2 4.8599999999999997E-2 5.0700000000000002E-2 5.1999999999999998E-2 5.3199999999999997E-2 5.5500000000000001E-2 5.6899999999999999E-2 5.6599999999999998E-2 5.79E-2 5.6899999999999999E-2 5.96E-2 6.0900000000000003E-2 0.06 6.1100000000000002E-2 6.1699999999999998E-2 5.7700000000000001E-2 5.1499999999999997E-2 4.8800000000000003E-2 4.4200000000000003E-2 3.8699999999999998E-2 3.6200000000000003E-2 3.49E-2 3.5099999999999999E-2 3.3599999999999998E-2 2.64E-2 2.1600000000000001E-2 1.8700000000000001E-2 1.6899999999999998E-2 1.6500000000000001E-2 1.7299999999999999E-2 1.7899999999999999E-2 1.72E-2 1.7299999999999999E-2 1.7000000000000001E-2 1.6799999999999999E-2 1.6199999999999999E-2 1.6299999999999999E-2 1.5800000000000002E-2 1.23E-2 1.1900000000000001E-2 1.17E-2 1.17E-2 1.1299999999999999E-2 1.1299999999999999E-2 1.0699999999999999E-2 9.1999999999999998E-3 8.9999999999999993E-3 9.4999999999999998E-3 9.4000000000000004E-3 9.1999999999999998E-3 9.2999999999999992E-3 8.9999999999999993E-3 8.8000000000000005E-3 9.2999999999999992E-3 9.4000000000000004E-3 9.4000000000000004E-3 1.0200000000000001E-2 1.2699999999999999E-2 1.3299999999999999E-2 1.4800000000000001E-2 1.6500000000000001E-2 1.7600000000000001E-2 2.07E-2 2.1899999999999999E-2 2.3300000000000001E-2 2.5399999999999999E-2 2.7400000000000001E-2 2.7799999999999998E-2 2.8400000000000002E-2 2.9700000000000001E-2 3.2199999999999999E-2 3.44E-2 3.4200000000000001E-2 3.7100000000000001E-2 3.8800000000000001E-2 3.8899999999999997E-2 4.24E-2 4.4299999999999999E-2 4.5100000000000001E-2 4.5999999999999999E-2 4.7199999999999999E-2 4.7899999999999998E-2 4.9500000000000002E-2 4.9599999999999998E-2 4.8099999999999997E-2 4.9200000000000001E-2 4.9399999999999999E-2 4.8500000000000001E-2 4.9799999999999997E-2 5.0299999999999997E-2 4.9399999999999999E-2 4.87E-2 4.7300000000000002E-2 4.6100000000000002E-2 4.82E-2 4.2000000000000003E-2 3.8899999999999997E-2 3.9E-2 3.27E-2 0.03 2.75E-2 2.12E-2 1.26E-2 1.29E-2 1.7299999999999999E-2 1.8599999999999998E-2 1.6299999999999999E-2 1.72E-2 1.1299999999999999E-2 6.7000000000000002E-3 1.9E-3 2.9999999999999997E-4 1.2999999999999999E-3 3.0000000000000001E-3 2.0999999999999999E-3 1.6000000000000001E-3 1.8E-3 1.8E-3 1.8E-3 1.6999999999999999E-3 1.1999999999999999E-3 6.9999999999999999E-4 5.0000000000000001E-4 5.0000000000000001E-4 5.9999999999999995E-4 1.1000000000000001E-3 1.5E-3 1.6000000000000001E-3 1.6000000000000001E-3 1.1999999999999999E-3 1.6000000000000001E-3 1.6000000000000001E-3 1.5E-3 1.2999999999999999E-3 1.4E-3 1.4E-3 1.5E-3 1.2999999999999999E-3 1E-3 5.9999999999999995E-4 4.0000000000000002E-4 4.0000000000000002E-4 4.0000000000000002E-4 2.0000000000000001E-4 1E-4 2.0000000000000001E-4 1E-4 1E-4 2.9999999999999997E-4 8.9999999999999998E-4 8.0000000000000004E-4 8.0000000000000004E-4 8.9999999999999998E-4 8.9999999999999998E-4 1E-3 1E-3 1.1000000000000001E-3 1E-3 8.9999999999999998E-4 6.9999999999999999E-4 6.9999999999999999E-4 1E-3 8.9999999999999998E-4 5.9999999999999995E-4 4.0000000000000002E-4 5.0000000000000001E-4 4.0000000000000002E-4 4.0000000000000002E-4 2.0000000000000001E-4 5.0000000000000001E-4 6.9999999999999999E-4 6.9999999999999999E-4 4.0000000000000002E-4 5.0000000000000001E-4 5.0000000000000001E-4 2.9999999999999997E-4 2.9999999999999997E-4

Inflation and nominal interest rates in 96 countries

Nominal interest rate (percent)

Inflation rate (percent)

Malawi

Georgia

Turkey

Ghana

Iraq

U.S.

Poland

Japan

Brazil

Kazakhstan

Mexico

‹#›

CHAPTER 5 Inflation

Sources:

Interest Rate Data - www.imf.org > Data > International Financial Statistics (IFS)

Inflation Data - www.imf.org > Data > World Economic Outlook

Each variable is measured as an annual average over 2000-2010.

The nominal interest rate is the rate on short-term government debt.

2.7676363636363641 3.0975454545454539 1.906363636363636 3.916363636363636 3.1391818181818181 7.0614545454545468 2.1725454545454541 1.6113636363636361 3.8013636363636372 2.1394545454545462 2.5584545454545449 4.8307272727272696 6.7293636363636402 6.406727272 7272719 10.63636363636364 2.08518181818182 1.9954545454545449 2.6422727272727271 2.6662727272727271 2.1460909090909088 7.5111818181818144 10.62127272727272 4.2701818181818174 1.861272727272727 6.3879090909090896 1.599818181818182 17.696090909090909 3.363 2.9180909090909091 5.9409999999999998 6.0108181818181814 6.1344545454545436 20.657833333333329 2.0727272727272732 2.2689090909090912 11.16209090909091 -0.30327272727272703 9.1490000000000009 8.1063636363636373 3.400727272727273 8.5543636363636377 9.0707272727272752 5.1894545454545451 2.665909090909091 6.9454545454545462 2.887909090909091 10.3199090909091 14.28727272727272 2.1409090909090911 3.487090909090909 2.471545454545454 6.2598181818181819 5.1199999999999974 11.56063636363637 9.1027272727272752 7.7077000000000009 10.795090909090909 7.1599999999999966 5.9094545454545457 2.1579999999999999 2.6487272727272742 12.459545454545459 7.9671818181818068 7.4817272727272721 5.1139999999999954 3.425636363636364 15.4379090909091 13.323454545454551 7.6149090909090846 2.3877272727272731 21.466727272727208 8.2040000000000006 8.6266363636363632 1.6087272727272719 4.6135454545454433 8.3872727272727179 5.9592727272727304 2.8889999999999998 10.603 3.1890000000000001 2.8455454545454542 2.6629090909090909 7.1513636363636399 1.8582727272727271 0.92990909090909102 6.3460909090909086 2.5265454545454542 6.6716363636363631 21.83127272727274 6.4815454545454543 1.982272727272727 2.4851818181818182 8.4075454545454544 6.9530909090909097 11.10454545454545 16.49218181818182 7.1727470372664053 2.3601893939393941 6.6812121212121296 10.874918683522999 4.5912605945298903 9.4352146463939395 1.73649393939394 2.969409090909092 3.6938636363636359 2.6037878787878781 3.8172151515151498 7.1822153309758274 16.017298642060311 3.4921113636363641 13.68285714285714 2.8346136363636361 5.4652889612423543 4.2872916666625009 2.8658428566981571 6.4 8.5496363636363668 1.211979056160382 2.9945653901888192 2.6873333333333331 25.38388701560898 2.9808332499999999 22.138370865962059 3.309886927504857 6.3106060606060508 4.8278030303030297 8.5934900523628546 10.374167884706671 11.493194444444439 5.1062035828939401 2.8498318181818179 15.97431818181817 0.16881818181818 201 5.5254545454545454 7.3779301767676682 2.6874682291458329 10.546670814692311 18.57693388417653 4.6728838384242346 6.8032196969696948 8.7276946969696994 4.5224318181818068 12.5296095234979 25.24930870852889 2.7947159090909102 5.5997916666666674 3.4156492424242431 8.8199408379614397 7.9792424242424298 12.383636363636359 9.416875000000001 4.2516833333333404 15.87458365972166 8.7330303030303007 4.1827272727272646 4.4809999999999999 5.6605110585520126 11.042272727272721 8.2418719696969482 8.9281060609090925 5.9976136363636376 7.3599015151515141 21.471354166583328 10.66076388888891 9.6223795384263653 0.38291666666666702 13.06770687056556 5.1650627565441196 18.10840151515152 1.386742424242424 5.71075 5.1518017676767656 8.8713636363636361 2.9248484848484759 12.4444696969697 7.0246212121212066 5.3993489583333334 5.745007575757576 8.3237121212121181 2.687999242424242 1.1512272727272721 7.9029643939393912 2.3617707549381382 5.6190530808080776 37.373593749999998 9.3164511229015687 3.8605568181818182 2.4843181818181801 11.99775 6.3519426214285719 14.70077361686514 20.59416516203704

NOW YOU TRY Applying the theory

Suppose V is constant, M is growing 5% per year, Y is growing 2% per year, and r = 4.

a. Solve for i.

b. If the Fed increases the money growth rate by 2 percentage points per year, find Δi.

c. Suppose the growth rate of Y falls to 1% per year.

What will happen to π?

What must the Fed do if it wishes to keep π constant?

‹#›

CHAPTER 5 Inflation

This exercise gives students an immediate application of the quantity theory of money and the Fisher effect. The math is not difficult.

ANSWERS Applying the theory

a. First, find π = 5 − 2 = 3.

Then, find i = r + π = 4 + 3 = 7.

b. Δi = 2, same as the increase in the money growth rate.

c. If the Fed does nothing, Δπ = 1.

To prevent inflation from rising, Fed must reduce the money growth rate by 1 percentage point per year.

V is constant, M grows 5% per year, Y grows 2% per year, r = 4.

‹#›

CHAPTER 1 The Science of Macroeconomics

Answers, the details:

First, we need to find .

Constant velocity implies  = (M/M) - (Y/Y) = 5 – 2 = 3.

Then, i = r +  = 4 + 3 = 7.

b. Changes in the money growth rate do not affect real GDP or its growth rate. So, a two-point increase in money growth causes a two-point increase in inflation. According to the Fisher effect, the nominal interest rate should rise by the increase in inflation: two points (from i = 7 to i = 9).

c.  = (M/M) – (Y/Y). If (Y/Y) falls by 1 point, then  will increase by 1 point; the Fed can prevent this by reducing (M/M) by 1 point. Intuition: With slower growth in the economy, the volume of transactions will be growing more slowly, which means that the need for new money will grow more slowly.

Two real interest rates

Notation:

π = actual inflation rate (not known until after it has occurred)

Eπ = expected inflation rate

Two real interest rates:

i – Eπ = ex ante real interest rate: the real interest rate people expect at the time they buy a bond or take out a loan

i – π = ex post real interest rate: the real interest rate actually realized

‹#›

CHAPTER 5 Inflation

Notation alert:

In the 7th and 8th (present) editions, Mankiw uses the expectation operator E, so expected inflation is written as E.

In earlier editions, he used a superscript E, so expected inflation was written as e.

Money demand and the nominal interest rate

In the quantity theory of money, the demand for real money balances depends only on real income Y.

Another determinant of money demand: the nominal interest rate, i.

the opportunity cost of holding money (instead of bonds or other interest-earning assets).

So, money demand depends negatively on i.

‹#›

CHAPTER 5 Inflation

The concept of “money demand” can be a bit awkward for students the first time they learn it. Here’s a good way to explain it.

A consumer has a certain amount of wealth, which she must divide between money and other assets.

Money is nice because it’s very liquid. But money doesn’t pay interest (loosely speaking—more precisely, the nominal interest rate on money is zero, while the real rate equals minus the inflation rate).

The other assets are typically less liquid than money, but they typically generate some type of income (e.g. interest income in the case of bonds).

Therefore, there’s a tradeoff between liquidity and income: the more money the consumer holds in her portfolio, the greater the liquidity of her wealth, but the less income she earns from it.

The money demand function

(M/P )d = real money demand, depends

negatively on i

i is the opp. cost of holding money

positively on Y

higher Y increases spending on g & s,

so increases need for money

(“L” is used for the money demand function because money is the most liquid asset.)

‹#›

CHAPTER 5 Inflation

An increase in the nominal interest rate represents the increase in the opportunity cost of holding money rather than bonds, and would motivate the typical consumer to hold less of his wealth in the form of money, and more in the form of bonds (or other interest-earning assets).

An increase in real income (other things equal) causes an increase in the consumer’s consumption and therefore spending. To facilitate this extra spending, the consumer will require more money. Thus, the consumer would like a larger fraction of his wealth to be in the form of money (rather than bonds, etc.). This might involve redeeming/selling. some of his bonds. Or it might simply involve holding the additional income in the form of money rather than putting it into bonds.

The money demand function

When people are deciding whether to hold money or bonds, they don’t know what inflation will turn out to be.

Hence, the nominal interest rate relevant for money demand is r + Eπ.

‹#›

CHAPTER 5 Inflation

Equilibrium

The supply of real money balances

Real money demand

‹#›

CHAPTER 5 Inflation

What determines what

variable how determined (in the long run)

M exogenous (the Fed)

r adjusts to ensure S = I

P adjusts to ensure

‹#›

CHAPTER 5 Inflation

Again, it is very important for students to learn the logical order in which variables are determined. I.e., we do not need to know P in order to determine Y. We do need to know Y in order to determine L, and we need to know L and M in order to determine P.

How P responds to ΔM

For given values of r, Y, and Eπ ,

a change in M causes P to change by the same percentage—just like in the quantity theory of money.

‹#›

CHAPTER 5 Inflation

This slide shows the connection between the money market equilibrium condition and the (simpler) quantity theory of money, presented earlier in this chapter.

What about expected inflation?

Over the long run, people don’t consistently over- or under-forecast inflation,

so Eπ = π on average.

In the short run, Eπ may change when people get new information.

EX: Fed announces it will increase M next year. People will expect next year’s P to be higher, so Eπ rises.

This affects P now, even though M hasn’t changed yet….

‹#›

CHAPTER 5 Inflation

This slide and the next correspond to the subsection of Chapter 5 entitled “Future Money and Current Prices” on pp.114-116.

How P responds to ΔE π

For given values of r, Y, and M ,

‹#›

CHAPTER 5 Inflation

NOW YOU TRY Discussion question

Why is inflation bad?

What costs does inflation impose on society? List all the ones you can think of.

Focus on the long run.

Think like an economist.

‹#›

CHAPTER 5 Inflation

Many of the social costs of inflation are not hard to figure out, if students “think like an economist.”

Suggestion: After you pose the question, don’t immediately ask for students to volunteer their answers. Instead, tell them to think about the question for a moment, jot down their answers, and THEN ask for volunteers. You will get more participation (quantity & quality) this way, especially from students who don’t consider themselves fast thinkers.

After presenting the following slides (which describe the costs), see how many of the costs presented here were anticipated by the students’ responses to the question on this slide.

A common misperception

Common misperception: inflation reduces real wages

This is true only in the short run, when nominal wages are fixed by contracts.

(Chap. 3) In the long run, the real wage is determined by labor supply and the marginal product of labor, not the price level or inflation rate.

Consider the data…

‹#›

CHAPTER 5 Inflation

Encourage your students to check out the case study “What economists and the public say about inflation” on p.117.

The CPI and Average Hourly Earnings, 1965–2014

1965 = 100

Hourly wage in 2014 dollars

Real average hourly earnings in 2014 dollars, right scale

Nominal average hourly earnings, (1965 = 100)

CPI (1965 = 100)

‹#›

CHAPTER 5 Inflation

The CPI has risen tremendously over the past 45 years. However, nominal wages have risen by a roughly similar magnitude.

If the common misperception were true, then the real wage should show exactly the opposite behavior as the CPI. It doesn’t. While the real wage is not constant, it exhibits no downward long-term trend.

(We wouldn’t expect the real wage to be constant over the long run – we would expect it to change in response to shifts in the labor supply and MPL curves.)

source: BLS

Obtained from: http://research.stlouisfed.org/fred2/

AHETPI = average hourly earnings: total private industries monthly

CPIAUCSL = CPI, all urban consumers, seasonally adjusted

AHETPI 1965 1965.083333333333 1965.166666666667 1965.25 1965.333333333333 1965.416666666667 1965.5 1965.583333333333 1965.666666666667 1965.75 1965.833333333333 1965.916666666667 1966 1966.0833333333301 1966.1666666666699 1966.25 1966.3333333333301 1966.4166666666699 1966.5 1966.5833333333 301 1966.6666666666699 1966.75 1966.8333333333301 1966.9166666666599 1967 1967.0833333333301 1967.1666666666599 1967.25 1967.3333333333301 1967.4166666666599 1967.5 1967.5833333333301 1967.6666666666599 1967.75 1967.8333333333301 1967.9166666666599 1968 1968.0833333333301 1968.1666666666599 1968.25 1968.3333333333301 1968.4166666666599 1968.5 1968.5833333333301 1968.6666666666599 1968.75 1968.8333333333301 1968.9166666666599 1969 1969.0833333333301 1969.1666666666599 1969.25 1969.3333333333301 1969.4166666666599 1969.5 1969.5833333333301 1969.6666666666599 1969.75 1969.8333333333301 1969.9166666666599 1970 1970.0833333333301 1970.1666666666599 1970.25 1970.3333333333301 1970.4166666666599 1970.49999999999 1970.5833333333301 1970.6666666666599 1970.74999999999 1970.8333333333301 1970.9166666666599 1970.99999999999 1971.0833333333301 1971.1666666666599 1971.24999999999 1971.3333333333301 1971.4166666666599 1971.49999999999 1971.5833333333301 1971.6666666666599 1971.74999999999 1971.8333333333301 1971.9166666666599 1971.99999999999 1972.0833333333301 1972.1666666666599 1972.24999999999 1972.3333333333301 1972.4166666666599 1972.49999999999 1972.5833333333301 1972.6666666666599 1972.74999999999 1972.8333333333301 1972.9166666666599 1972.99999999999 1973.0833333333301 1973.1666666666599 1973.24999999999 1973.3333333333301 1973.4166666666599 1973.49999999999 1973.5833333333301 1973.6666666666599 1973.74999999999 1973.8333333333301 1973.9166666666599 1973.99999999999 1974.0833333333301 1974.1666666666599 1974.24999999999 1974.3333333333201 1974.4166666666599 1974.49999999999 1974.5833333333201 1974.6666666666599 1974.74999999999 1974.8333333333201 1974.9166666666599 1974.99999999999 1975.0833333333201 1975.1666666666599 1975.24999999999 1975.3333333333201 1975.4166666666599 1975.49999999999 1975.5833333333201 1975.6666666666599 1975.74999999999 1975.8333333333201 1975.9166666666599 1975.99999999999 1976.0833333333201 1976.1666666666599 1976.24999999999 1976.3333333333201 1976.4166666666599 1976.49999999999 1976.5833333333201 1976.6666666666599 1976.74999999999 1976.8333333333201 1976.9166666666599 1976.99999999999 1977.0833333333201 1977.1666666666599 1977.24999999999 1977.3333333333201 1977.4166666666599 1977.49999999999 1977.5833333333201 1977.6666666666599 1977.74999999999 1977.8333333333201 1977.9166666666499 1977.99999999999 1978.0833333333201 1978.1666666666499 1978.24999999999 1978.3333333333201 1978.4166666666499 1978.49999999999 1978.5833333333201 1978.6666666666499 1978.74999999999 1978.8333333333201 1978.9166666666499 1978.99999999999 1979.0833333333201 1979.1666666666499 1979.24999999999 1979.3333333333201 1979.4166666666499 1979.49999999999 1979.5833333333201 1979.6666666666499 1979.74999999999 1979.8333333333201 1979.9166666666499 1979.99999999999 1980.0833333333201 1980.1666666666499 1980.249999999 99 1980.3333333333201 1980.4166666666499 1980.49999999999 1980.5833333333201 1980.6666666666499 1980.74999999999 1980.8333333333201 1980.9166666666499 1980.99999999999 1981.0833333333201 1981.1666666666499 1981.24999999999 1981.3333333333201 1981.4166666666499 1981.49999999998 1981.5833333333201 1981.6666666666499 1981.74999999998 1981.8333333333201 1981.9166666666499 1981.99999999998 1982.0833333333201 1982.1666666666499 1982.24999999998 1982.3333333333201 1982.4166666666499 1982.49999999998 1982.5833333333201 1982.6666666666499 1982.74999999998 1982.8333333333201 1982.9166666666499 1982.99999999998 1983.0833333333201 1983.1666666666499 1983.24999999998 1983.3333333333201 1983.4166666666499 1983.49999999998 1983.58333 33333201 1983.6666666666499 1983.74999999998 1983.8333333333201 1983.9166666666499 1983.99999999998 1984.0833333333201 1984.1666666666499 1984.24999999998 1984.3333333333201 1984.4166666666499 1984.49999999998 1984.5833333333201 1984.6666666666499 1984.74999999998 1984.8333333333201 1984.9166666666499 1984.99999999998 1985.0833333333201 1985.1666666666499 1985.24999999998 1985.3333333333101 1985.4166666666499 1985.49999999998 1985.5833333333101 1985.6666666666499 1985.74999999998 1985.8333333333101 1985.9166666666499 1985.99999999998 1986.0833333333101 1986.1666666666499 1986.24999999998 1986.3333333333101 1986.4166666666499 1986.49999999998 1986.5833333333101 1986.6666666666499 1986.74999999998 1986.8333333333101 1986 .9166666666499 1986.99999999998 1987.0833333333101 1987.1666666666499 1987.24999999998 1987.3333333333101 1987.4166666666499 1987.49999999998 1987.5833333333101 1987.6666666666499 1987.74999999998 1987.8333333333101 1987.9166666666499 1987.99999999998 1988.0833333333101 1988.1666666666499 1988.24999999998 1988.3333333333101 1988.4166666666499 1988.49999999998 1988.5833333333101 1988.6666666666499 1988.74999999998 1988.8333333333101 1988.9166666666399 1988.99999999998 1989.0833333333101 1989.1666666666399 1989.24999999998 1989.3333333333101 1989.4166666666399 1989.49999999998 1989.5833333333101 1989.6666666666399 1989.74999999998 1989.8333333333101 1989.9166666666399 1989.99999999998 1990.0833333333101 1990.1666666666399 1990.24999999998 1990.3333333333101 1990.4166666666399 1990.49999999998 1990.5833333333101 1990.6666666666399 1990.74999999998 1990.8333333333101 1990.9166666666399 1990.99999999998 1991.0833333333101 1991.1666666666399 1991.24999999998 1991.3333333333101 1991.4166666666399 1991.49999999998 1991.5833333333101 1991.6666666666399 1991.74999999998 1991.8333333333101 1991.9166666666399 1991.99999999998 1992.0833333333101 1992.1666666666399 1992.24999999998 1992.3333333333101 1992.4166666666399 1992.49999999997 1992.5833333333101 1992.6666666666399 1992.74999999997 1992.8333333333101 1992.9166666666399 1992.99999999997 1993.0833333333101 1993.1666666666399 1993.24999999997 1993.3333333333101 1993.4166666666399 1993.49999999997 1993.5833333333101 1993.6666666666399 1993.74999999997 1993.8333333333101 1993.9166666666399 1993.99999999997 1994.0833333333101 1994.1666666666399 1994.24999999997 1994.3333333333101 1994.4166666666399 1994.49999999997 1994.5833333333101 1994.6666666666399 1994.74999999997 1994.8333333333101 1994.9166666666399 1994.99999999997 1995.0833333333101 1995.1666666666399 1995.24999999997 1995.3333333333101 1995.4166666666399 1995.49999999997 1995.5833333333101 1995.6666666666399 1995.74999999997 1995.8333333333101 1995.9166666666399 1995.99999999997 1996.0833333333101 1996.1666666666399 1996.24999999997 1996.3333333333001 1996.4166666666399 1996.49999999997 1996.5833333333001 1996.6666666666399 1996.74999999997 1996.8333333333001 1996.9166666666399 1996.99999999997 1997.0833333333001 1997.1666666666399 1997.24999999997 1997.3333333333001 1997.4166666666399 1997.49999999997 1997.5833333333001 1997.6666666666399 1997.74999999997 1997.8333333333001 1997.9166666666399 1997.99999999997 1998.0833333333001 1998.1666666666399 1998.24999999997 1998.3333333333001 1998.4166666666399 1998.49999999997 1998.5833333333001 1998.6666666666399 1998.74999999997 1998.8333333333001 1998.9166666666399 1998.99999999997 1999.0833333333001 1999.1666666666399 1999.24999999997 1999.3333333333001 1999.4166666666399 1999.49999999997 1999.5833333333001 1999.6666666666399 1999.74999999997 1999.8333333333001 1999.9166666666299 1999.99999999997 2000.0833333333001 2000.1666666666299 2000.24999999997 2000.3333333333001 2000.4166666666299 2000.49999999997 2000.5833333333001 2000.6666666666299 2000.74999999997 2000.8333333333001 2000.9166666666299 2000.99999999997 2001.0833333333001 2001.1666666666299 2001.24999999997 2001.3333333333001 2001.4166666666299 2001.49999999997 2001.5833333333001 2001.6666666666299 2001.74999999997 2001.8333333333001 2001.9166666666299 2001.99999999997 2002.0833333333001 2002.1666666666299 2002.24999999997 2002.3333333333001 2002.4166666666299 2002.49999999997 2002.5833333333001 2002.6666666666299 2002.74999999997 2002.8333333333001 2002.9166666666299 2002.99999999997 2003.0833333333001 2003.1666666666299 2003.24999999997 2003.3333333333001 2003.4166666666299 2003.49999999996 2003.5833333333001 2003.6666666666299 2003.74999999996 2003.8333333333001 2003.9166666666299 2003.99999999996 2004.0833333333001 2004.1666666666299 2004.24999999996 2004.3333333333001 2004.4166666666299 2004.49999999996 2004.5833333333001 2004.6666666666299 2004.74999999996 2004.8333333333001 2004.9166666666299 2004.99999999996 2005.0833333333001 2005.1666666666299 2005.24999999996 2005.3333333333001 2005.4166666666299 2005.49999999996 2005.5833333333001 2005.6666666666299 2005.74999999996 2005.8333333333001 2005.9166666666299 2005.99999999996 2006.0833333333001 2006.1666666666299 2006.24999999996 2006.3333333333001 2006.4166666666299 2006.49999999996 2006.5833333333001 2006.6666666666299 2006.74999999996 2006.8333333333001 2006.9166666666299 2006.99999999996 2007.0833333333001 2007.1666666666299 2007.24999999996 2007.3333333332901 2007.4166666666299 2007.49999999996 2007.5833333332901 2007.6666666666299 2007.74999999996 2007.8333333332901 2007.9166666666299 2007.99999999996 2008.0833333332901 2008.1666666666299 2008.24999999996 2008.3333333332901 2008.4166666666299 2008.49999999996 2008.5833333332901 2008.6666666666299 2008.74999999996 2008.8333333332901 2008.9166666666299 2008.99999999996 2009.0833333332901 2009.1666666666299 2009.24999999996 2009.3333333332901 2009.4166666666299 2009.49999999996 2009.5833333332901 2009.6666666666299 2009.74999999996 2009.8333333332901 2009.9166666666299 2009.99999999996 2010.0833333332901 2010.166666666 6299 2010.24999999996 2010.3333333332901 2010.4166666666299 2010.49999999996 2010.5833333332901 2010.6666666666299 2010.74999999996 2010.8333333332901 2010.9166666666199 2010.99999999996 2011.0833333332901 2011.1666666666199 2011.24999999996 2011.3333333332901 2011.4166666666199 2011.49999999996 2011.5833333332901 2011.6666666666199 2011.74999999996 2011.8333333332901 2011.9166666666199 2011.99999999996 2012.0833333332901 2012.1666666666199 2012.24999999996 2012.3333333332901 2012.4166666666199 2012.49999999996 2012.5833333332901 2012.6666666666199 2012.74999999996 2012.8333333332901 2012.9166666666199 2012.99999999996 2013.0833333332901 2013.1666666666199 2013.24999999996 2013.3333333332901 2013.4166666666099 2013.499 99999994 2013.58333333327 2013.6666666665999 2013.74999999993 2013.83333333326 2013.9166666665899 2013.99999999992 2014.08333333325 2014.1666666665801 2014.24999999991 2014.33333333324 100.00002600000001 100.387623 100.77522 100.77522 101.550414 101.550414 101.938011 102.325608 102.713205 103.100802 103.488399 103.875996 103.875996 104.263593 104.65119 105.038787 105.426384 105.426384 106.201578 106.589175 106.976772 107.364369 107.751966 107.751966 108.139563 108.91475699999999 108.91475699999999 109.30235399999999 109.68995099999999 110.07754799999999 110.85274200000001 111.24033900000001 111.62793600000001 112.015533 112.790727 113.178324 113.953518 114.341115 115.116309 115.503906 116.2791 116.666697 117.441891 117.441891 118.604682 118.992279 119.767473 120.54266699999999 120.93026399999999 121.70545799999999 122.09305500000001 122.86824900000001 123.643443 124.03104 124.806234 125.581428 126.356622 127.131816 127.519413 127.90701 128.29460700000001 129.06980100000001 129.84499500000001 130.23259200000001 131.00778600000001 131.39538300000001 132.17057700000001 132.94577100000001 133.72096500000001 134.10856200000001 134.49615900000001 135.65895 136.434144 137.209338 137.984532 138.372129 139.53492 140.310114 140.697711 141.860502 142.248099 142.635696 143.023293 144.57368099999999 147.28685999999999 148.06205399999999 148.8372480000001 149.61244199999999 150.00003899999999 150.38763599999999 151.16283000000001 151.93802400000001 152.71321800000001 153.87600900000001 154.26360600000001 155.42639700000001 156.20159100000001 156.58918800000001 157.36438200000001 158.13957600000001 158.91477 159.689964 160.852755 161.240352 162.403143 163.178337 163.953531 164.728725 165.116322 166.279113 167.05430699999999 168.21709799999999 170.15508299999999 171.70547099999999 172.48066499999999 174.03105300000001 175.58144100000001 176.74423200000001 177.13182900000001 178.68221700000009 178.68221700000009 179.45741100000001 180.62020200000001 180.62020200000001 181.39539600000001 182.945784 183.333381 184.883769 185.658963 186.434157 187.984545 188.759739 189.92253000000011 191.47291799999999 192.24811199999999 193.02330599999999 194.57369399999999 195.34888799999999 196.51167899999999 198.44966400000001 199.61245500000001 200.38764900000001 201.93803700000001 202.71323100000001 203.87602200000001 205.42641 206.589201 208.139589 209.30238000000011 210.465171 211.627962 212.403156 213.56594699999999 215.50393199999999 216.66672299999999 217.44191699999999 219.37990199999999 220.54269300000001 222.09308100000001 224.41866300000001 225.58145400000001 227.51943900000001 228.68223000000009 229.845021 231.395409 233.720991 234.883782 236.43416999999999 237.98455799999999 239.53494599999999 241.08533399999999 241.08533399999999 243.41091599999999 244.96130400000001 246.51169200000001 248.06208000000001 250.00006500000001 250.77525900000001 252.325647 254.65122900000009 254.65122900000009 256.97681099999909 259.68999000000002 260.46518400000002 262.01557200000002 264.34115400000002 265.89154200000002 267.82952699999998 269.37991499999998 272.09309400000001 274.80627299999998 276.35666100000009 278.68224300000008 280.23263100000003 282.55821300000002 284.10860100000002 285.65898900000002 287.59697399999908 289.1473620000001 291. 86054100000001 293.41092900000001 294.18612300000001 296.12410799999992 296.12410799999992 299.22488400000009 299.61248100000012 300.77527199999997 301.162869 303.48845099999909 304.263645 305.81403299999999 307.75201800000002 307.75201800000002 308.52721200000002 309.30240600000002 310.85279400000002 312.40318200000002 313.95357000000001 313.95357000000001 315.11636099999998 316.66674899999998 317.44194299999992 318.99233099999918 317.82954000000001 320.15512200000001 322.09310699999918 322.48070399999921 322.86830099999997 324.80628600000011 324.41868899999992 325.96907700000003 327.51946500000003 327.131868 328.68225600000011 330.23264399999999 330.23264399999999 331.7830319999992 331.39543500000002 332.17062900000002 333.72101699999911 333.72101699999911 334.88380799999999 336.04659900000001 336.82179300000001 337.20938999999993 338.75977799999998 338.75977799999998 339.92256900000001 341.08535999999998 340.69776300000001 341.86055399999998 343.7985389999991 343.02334499999961 344.18613599999918 344.57373299999921 344.57373299999921 344.96132999999918 345.348927 345.73652399999918 346.51171799999912 346.51171799999912 347.28691199999918 348.83730000000003 349.224897 349.61249400000008 350.77528500000011 351.55047900000011 351.93807599999911 353.10086699999999 353.10086699999999 353.48846399999991 355.81404600000002 356.20164299999999 357.36443400000007 359.30241899999999 359.69001600000001 360.07761299999999 360.07761299999999 360.8528070000001 362.79079200000001 364.72877699999918 365.11637400000001 366.27916499999992 366.66676200000012 368.60474700000009 370.54273200000011 371.317926 372.09311999999892 374.03110499999917 375.193896 375.96908999999999 377.90707500000002 377.13188100000002 378.68226900000002 380.62025399999999 381.00785100000002 382.55823900000001 384.88382100000001 384.88382100000001 386.82180599999998 388.37219399999992 390.31017899999961 391.860567 392.63576100000012 393.79855199999918 395.73653699999892 396.12413400000003 396.89932800000003 398.44971600000002 399.22491000000002 400.00010400000002 401.16289499999999 402.32568600000008 402.71328299999999 403.48847699999919 405.42646200000001 406.58925299999999 407.75204400000001 408.52723800000001 409.30243200000012 410.07762600000001 410.46522299999998 411.24041699999992 412.40320799999961 412.79080499999998 413.56599899999998 414.72878999999921 415.50398400000012 416.27917799999921 417.44196899999997 418.21716299999991 419.37995400000011 419.37995400000011 420.93034199999909 421.31793899999991 422.4807299999992 424.03111799999891 424.41871499999911 425.96910300000002 426.35669999999999 427.13189399999999 427.90708799999999 428.6822820000001 429.45747599999999 430.23266999999993 431.39546100000013 432.17065500000001 433.33344599999998 434.49623699999921 436.04662500000001 436.04662500000001 436.82181899999961 437.98460999999998 438.75980400000009 439.53499799999997 440.31019199999997 441.47298300000011 443.02337099999909 443.79856499999909 444.96135599999911 445.34895300000011 446.89934099999999 447.67453499999999 448.44972899999999 449.61252000000002 450.77531099999919 452.32569899999999 453.48849000000001 454.6512810000001 455.81407200000001 456.58926600000001 457.75205699999998 460.07763899999992 460.07763899999992 460.85283300000009 463.5660119999992 464.34120600000011 466.666788 467.44198200000011 468.99236999999908 470.54275799999999 471.31795199999999 473.25593700000002 474.80632500000002 476.74430999999998 477.51950399999998 479.45748900000001 480.23268300000012 481.78307099999961 483.33345899999961 484.49624999999918 487.20942900000011 488.759817 491.0853989999992 493.02338400000002 494.57377200000002 496.12416000000007 498.06214499999999 499.61253299999998 501.1629210000001 502.71330899999919 503.87610000000001 504.26369699999998 507.36447300000009 508.527264 509.69005499999997 510.852846 512.40323400000011 514.72881600000005 515.50401000000011 517.05439799999999 518.99238300000002 520.54277100000002 522.48075600000004 524.03114399999936 525.19393500000001 527.90711399999884 528.68230800000003 529.45750199999884 531.39548700000012 533.33347200000003 534.88386000000003 536.82184499999937 539.14742699999886 540.31021799999849 542.24820299999999 543.79859099999999 545.3489790000001 547.67456100000004 549.61254600000007 551.93812799999898 553.87611299999901 554.26371000000006 556.97688900000003 559.30247099999997 560.46526199999823 562.01564999999937 563.95363500000008 564.34123199999897 565.89161999999885 567.82960499999899 568.60479900000007 570.93038100000001 572.09317199999998 572.48076900000001 573.25596299999938 574.80635100000006 575.19394799999998 577.131933 579.45751499999824 581.00790300000006 582.55829099999937 584.49627600000008 586.43426099999897 587.59705200000008 589.92263399999899 590.31023099999936 593.02341000000001 593.02341000000001 592.63581299999998 594.57379800000001 595.73658899999998 597.28697700000055 598.06217099999935 598.06217099999935 598.44976800000006 600.00015600000006 600.00015600000006 601.16294699999901 602.71333500000003 603.48852900000009 604.65132000000006 606.58930500000008 607.75209599999937 608.91488700000002 610.465274999999 612.01566299999899 613.56605099999899 614.34124499999859 615.50403600000004 617.05442399999936 617.82961799999885 619.38000600000009 620.93039399999998 622.09318500000006 623.64357300000006 626.74434900000006 627.13194599999997 628.29473700000005 631.78311000000008 632.55830400000002 634.49628899999936 637.20946800000013 639.14745299999936 641.47303500000055 645.34900499999935 645.73660200000006 648.83737799999938 651.16295999999898 652.713348 654.26373599999999 656.97691499999996 658.52730299999996 661.24048200000004 662.79087000000004 665.50404900000012 668.21722799999861 670.54280999999901 672.48079500000006 675.58157100000005 677.51955600000008 679.06994400000008 681.39552599999899 681.78312300000005 684.49630200000001 686.43428699999936 687.98467500000004 689.92265999999859 692.63583900000003 694.57382400000006 696.89940600000011 699.22498800000005 701.938166999999 704.65134599999999 705.81413700000007 708.13971900000001 710.07770400000004 712.40328599999998 713.56607700000006 715.11646500000006 717.05445000000009 717.44204699999898 718.21724100000006 719.76762899999824 720.93041999999912 723.25600200000008 725.19398700000045 726.74437499999999 729.06995699999936 730.23274800000002 732.17073300000004 732.94592699999896 733.3335239999991 734.88391200000012 736.82189699999935 737.59709100000009 738.75988199999995 740.69786699999997 741.47306100000003 744.96143399999937 744.96143399999937 744.96143399999937 748.44980699999996 748.44980699999996 748.83740399999897 750.38779199999999 752.32577700000002 752.71337400000095 755.42655299999899 755.42655299999899 756.20174700000007 757.75213500000007 758.52732899999899 758.52732899999899 758.91492599999935 759.69012000000009 761.62810500000001 763.56608999999901 763.17849300000046 764.34128399999861 765.89167200000009 765.50407500000006 766.66686599999912 767.44205999999872 769.38004500000011 770.93043300000011 773.25601499999937 775.19400000000007 775.96919399999899 776.74438799999996 777.51958200000001 779.84516399999859 781.00795499999936 781.78314900000055 783.33353700000009 784.88392500000009 786.82190999999898 788.75989500000014 790.310282999999 794.18625299999997 793.79865600000005 794.96144699999911 796.12423799999999 CPI 1965 1965.083333333333 1965.166666666667 1965.25 1965.333333333333 1965.416666666667 1965.5 1965.583333333333 1965.666666666667 1965.75 1965.833333333333 1965.916666666667 1966 1966.0833333333301 1966.1666666666699 1966.25 1966.3333333333301 1966.4166666666699 1966.5 1966.5833333333301 1966.6666666666699 1966.75 1966.8333333333301 1966.9166666666599 1967 1967.0833333333301 1967.1666666666599 1967.25 1967.3333333333301 1967.4166666666599 1967.5 1967.5833333333301 1967.6666666666599 1967.75 1967.8333333333301 1967.9166666666599 1968 1968.0833333333301 1968.1666666666599 1968.25 1968.3333333333301 1968.4166666666599 1968.5 1968.5833333333301 1968.6666666666599 1968.75 1968.8333333333301 1968.9166666666599 1969 1969.0833333333301 1969.1666666666599 1969.25 1969.3333333333301 1969.4166666666599 1969.5 1969.5833333333301 1969.6666666666599 1969.75 1969.8333333333301 1969.9166666666599 1970 1970.0833333333301 1970.1666666666599 1970.25 1970.3333333333301 1970.4166666666599 1970.49999999999 1970.5833333333301 1970.6666666666599 1970.74999999999 1970.8333333333301 1970.9166666666599 1970.99999999999 1971.0833333333301 1971.1666666666599 1971.24999999999 1971.3333333333301 1971.4166666666599 1971.49999999999 1971.5833333333301 1971.6666666666599 1971.74999999999 1971.8333333333301 1971.9166666666599 1971.99999999999 1972.0833333333301 1972.1666666666599 1972.24999999999 1972.3333333333301 1972.4166666666599 1972.49999999999 1972.5833333333301 1972.6666666666599 1972.74999999999 1972.8333333333301 1972.9166666666599 1972.99999999999 1973.0833333333301 1973.1666666666599 1973.24999999999 1973.3333333333301 1973.4166666666599 1973.49999999999 1973.5833333333301 1973.6666666666599 1973.74999999999 1973.8333333333301 1973.9166666666599 1973.99999999999 1974.0833333333301 1974.1666666666599 1974.24999999999 1974.3333333333201 1974.4166666666599 1974.49999999999 1974.5833333333201 1974.6666666666599 1974.74999999999 1974.8333333333201 1974. 9166666666599 1974.99999999999 1975.0833333333201 1975.1666666666599 1975.24999999999 1975.3333333333201 1975.4166666666599 1975.49999999999 1975.5833333333201 1975.6666666666599 1975.74999999999 1975.8333333333201 1975.9166666666599 1975.99999999999 1976.0833333333201 1976.1666666666599 1976.24999999999 1976.3333333333201 1976.4166666666599 1976.49999999999 1976.5833333333201 1976.6666666666599 1976.74999999999 1976.8333333333201 1976.9166666666599 1976.99999999999 1977.0833333333201 1977.1666666666599 1977.24999999999 1977.3333333333201 1977.4166666666599 1977.49999999999 1977.5833333333201 1977.6666666666599 1977.74999999999 1977.8333333333201 1977.9166666666499 1977.99999999999 1978.0833333333201 1978.1666666666499 1978.24999999999 1978.3333333333201 1978.4166666666499 1978.49999999999 1978.5833333333201 1978.6666666666499 1978.74999999999 1978.8333333333201 1978.9166666666499 1978.99999999999 1979.0833333333201 1979.1666666666499 1979.24999999999 1979.3333333333201 1979.4166666666499 1979.49999999999 1979.5833333333201 1979.6666666666499 1979.74999999999 1979.8333333333201 1979.9166666666499 1979.99999999999 1980.0833333333201 1980.1666666666499 1980.24999999999 1980.3333333333201 1980.4166666666499 1980.49999999999 1980.5833333333201 1980.6666666666499 1980.74999999999 1980.8333333333201 1980.9166666666499 1980.99999999999 1981.0833333333201 1981.1666666666499 1981.24999999999 1981.3333333333201 1981.4166666666499 1981.49999999998 1981.5833333333201 1981.6666666666499 1981.74999999998 1981.8333333333201 1981.9166666666499 1981.99999999998 1982.0833333333201 1982.1666666666499 1982.24999999998 1982.3333333333201 1982.4166666666499 1982.49999999998 1982.5833333333201 1982.6666666666499 1982.74999999998 1982.8333333333201 1982.9166666666499 1982.99999999998 1983.0833333333201 1983.1666666666499 1983.24999999998 1983.3333333333201 1983.4166666666499 1983.49999999998 1983.5833333333201 1983.6666666666499 1983.74999999998 1983.8333333333201 1983.9166666666499 1983.99999999998 1984.0833333333201 1984.1666666666499 1984.24999999998 1984.3333333333201 1984.4166666666499 1984.49999999998 1984.5833333333201 1984.6666666666499 1984.74999999998 1984.8333333333201 1984.9166666666499 1984.99999999998 1985.0833333333201 1985.1666666666499 1985.24999999998 1985.3333333333101 1985.4166666666499 1985.49999999998 1985.5833333333101 1985.6666666666499 1985.74999999998 1985.8333333333101 1985.9166666666499 1985.99999999998 1986.0833333333101 1986.1666666666499 1986.24999999998 1986.3333333333101 1986.4166666666499 1986.49999999998 1986.5833333333101 1986.6666666666499 1986.74999999998 1986.8333333333101 1986.9166666666499 1986.99999999998 1987.0833333333101 1987.1666666666499 1987.24999999998 1987.3333333333101 1987.4166666666499 1987.49999999998 1987.5833333333101 1987.6666666666499 1987.74999999998 1987.8333333333101 1987.9166666666499 1987.99999999998 1988.0833333333101 1988.1666666666499 1988.24999999998 1988.3333333333101 1988.4166666666499 1988.49999999998 1988.5833333333101 1988.6666666666499 1988.74999999998 1988.8333333333101 1988.9166666666399 1988.99999999998 1989.0833333333101 1989.1666666666399 1989.24999999998 1989.3333333333101 1989.4166666666399 1989.49999999998 1989.5833333333101 1989.6666666666399 1989.74999999998 1989.8333333333101 1989.9166666666399 1989.99999999998 1990.0833333333101 1990.1666666666399 1990.24999999998 1990.3333333333101 1990.4166666666399 1990.49999999998 1990.5833333333101 1990.6666666666399 1990.74999999998 1990.8333333333101 1990.9166666666399 1990.99999999998 1991.0833333333101 1991.1666666666399 1991.24999999998 1991.3333333333101 1991.4166666666399 1991.49999999998 1991.5833333333101 1991.6666666666399 1991.74999999998 1991.8333333333101 1991.9166666666399 1991.99999999998 1992.0833333333101 1992.1666666666399 1992.24999999998 1992.3333333333101 1992.4166666666399 1992.49999999997 1992.5833333333101 1992.6666666666399 1992.74999999997 1992.8333333333101 1992.9166666666399 1992.99999999997 1993.0833333333101 1993.1666666666399 1993.24999999997 1993.3333333333101 1993.4166666666399 1993.49999999997 1993.5833333333101 1993.6666666666399 1993.74999999997 1993.8333333333101 1993.9166666666399 1993.99999999997 1994.0833333333101 1994.1666666666399 1994.24999999997 1994.3333333333101 1994.4166666666399 1994.49999999997 1994.5833333333101 1994.6666666666399 1994.74999999997 1994.8333333333101 1994.9166666666399 1994.99999999997 1995.0833333333101 1995.1666666666399 1995.24999999997 1995.3333333333101 1995.4166666666399 1995.49999999997 1995.5833333333101 1995.6666666666399 1995.74999999997 1995.8333333333101 1995.9166666666399 1995.99999999997 1996.0833333333101 1996.1666666666399 1996.24999999997 1996.3333333333001 1996.4166666666399 1996.49999999997 1996.5833333333001 1996.6666666666399 1996.74999999997 1996.8333333333001 1996.9166666666399 1996.99999999997 1997.0833333333001 1997.1666666666399 1997.24999999997 1997.3333333333001 1997.4166666666399 1997.49999999997 1997.5833333333001 1997.6666666666399 1997.74999999997 1997.8333333333001 1997.9166666666399 1997.99999999997 1998.0833333333001 1998.166666666 6399 1998.24999999997 1998.3333333333001 1998.4166666666399 1998.49999999997 1998.5833333333001 1998.6666666666399 1998.74999999997 1998.8333333333001 1998.9166666666399 1998.99999999997 1999.0833333333001 1999.1666666666399 1999.24999999997 1999.3333333333001 1999.4166666666399 1999.49999999997 1999.5833333333001 1999.6666666666399 1999.74999999997 1999.8333333333001 1999.9166666666299 1999.99999999997 2000.0833333333001 2000.1666666666299 2000.24999999997 2000.3333333333001 2000.4166666666299 2000.49999999997 2000.5833333333001 2000.6666666666299 2000.74999999997 2000.8333333333001 2000.9166666666299 2000.99999999997 2001.0833333333001 2001.1666666666299 2001.24999999997 2001.3333333333001 2001.4166666666299 2001.499 99999997 2001.5833333333001 2001.6666666666299 2001.74999999997 2001.8333333333001 2001.9166666666299 2001.99999999997 2002.0833333333001 2002.1666666666299 2002.24999999997 2002.3333333333001 2002.4166666666299 2002.49999999997 2002.5833333333001 2002.6666666666299 2002.74999999997 2002.8333333333001 2002.9166666666299 2002.99999999997 2003.0833333333001 2003.1666666666299 2003.24999999997 2003.3333333333001 2003.4166666666299 2003.49999999996 2003.5833333333001 2003.6666666666299 2003.74999999996 2003.8333333333001 2003.9166666666299 2003.99999999996 2004.0833333333001 2004.1666666666299 2004.24999999996 2004.3333333333001 2004.4166666666299 2004.49999999996 2004.5833333333001 2004.6666666666299 2004.74999999996 2004 .8333333333001 2004.9166666666299 2004.99999999996 2005.0833333333001 2005.1666666666299 2005.24999999996 2005.3333333333001 2005.4166666666299 2005.49999999996 2005.5833333333001 2005.6666666666299 2005.74999999996 2005.8333333333001 2005.9166666666299 2005.99999999996 2006.0833333333001 2006.1666666666299 2006.24999999996 2006.3333333333001 2006.4166666666299 2006.49999999996 2006.5833333333001 2006.6666666666299 2006.74999999996 2006.8333333333001 2006.9166666666299 2006.99999999996 2007.0833333333001 2007.1666666666299 2007.24999999996 2007.3333333332901 2007.4166666666299 2007.49999999996 2007.5833333332901 2007.6666666666299 2007.74999999996 2007.8333333332901 2007.9166666666299 2007.99999999996 2008.0833333332901 2008.1666666666299 2008.24999999996 2008.3333333332901 2008.4166666666299 2008.49999999996 2008.5833333332901 2008.6666666666299 2008.74999999996 2008.8333333332901 2008.9166666666299 2008.99999999996 2009.0833333332901 2009.1666666666299 2009.24999999996 2009.3333333332901 2009.4166666666299 2009.49999999996 2009.5833333332901 2009.6666666666299 2009.74999999996 2009.8333333332901 2009.9166666666299 2009.99999999996 2010.0833333332901 2010.1666666666299 2010.24999999996 2010.3333333332901 2010.4166666666299 2010.49999999996 2010.5833333332901 2010.6666666666299 2010.74999999996 2010.8333333332901 2010.9166666666199 2010.99999999996 2011.0833333332901 2011.1666666666199 2011.24999999996 2011.3333333332901 2011.4166666666199 2011.49999999996 2011.5833333332901 2011.6666666666199 2011.74999999996 2011.8333333332901 2011.9166666666199 2011.99999999996 2012.0833333332901 2012.1666666666199 2012.24999999996 2012.3333333332901 2012.4166666666199 2012.49999999996 2012.5833333332901 2012.6666666666199 2012.74999999996 2012.8333333332901 2012.9166666666199 2012.99999999996 2013.0833333332901 2013.1666666666199 2013.24999999996 2013.3333333332901 2013.4166666666099 2013.49999999994 2013.58333333327 2013.6666666665999 2013.74999999993 2013.83333333326 2013.9166666665899 2013.99999999992 2014.08333333325 2014.1666666665801 2014.24999999991 2014.33333333324 100 100 100.0959079283887 100.3196930946291 100.6393861892583 101.0549872122762 100.9590792838875 100.86317135549869 101.0869565217391 101.18286445012789 101.502557544757 101.8222506393862 101.9181585677749 102.5575447570332 102.8772378516624 103.1969309462915 103.42071611253191 103.5166240409207 103.74040920716109 104.3797953964194 104.6994884910486 105.0191815856778 105.1150895140665 105.2429667519182 105.1790281329923 105.4987212276215 105.4987212276215 105.8184143222506 105.8184143222506 106.45780051150891 106.77749360613809 107.0971867007673 107.4168797953964 107.7365728900256 108.3759590792839 108.695652173913 109.01534526854221 109.33503836317129 109.65473145780049 109.9744245524296 110.2941176470588 110.9335038363171 111.5728900255754 111.89258312020461 112.21227621483381 112.8516624040921 113.1713554987212 113.8107416879795 114.1304347826087 114.4501278772378 115.40920716112529 116.0485933503836 116.3682864450128 117.0076726342711 117.64705882352941 117.96675191815859 118.6061381074168 119.2455242966752 119.8849104859335 120.52429667519181 121.1636828644501 121.8030690537084 122.4424552429667 123.081841432225 123.40153452685421 124.0409207161125 124.3606138107417 124.6803069053708 125.3196930946292 125.9590792838875 126.59846547314579 127.2378516624041 127.5575447570332 127.5575447570332 127.8772378516624 128.19693094629159 128.83631713554999 129.47570332480811 129.7953964194374 130.11508951406651 130.4347826086956 130.7544757033248 131.07416879795389 131.39386189258309 131.7135549 8721209 132.35294117647061 132.35294117647061 132.6726342710997 132.99232736572901 133.31202046035801 133.63171355498719 133.95140664961639 134.59079283887471 134.91048593350379 135.54987212276211 135.86956521739131 136.5089514066496 137.46803069053709 138.7468030690537 139.70588235294119 140.34526854219951 141.304347826087 141.304347826087 143.86189258312021 144.5012787723785 145.7800511508951 146.7391304347826 148.0179028132992 149.61636828644501 151.2148337595907 152.81329923273651 153.77237851662409 155.37084398976981 156.64961636828639 157.60869565217399 159.52685421994869 161.7647058823529 163.04347826086951 164.64194373401531 165.92071611253201 167.19948849104861 168.15856777493599 168.79795396419431 169.43734015345271 169.757 0332480818 171.03580562659829 172.63427109974421 173.2736572890017 174.55242966751919 175.5115089514066 176.79028132992329 177.74936061381069 178.3887468030691 178.70843989769821 179.02813299232739 179.3478260869565 180.30690537084399 181.2659846547314 182.22506393861889 183.18414322250641 184.14322250639381 185.1023017902813 185.74168797953959 186.70076726342711 187.6598465473146 189.5780051150895 190.53708439897699 191.81585677749359 192.455242966752 193.4143222506394 194.37340153452681 195.3324808184143 195.97186700767261 196.9309462915601 198.20971867007671 199.1687979539642 200.44757033248081 201.40664961636821 202.68542199488499 204.28388746803071 206.20204603580561 207.80051150895139 209.3989769820972 210.6777493606138 212.5959079283887 214.51406649616359 215.79283887468031 217.07161125319689 218.98976982097179 221.227621483376 223.46547314578001 225.70332480818411 228.2608695652174 230.81841432225059 233.375959079284 235.6138107416879 237.85166240409211 240.40920716112529 242.96675191815851 245.84398976982101 249.36061381074171 252.55754475703321 256.07416879795397 258.63171355498662 261.18925831202051 263.74680306905373 264.06649616368281 265.98465473145779 268.22250639386198 270.78005115089508 273.65728900255749 276.21483375959059 278.77237851662392 281.3299232736573 283.24808184143222 284.84654731457789 286.76470588235298 289.32225063938631 292.51918158567759 294.75703324808097 297.63427109974418 298.59335038363167 299.87212276214831 300.83120204603563 301.7902813299234 302.74936061381072 302.74936061381072 303.7084398976973 306.58567774936068 310.10230179028127 311.70076726342711 312.34015345268438 312.34015345268438 313.61892583120198 313.29923273657221 312.34015345268438 312.97953964194357 313.29923273657221 313.61892583120198 315.8567774936061 317.13554987212262 317.77493606138103 319.05370843989772 320.0127877237851 320.97186700767179 322.25063938618922 323.20971867007671 324.1687979539642 326.40664961636821 328.00511508951388 328.9641943734016 330.24296675191812 330.88235294117561 331.52173913043458 332.80051150895139 333.75959079283899 334.71867007672631 335.99744245524221 336.63682864450129 337.27621483375958 337.91560102301798 339.83375959079262 341.43222506393857 342.07161125319692 342.71099744245521 343.6700767263427 344.30946291560099 344.94884910485939 345.58823529411762 346.86700767263432 348.46547314577998 350.06393861892582 351.34271099744251 350.7033248081832 348.78516624040861 347.50639386189192 348.46547314577998 349.74424552429667 350.06393861892582 350.38363171355502 351.6624040920716 352.30179028132989 352.94117647058732 354.21994884910481 356.13810741687888 357.41687979539631 358.695652173913 360.29411764705861 361.25319693094627 362.85166240409211 363.81074168797949 365.40920716112532 366.68797953964201 367.64705882352939 368.92583120204603 369.56521739130432 370.84398976982101 371.48337595907822 372.44245524296667 374.68030690537063 375.6393861892584 377.23785166240401 378.83631713554962 380.43478260869563 382.03324808184141 383.3120204603581 384.59079283887462 385.86956521739131 387.46803069053698 388.74680306905373 390.66496163682899 393.54219948849101 395.46035805626508 396.73913043478251 398.0179028132992 398.0179028132992 398.97698209718658 400.89514066496162 402.49360613810722 403.77237851662392 407.60869565217382 409.20716112531971 411.12531969309453 412.08439897698162 412.72378516624019 415.28132992327278 417.19948849104861 420.71611253196892 423.59335038363167 426.47058823529392 427.42966751918152 429.02813299232662 430.62659846547223 430.94629156010222 430.94629156010222 431.90537084398892 433.50383631713549 434.78260869565219 435.42199488491042 436.70076726342711 437.97953964194357 438.61892583120198 440.53708439897702 441.81585677749348 442.13554987212262 443.09462915601023 444.69309462915601 445.6521739130435 446.61125319693099 447.89002557544751 449.16879795396409 450.12787723785169 451.08695652173901 453.00511508951388 454.28388746803063 454.92327365728812 456.52173913043458 457.48081841432219 458.12020460358059 459.71867007672631 460.99744245524221 461.31713554987192 461.95652173913032 462.91560102301798 463.55498721227622 465.47314578005103 466.75191815856721 467.71099744245521 467.71099744245521 468.98976982097179 470.26854219948842 470.58823529411751 471.5473145780042 472.82608695652158 474.42455242966741 476.3427109974424 477.30179028132989 477.62148337595909 478.90025575447561 479.8593350383631 481.13810741687882 482.4168797953 9631 483.37595907928358 485.29411764705861 486.25319693094622 487.21227621483382 487.851662404092 488.81074168797949 489.45012787723721 490.72890025575441 491.36828644501259 492.0076726342711 494.56521739130432 495.52429667519169 497.12276214833759 499.04092071611251 500 500.95907928388732 501.91815856777362 502.55754475703321 504.15601023017888 505.75447570332472 507.35294117647049 508.63171355498662 509.59079283887462 510.54987212276228 510.86956521739131 511.18925831202051 511.18925831202051 512.14833759590783 512.78772378516624 514.06649616368281 515.34526854219939 516.304347826087 516.94373401534517 517.26342710997437 517.90281329923266 517.90281329923266 517.90281329923266 518.54219948848925 519.82097186700764 52 0.46035805626605 521.73913043478251 522.37851662404103 522.69820971867 523.97698209718703 524.61636828644498 525.57544757033304 526.53452685421826 526.53452685421826 526.85421994884837 530.37084398976981 530.6905370843989 530.6905370843989 532.92838874680308 534.20716112531829 536.44501278772236 537.40409207161144 538.36317135549837 539.64194373401529 541.24040920716197 543.47826086956513 546.67519181585669 546.35549872122738 547.31457800511498 550.51150895140643 552.10997442455255 552.10997442455255 554.98721227621479 555.94629156010228 556.90537084398966 558.18414322250646 561.38107416879802 562.65984654731506 562.97953964194369 563.93861892583118 566.81585677749342 568.09462915601011 567.13554987212274 567.13554987212274 569.37340153452703 567.77493606138103 567.45524296675183 567.13554987212274 568.09462915601011 569.05370843989795 570.65217391304338 573.209718670077 573.84910485933437 574.16879795396414 575.44757033248038 577.04603580562639 578.00511508951297 579.28388746803103 580.24296675191738 581.20204603580567 583.75959079283837 586.95652173913038 587.91560102301787 585.67774936061403 584.71867007672699 585.35805626598437 587.27621483375935 589.83375959079274 591.75191815856772 591.11253196930954 591.43222506393658 593.03069053708452 595.58823529411768 596.86700767263312 598.14578005115095 599.10485933503833 601.66240409207137 603.90025575447464 604.53964194373339 604.85933503836304 606.77749360613848 609.9744245524297 612.85166240409001 612.85166240409001 612.5319693094624 615.08951406649646 617.32736572889939 619.24552429667506 618.92583120204597 619.24552429667506 623.08184143222502 626.91815856777498 635.54987212276217 636.50895140664954 633.31202046035787 633.31202046035787 637.14833759590795 637.46803069053703 638.42710997442316 641.62404092071597 643.54219948848959 645.14066496163684 648.65728900255738 651.53452685421848 648.33759590792738 645.46035805626605 645.78005115089547 649.29667519181578 650.37404092071608 652.89641943734011 656.29156010230179 658.26086956521738 660.98145780051141 662.5127877237851 663.69245524296673 663.89705882352791 666.71035805626605 668.76598465473137 674.02173913043441 675.97506393861897 678.3056265984643 679.94565217391175 682.37851662404103 683.95780051150837 688.00511508951286 695.2141943734016 700.17902813299224 699.13682864450118 699.73465473145779 693.71803069053703 681.43542199488377 675.82480818414285 677.5351662404081 680.00319693094627 679.331841432224 680.01598465473137 681.01662404091928 686.66879795396414 686.46419437340137 688.7627877237851 690.09271099744251 692.16432225063954 694.48209718669989 694.84335038363167 695.22378516624099 694.53644501278768 694.70907928388795 694.9360613810727 694.68989769820973 694.64514066496156 695.89833759590783 696.96930946291536 697.82928388746689 700.20460358056255 701.86700767263426 704.72186700767259 706.78388746803103 709.1304347826084 712.77173913043475 716.29156010230179 719.04731457800506 719.27749360613802 721.07736572890019 722.98273657288996 724.66112531969304 724.93925831201921 726.13810741687973 726.00063938618916 727.83248081841305 729.34143222506339 731.24040920716197 732.68542199488479 731.72634271099753 731.5377237851651 731.39066496163673 735.14066496163673 738.7659846547316 740.57544757033304 739.09846547314567 738.80754475703316 739.51726342710936 743.60294117647061 741.92774936061369 740.75127877237844 742.08439897698202 744.4373401534524 745.6905370843989 746.26918158567764 747.2602301790281 747.38491048593221 748.18734015345262 749.98081841432213 751.06457800511498 751.81905370843936 753.32480818414285 755.28772378516612 757.93797953964201 AHE2012dollars 1965 1965.083333333333 1965.166666666667 1965.25 1965.333333333333 1965.416666666667 1965.5 1965.583333333333 1965.666666666667 1965.75 1965.833333333333 1965.916666666667 1966 1966.0833333333301 1966.1666666666699 1966.25 1966.3333333333301 1966.4166666666699 1966.5 1966.5833333333301 1966.6666666666699 1966.75 1966.8333333333301 1966.9166666666599 1967 1967.0833333333301 1967.1666666666599 1967.25 1967.3333333333301 1967.4166666666599 1967.5 1967.5833333333301 1967.6666666666599 1967.75 1967.8333333333301 1967.9166666666599 1968 1968.0833333333301 1968.1666666666599 1968.25 1968.3333333333301 1968.4166666666599 1968.5 1968.5833333333301 1968.6666666666599 1968.75 1968.8333333333301 1968.9166666666599 1969 1969.0833333333301 1969.1666666666599 1969.25 1969.3333333333301 1969.4166666666599 1969.5 1969.5833333333301 1969.6666666666599 1969.75 1969.8333333333301 1969.9166666666599 1970 1970.0833333333301 1970.1666666666599 1970.25 1970.3333333333301 1970.4166666666599 1970.49999999999 1970.5833333333301 1970.6666666666599 1970.74999999999 1970.8333333333301 1970.9166666666599 1970.99999999999 1971.0833333333301 1971.1666666666599 1971.24999999999 1971.3333333333301 1971.4166666666599 1971.49999999999 1971.5833333333301 1971.6666666666599 1971.74999999999 1971.8333333333301 1971.9166666666599 1971.99999999999 1972.0833333333301 1972.1666666666599 1972.24999999999 1972.3333333333301 1972.4166666666599 1972.49999999999 1972.5833333333301 1972.6666666666599 1972.74999999999 1972.8333333333301 1972.9166666666599 1972.99999999999 1973.0833333333301 1973.1666666666599 1973.24999999999 1973.3333333333301 1973.4166666666599 1973.49999999999 1973.5833333333301 1973.6666666666599 1973.74999999999 1973.8333333333301 1973.9166666666599 1973.99999999999 1974.0833333333301 1974.1666666666599 1974.24999999999 1974.3333333333201 1974.4166666666599 1974.49999999999 1974.5833333333201 1974.6666666666599 1974.74999999999 1974.8333333333201 1974.9166666666599 1974.99999999999 1975.0833333333201 1975.1666666666599 1975.24999999999 1975.3333333333201 1975.4166666666599 1975.49999999999 1975.5833333333201 1975.6666666666599 1975.74999999999 1975.8333333333201 1975.9166666666599 1975.99999999999 1976.0833333333201 1976.1666666666599 1976.24999999999 1976.3333333333201 1976.4166666666599 1976.49999999999 1976.5833333333201 1976.6666666666599 1976.74999999999 1976.8333333333201 1976.9166666666599 1976.99999999999 1977.0833333333201 1977.1666666666599 1977.24999999999 1977.3333333333201 1977.4166666666599 1977.49999999999 1977.5833333333201 1977.6666666666599 1977.74999999999 1977.8333333333201 1977.9166666666499 1977.99999999999 1978.0833333333201 1978.1666666666499 1978.24999999999 1978.3333333333201 1978.4166666666499 1978.49999999999 1978.5833333333201 1978.6666666666499 1978.74999999999 1978.8333333333201 1978.9166666666499 1978.99999999999 1979.0833333333201 1979.1666666666499 1979.24999999999 1979.3333333333201 1979.4166666666499 1979.49999999999 1979.5833333333201 1979.6666666666499 1979.74999999999 1979.8333333333201 1979.9166666666499 1979.99999999999 1980.0833333333201 1980.1666666666499 1980.24999999999 1980.3333333333201 1980.4166666666499 1980.49999999999 1980.5833333333201 1980.6666666666499 1980.74999999999 1980.8333333333201 1980.9166666666499 1980.99999999999 1981.0833333333201 1981.1666666666499 1981.24999999999 1981.3333333333201 1981.4166666666499 1981.49999999998 1981.5833333333201 1981.6666666666499 1981.74999999998 1981.8333333333201 1981.9166666666499 1981.99999999998 1982.0833333333201 1982.1666666666499 1982.24999999998 1982.3333333333201 1982.4166666666499 1982.49999999998 1982.5833333333201 1982.6666666666499 1982.74999999998 1982.8333333333201 1982.9166666666499 1982.99999999998 1983.0833333333201 1983.1666666666499 1983.24999999998 1983.3333333333201 1983.4166666666499 1983.49999999998 1983.5833333333201 1983.6666666666499 1983.74999999998 1983.8333333333201 1983.9166666666499 1983.99999999998 1984.0833333333201 1984.1666666666499 1984.24999999998 1984.3333333333201 1984.4166666666499 1984.49999999998 1984.5833333333201 1984.6666666666499 1984.74999999998 1984.8333333333201 1984.9166666666499 1984.99999999998 1985.0833333333201 1985.1666666666499 1985.24999999998 1985.3333333333101 1985.4166666666499 1985.49999999998 1985.5833333333101 1985.6666666666499 1985.74999999998 1985.8333333333101 1985.9166666666499 1985.99999999998 1986.0833333333101 1986.1666666666499 1986.24999999998 1986.3333333333101 1986.4166666666499 1986.49999999998 1986.5833333333101 1986.6666666666499 1986.74999999998 1986.8333333333101 1986.9166666666499 1986.99999999998 1987.0833333333101 1987.1666666666499 1987.24999999998 1987.3333333333101 1987.4166666666499 1987.49999999998 1987.5833333333101 1987.6666666666499 1987.74999999998 1987.8333333333101 1987.9166666666499 1987.99999999998 1988.0833333333101 1988.1666666666499 1988.24999999998 1988.3333333333101 1988.4166666666499 1988.49999999998 1988.5833333333101 1988.6666666666499 1988.74999999998 1988.8333333333101 1988.9166666666399 1988.99999999998 1989.0833333333101 1989.1666666666399 1989.24999999998 1989.3333333333101 1989.4166666666399 1989.49999999998 1989.5833333333101 1989.6666666666399 1989.74999999998 1989.8333333333101 1989.9166666666399 1989.99999999998 1990.0833333333101 1990.1666666666399 1990.24999999998 1990.3333333333101 1990.4166666666399 1990.49999999998 1990.5833333333101 1990.6666666666399 1990.74999999998 1990.8333333333101 1990.9166666666399 1990.99999999998 1991.0833333333101 1991.1666666666399 1991.249999999 98 1991.3333333333101 1991.4166666666399 1991.49999999998 1991.5833333333101 1991.6666666666399 1991.74999999998 1991.8333333333101 1991.9166666666399 1991.99999999998 1992.0833333333101 1992.1666666666399 1992.24999999998 1992.3333333333101 1992.4166666666399 1992.49999999997 1992.5833333333101 1992.6666666666399 1992.74999999997 1992.8333333333101 1992.9166666666399 1992.99999999997 1993.0833333333101 1993.1666666666399 1993.24999999997 1993.3333333333101 1993.4166666666399 1993.49999999997 1993.5833333333101 1993.6666666666399 1993.74999999997 1993.8333333333101 1993.9166666666399 1993.99999999997 1994.0833333333101 1994.1666666666399 1994.24999999997 1994.3333333333101 1994.4166666666399 1994.49999999997 1994.58333 33333101 1994.6666666666399 1994.74999999997 1994.8333333333101 1994.9166666666399 1994.99999999997 1995.0833333333101 1995.1666666666399 1995.24999999997 1995.3333333333101 1995.4166666666399 1995.49999999997 1995.5833333333101 1995.6666666666399 1995.74999999997 1995.8333333333101 1995.9166666666399 1995.99999999997 1996.0833333333101 1996.1666666666399 1996.24999999997 1996.3333333333001 1996.4166666666399 1996.49999999997 1996.5833333333001 1996.6666666666399 1996.74999999997 1996.8333333333001 1996.9166666666399 1996.99999999997 1997.0833333333001 1997.1666666666399 1997.24999999997 1997.3333333333001 1997.4166666666399 1997.49999999997 1997.5833333333001 1997.6666666666399 1997.74999999997 1997.8333333333001 1997 .9166666666399 1997.99999999997 1998.0833333333001 1998.1666666666399 1998.24999999997 1998.3333333333001 1998.4166666666399 1998.49999999997 1998.5833333333001 1998.6666666666399 1998.74999999997 1998.8333333333001 1998.9166666666399 1998.99999999997 1999.0833333333001 1999.1666666666399 1999.24999999997 1999.3333333333001 1999.4166666666399 1999.49999999997 1999.5833333333001 1999.6666666666399 1999.74999999997 1999.8333333333001 1999.9166666666299 1999.99999999997 2000.0833333333001 2000.1666666666299 2000.24999999997 2000.3333333333001 2000.4166666666299 2000.49999999997 2000.5833333333001 2000.6666666666299 2000.74999999997 2000.8333333333001 2000.9166666666299 2000.99999999997 2001.0833333333001 2001.1666666666299 2001.24999999997 2001.3333333333001 2001.4166666666299 2001.49999999997 2001.5833333333001 2001.6666666666299 2001.74999999997 2001.8333333333001 2001.9166666666299 2001.99999999997 2002.0833333333001 2002.1666666666299 2002.24999999997 2002.3333333333001 2002.4166666666299 2002.49999999997 2002.5833333333001 2002.6666666666299 2002.74999999997 2002.8333333333001 2002.9166666666299 2002.99999999997 2003.0833333333001 2003.1666666666299 2003.24999999997 2003.3333333333001 2003.4166666666299 2003.49999999996 2003.5833333333001 2003.6666666666299 2003.74999999996 2003.8333333333001 2003.9166666666299 2003.99999999996 2004.0833333333001 2004.1666666666299 2004.24999999996 2004.3333333333001 2004.4166666666299 2004.49999999996 2004.5833333333001 2004.6666666666299 2004.74999999996 2004.8333333333001 2004.9166666666299 2004.99999999996 2005.0833333333001 2005.1666666666299 2005.24999999996 2005.3333333333001 2005.4166666666299 2005.49999999996 2005.5833333333001 2005.6666666666299 2005.74999999996 2005.8333333333001 2005.9166666666299 2005.99999999996 2006.0833333333001 2006.1666666666299 2006.24999999996 2006.3333333333001 2006.4166666666299 2006.49999999996 2006.5833333333001 2006.6666666666299 2006.74999999996 2006.8333333333001 2006.9166666666299 2006.99999999996 2007.0833333333001 2007.1666666666299 2007.24999999996 2007.3333333332901 2007.4166666666299 2007.49999999996 2007.5833333332901 2007.6666666666299 2007.74999999996 2007.8333333332901 2007.9166666666299 2007.99999999996 2008.0833333332901 2008.1666666666299 2008.24999999996 2008.3333333332901 2008.4166666666299 2008.49999999996 2008.5833333332901 2008.6666666666299 2008.74999999996 2008.8333333332901 2008.9166666666299 2008.99999999996 2009.0833333332901 2009.1666666666299 2009.24999999996 2009.3333333332901 2009.4166666666299 2009.49999999996 2009.5833333332901 2009.6666666666299 2009.74999999996 2009.8333333332901 2009.9166666666299 2009.99999999996 2010.0833333332901 2010.1666666666299 2010.24999999996 2010.3333333332901 2010.4166666666299 2010.49999999996 2010.5833333332901 2010.6666666666299 2010.74999999996 2010.8333333332901 2010.9166666666199 2010.99999999996 2011.0833333332901 2011.1666666666199 2011.24999999996 2011.3333333332901 2011.4166666666199 2011.49999999996 2011.5833333332901 2011.6666666666199 2011.74999999996 2011.8333333332901 2011.9166666666199 2011.99999999996 2012.0833333332901 2012.1666666666199 2012.24999999996 2012.3333333332901 2012.4166666666199 2012.49999999996 2012.5833333332901 2012.6666666666199 2012.74999999996 2012.8333333332901 2012.9166666666199 2012.99999999996 2013.0833333332901 2013.1666666666199 2013.24999999996 2013.3333333332901 2013.4166666666099 2013.49999999994 2013.58333333327 2013.6666666665999 2013.74999999993 2013.83333333326 2013.9166666665899 2013.99999999992 2014.08333333325 2014.1666666665801 2014.24999999991 2014.33333333324 18.878539641943679 18.95171227621482 19.006656020440751 18.9642574888464 19.04943074968233 18.97108763049668 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17.593106447534769 17.609789792060489 17.623060967944699 17.661688833124209 17.657175203506579 17.71774142678348 17.735289305816131 17.792546091306981 17.816376279650441 17.836970074812971 17.892238059701491 17.904635483870969 17.956410402476781 18.00497513914657 18.050431644004941 18.084661728395069 18.155304938271598 18. 21181950617283 18.24580838471023 18.25722927429274 18.276977886977878 18.246206127450989 18.335933659730721 18.36671608562688 18.36378645515558 18.383248750761719 18.405392214111838 18.45524905889496 18.483043108682448 18.527382038834951 18.473518746232671 18.517542891566219 18.58648385542168 18.5633574085183 18.560013165769 18.57806960667461 18.572146103509809 18.566243705463179 18.590045260663501 18.60273975191966 18.579995294117651 18.538265497076029 18.62947009947337 18.636933177570089 18.595163530778159 18.59434001158078 18.647353097857561 18.62978640552992 18.663456699252439 18.71015017221584 18.73283138602519 18.639186788154898 18.687858409090911 18.755230664395221 18.76225986394557 18.71865764241398 18.7409240292628 18.785518827508451 18.837127395715889 18.827347557551921 18.906127702702701 18.994148281690141 19.04356166854566 19.02429195272931 19.01794584269663 19.01596481792717 18.943884885666481 18.986533481894149 19.052426503340719 19.06095088888889 19.05887268698061 19.090546017699111 19.11156136865343 19.117804077134998 19.16179581958195 19.090379627601308 19.073666666666671 19.04255138662316 19.102818558951959 19.196722580645119 19.213255488803931 19.20033990201415 19.1418976693767 19.079849378714201 19.11286619794484 19.15202335135135 19.100400646900269 19.055238003220609 19.063450455275841 19.047161304115448 19.053310565635002 19.033127523910739 18.99894716781365 19.015164674775249 19.05350422832981 19.041508746048471 18.989694549266179 18.924420448617632 18.960239540949321 19.017918997912322 18.96263492723492 18.94130668047643 18.92990025813112 18.975145661157029 19.01261517811048 18.989503745510511 18.884972565017851 18.66302635814889 18.738368658965339 18.856067036850082 18.913836850075711 18.880346011038629 18.928270611835501 18.968603905858789 18.988134529147889 18.942908296075501 18.98671040634288 18.951459832429769 18.912691658488711 19.051094280078889 19.215372956909359 19.251183960396041 19.22580521910389 19.238960464418959 19.243085013661329 19.221582167491519 19.230773564379511 19.206971536359461 19.250934306146679 19.27184250709286 19.309989935810702 19.29435916124423 19.245994359194992 19.171914586831338 19.170638416609521 19.147921045933991 19.1555 4406240155 19.162311570031079 19.17155715100354 19.12258986654771 18.987447795716971 18.92596540891989 19.027441218162689 19.04255650433802 19.27100016129404 19.672042523445601 19.900320343617249 19.882483803843659 19.853364048799978 19.92684063154427 19.91755327701226 19.909777018336129 19.788518459891051 19.826394567961021 19.8239710366915 19.83878347640379 19.82169332452693 19.818757837170971 19.840046377451721 19.881814904398851 19.92256164528586 19.92814376107312 19.96375239216832 20.02349223880459 20.045850012656199 20.04129531369874 20.062993046254331 20.05923978724671 20.08524399152595 20.037671172976719 19.956497684145571 19.991451316706019 19.925298625888122 19.833773093225091 19.777172849644732 19.75225833414844 19.756110404906881 19.77783119710223 19.725708095105421 19.700216345941719 19.73303257614845 19.720607389405458 19.724341481243361 19.684751873358341 19.664091032620611 19.663058076701109 19.674212859536439 19.690000000000001 19.725084584289281 19.769069014201481 19.65827216114668 19.591517963009441 19.563410633191079 19.652006574678829 19.699361572313158 19.739823881100289 19.680566124531911 19.744727695788001 19.79584285325863 19.78000137857352 19.776458301125121 19.77266047022102 19.776939335912221 19.789878798509481 19.82573936402288 19.85337623326625 19.854682557951179 19.865003043420881 19.942395298700081 19.89282091325752 19.87018564765042 19.829668765790881

The costs of expected inflation: 1. Shoeleather cost

def: the costs and inconveniences of reducing money balances to avoid the inflation tax.

If π increases, i increases (why?), so people reduce their real money balances.

Remember: In long run, inflation does not affect real income or real spending.

So, same monthly spending but lower average money holdings means more frequent trips to the bank to withdraw smaller amounts of cash.

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CHAPTER 5 Inflation

In the second bullet, the answer to the parenthetical “why?” is the Fisher effect.

Thanks to ATMs and internet banking, the shoeleather cost is likely to be very small.

The costs of expected inflation: 2. Menu costs

def: The costs of changing prices.

Examples:

cost of printing new menus

cost of printing & mailing new catalogs

The higher is inflation, the more frequently firms must change their prices and incur these costs.

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CHAPTER 5 Inflation

The costs of expected inflation: 3. Relative price distortions

Firms facing menu costs change prices infrequently.

Example: A firm issues new catalog each January. As the general price level rises throughout the year, the firm’s relative price will fall.

Different firms change their prices at different times, leading to relative price distortions…

…causing microeconomic inefficiencies in the allocation of resources.

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CHAPTER 5 Inflation

The costs of expected inflation: 4. Unfair tax treatment

Some taxes are not adjusted to account for inflation, such as the capital gains tax.

Example:

Jan 1: you buy $10,000 worth of IBM stock

Dec 31: you sell the stock for $11,000, so your nominal capital gain is $1,000 (10%).

Suppose π = 10% during the year. Your real capital gain is $0.

Yet, you must pay taxes on your $1,000 nominal gain!

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CHAPTER 5 Inflation

In the 1970s, the income tax was not adjusted for inflation. There were a lot of people who received nominal salary increases large enough to push them into a higher tax bracket, but not large enough to prevent their real salaries from falling in the face of high inflation. This led to political pressure to index the income tax brackets.

If inflation had been higher during 1995-2000, when lots of people were earning high capital gains, then there might have been more political pressure to index the capital gains tax.

The costs of expected inflation: 5. General inconvenience

Inflation makes it harder to compare nominal values from different time periods.

This complicates long-range financial planning.

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CHAPTER 5 Inflation

Examples:

Parents trying to decide how much to save for the future college expenses of their (now) young child.

Thirty-somethings trying to decide how much to save for retirement.

The CEO of a big corporation trying to decide whether to build a new factory, which will yield a revenue stream for 20 years or more.

Additional cost of unexpected inflation: Arbitrary redistribution of purchasing power

Many long-term contracts not indexed, but based on Eπ.

If π turns out different from Eπ , then some gain at others’ expense.

Example: borrowers & lenders

If π > Eπ , then (i − π) < (i − Eπ ) and purchasing power is transferred from lenders to borrowers.

If π < E π, then purchasing power is transferred from borrowers to lenders.

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CHAPTER 5 Inflation

The text gives a simple numerical example on p.119.

(In the short run, when many nominal wages are fixed by contracts, there are transfers of purchasing power between firms and their employees whenever inflation is different than expected when the contract was written and signed.)

Additional cost of high inflation: Increased uncertainty

When inflation is high, it’s more variable and unpredictable: π turns out different from Eπ more often, and the differences tend to be larger, though not systematically positive or negative.

So, arbitrary redistributions of wealth more likely.

This increases uncertainty, making risk-averse people worse off.

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CHAPTER 5 Inflation

One benefit of inflation

Nominal wages are rarely reduced, even when the equilibrium real wage falls. This hinders labor market clearing.

Inflation allows the real wages to reach equilibrium levels without nominal wage cuts.

Therefore, moderate inflation improves the functioning of labor markets.

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CHAPTER 5 Inflation

Students will better appreciate this point when they learn about the natural rate of unemployment in Chapter 7. In that chapter, we will see how the failure of wages to adjust contributes to a long-term unemployment problem.

Hyperinflation

Common definition: π ≥ 50% per month

All the costs of moderate inflation described above become HUGE under hyperinflation.

Money ceases to function as a store of value, and may not serve its other functions (unit of account, medium of exchange).

People may conduct transactions with barter or a stable foreign currency.

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CHAPTER 5 Inflation

Page 123 has an excellent example of life during a hyperinflation.

See also the two excellent case studies: “Hyperinflation in Interwar Germany” (pp.123-125) and “Hyperinflation in Zimbabwe” (pp.125-126).

What causes hyperinflation?

Hyperinflation is caused by excessive money supply growth:

When the central bank prints money, the price level rises.

If it prints money rapidly enough, the result is hyperinflation.

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CHAPTER 5 Inflation

A few examples of hyperinflation

country	period	CPI Inflation % per year	M2 Growth % per year
Israel	1983-85	338%	305%
Brazil	1987-94	1,256	1,451
Bolivia	1983-86	1,818	1,727
Ukraine	1992-94	2,089	1,029
Argentina	1988-90	2,671	1,583
Dem. Republic of Congo / Zaire	1990-96	3,039	2,373
Angola	1995-96	4,145	4,106
Peru	1988-90	5,050	3,517
Zimbabwe	2005-07	5,316	9,914

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CHAPTER 5 Inflation

source: World Development Indicators, World Bank.

Notes:

The inflation and money growth figures are computed as annual averages from the end of the first year to the end of the last year shown in each period.

During 2008, Zimbabwe’s hyperinflation continued and became spectacular. The table on this slide excludes 2008 data because it is missing from the WDI database. It’s easy to find estimates of Zimbabwe’s 2008 inflation, for example here: http://www.cato.org/zimbabwe. However, I cannot verify their reliability or find good data on Zimbabwe’s money supply in 2008.

Why governments create hyperinflation

When a government cannot raise taxes or sell bonds, it must finance spending increases by printing money.

In theory, the solution to hyperinflation is simple: stop printing money.

In the real world, this requires drastic and painful fiscal restraint.

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CHAPTER 5 Inflation

The Classical Dichotomy

Real variables: Measured in physical units – quantities and relative prices, for example:

quantity of output produced

real wage: output earned per hour of work

real interest rate: output earned in the future by lending one unit of output today

Nominal variables: Measured in money units, e.g.,

nominal wage: Dollars per hour of work.

nominal interest rate: Dollars earned in future by lending one dollar today.

the price level: The amount of dollars needed to buy a representative basket of goods.

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CHAPTER 5 Inflation

The Classical Dichotomy

Recall: Real variables were explained in Chap. 3, nominal ones in Chap. 5.

Classical dichotomy: the theoretical separation of real and nominal variables in the classical model, which implies nominal variables do not affect real variables.

Neutrality of money: Changes in the money supply do not affect real variables.

In the real world, money is approximately neutral in the long run.

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CHAPTER 5 Inflation

CHAPTER SUMMARY

Velocity: the ratio of nominal expenditure to money supply, the rate at which money changes hands

Quantity theory of money

assumes velocity is constant

concludes that the money growth rate determines the inflation rate

applies in the long run

consistent with cross-country and time-series data

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CHAPTER 5 Inflation

CHAPTER SUMMARY

Nominal interest rate

equals real interest rate + inflation rate

the opp. cost of holding money

Fisher effect: Nominal interest rate moves one-for-one with expected inflation.

Money demand

depends only on income in the quantity theory

also depends on the nominal interest rate

if so, then changes in expected inflation affect the current price level.

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CHAPTER 5 Inflation

CHAPTER SUMMARY

Costs of inflation

Expected inflation shoeleather costs, menu costs, tax & relative price distortions, inconvenience of correcting figures for inflation

Unexpected inflation all of the above plus arbitrary redistributions of wealth between debtors and creditors

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CHAPTER 5 Inflation

CHAPTER SUMMARY

Hyperinflation

caused by rapid money supply growth when money printed to finance govt budget deficits

stopping it requires fiscal reforms to eliminate govt’s need for printing money

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CHAPTER 5 Inflation

CHAPTER SUMMARY

Classical dichotomy

In classical theory, money is neutral—does not affect real variables.

So, we can study how real variables are determined w/o reference to nominal ones.

Then, money market eq’m determines price level and all nominal variables.

Most economists believe the economy works this way in the long run.

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CHAPTER 5 Inflation

´=´

MVPY

´=´

MVPY

gM +gV =gP +gY

The quantity theory of money assumes V is constant, so g

V = 0.

gM = gP +gY

π = gp

π = gM − gY

()(,)

MPLiY

(,)

LrY

(,)

YFKL

(,)

LiY

(,)

LrY

(the Fisher effect)

(

)

Þ¯

(

)

to make fall

to re-establish eq'm

PMP