N. Gregory Mankiw
Macroeconomics
Brief Principles of
Sixth Edition
12
Money Growth and Inflation
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Slides by
Ron Cronovich
2012 UPDATE
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For most students, the hardest concepts to grasp in this chapter are the most theoretical ones: the classical dichotomy and monetary neutrality. Most of the other material in the chapter is fairly straightforward.
In the last section of the chapter, “The Costs of Inflation,” the Shoeleather cost is not difficult for students to understand, but it’s difficult for them to relate to, due to the ready availability of ATMs and Internet access to bank accounts. Most students have a harder time learning about the arbitrary redistributions of wealth that arise when inflation is different from expected.
This chapter is longer than average. To get through it more quickly, you might consider skipping or moving fairly quickly through some of the easier concepts, telling students to learn them from the textbook. Such concepts might include:
some of the costs of inflation (menu costs, confusion and inconvenience)
the inflation tax
hyperinflation
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In this chapter,
look for the answers to these questions:
How does the money supply affect inflation and nominal interest rates?
Does the money supply affect real variables like real GDP or the real interest rate?
How is inflation like a tax?
What are the costs of inflation? How serious are they?
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Introduction
This chapter introduces the quantity theory of money to explain one of the Ten Principles of Economics from Chapter 1:
Prices rise when the govt prints
too much money.
Most economists believe the quantity theory
is a good explanation of the long run behavior
of inflation.
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The Value of Money
P = the price level
(e.g., the CPI or GDP deflator)
P is the price of a basket of goods, measured in money.
1/P is the value of $1, measured in goods.
Example: basket contains one candy bar.
If P = $2, value of $1 is 1/2 candy bar
If P = $3, value of $1 is 1/3 candy bar
Inflation drives up prices and drives down the value of money.
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The Quantity Theory of Money
Developed by 18th century philosopher
David Hume and the classical economists
Advocated more recently by Nobel Prize Laureate Milton Friedman
Asserts that the quantity of money determines the value of money
We study this theory using two approaches:
A supply-demand diagram
An equation
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Money Supply (MS)
In real world, determined by Federal Reserve,
the banking system, consumers.
In this model, we assume the Fed precisely controls MS and sets it at some fixed amount.
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Money Demand (MD)
Refers to how much wealth people want to hold in liquid form.
Depends on P:
An increase in P reduces the value of money,
so more money is required to buy g&s.
Thus, quantity of money demanded
is negatively related to the value of money
and positively related to P, other things equal.
(These “other things” include real income, interest rates, availability of ATMs.)
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6
6
Some students may think that money demand is negatively related to P, reasoning that an increase in P reduces the demand for goods and services, so less money is required to buy goods and services. However, the relationship between P and money demand holds real income constant. Thus, “other things equal” means that an increase in P does NOT reduce real income, and therefore does not reduce the demand for goods and services.
Here’s a handy way to explain it:
Real income determines the quantity of g&s people demand.
P determines how many dollars will be needed to buy this quantity of g&s.
The Money Supply-Demand Diagram
Value of Money, 1/P
Price
Level, P
Quantity of Money
1
1
¾
1.33
½
2
¼
4
As the value of money rises, the price level falls.
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The Money Supply-Demand Diagram
Value of Money, 1/P
Price
Level, P
Quantity of Money
1
¾
½
¼
1
1.33
2
4
MS1
$1000
The Fed sets MS
at some fixed value, regardless of P.
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The Money Supply-Demand Diagram
Value of Money, 1/P
Price
Level, P
Quantity of Money
1
¾
½
¼
1
1.33
2
4
MD1
A fall in value of money (or increase in P) increases the quantity of money demanded:
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MS1
$1000
Value of Money, 1/P
Price
Level, P
Quantity of Money
1
¾
½
¼
1
1.33
2
4
The Money Supply-Demand Diagram
MD1
P adjusts to equate quantity of money demanded with money supply.
eq’m
price
level
eq’m
value
of money
A
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MS1
$1000
The Effects of a Monetary Injection
Value of Money, 1/P
Price
Level, P
Quantity of Money
1
¾
½
¼
1
1.33
2
4
MD1
eq’m
price
level
eq’m
value
of money
A
MS2
$2000
B
Then the value of money falls,
and P rises.
Suppose the Fed increases the money supply.
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A Brief Look at the Adjustment Process
How does this work? Short version:
At the initial P, an increase in MS causes
excess supply of money.
People get rid of their excess money by spending it on g&s or by loaning it to others, who spend it. Result: increased demand for goods.
But supply of goods does not increase,
so prices must rise.
(Other things happen in the short run, which we will study in later chapters.)
Result from graph: Increasing MS causes P to rise.
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Real vs. Nominal Variables
Nominal variables are measured in monetary units.
Examples: nominal GDP,
nominal interest rate (rate of return measured in $)
nominal wage ($ per hour worked)
Real variables are measured in physical units.
Examples: real GDP,
real interest rate (measured in output)
real wage (measured in output)
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13
Students seem to readily understand that the real wage is the purchasing power of the wage, or that the real wage is corrected for inflation. From either of these interpretations of the real wage, it is just a small step to understand that the real wage is measured in units of output.
What does “the purchasing power of the wage” mean? If students think about it, they will grasp that it means the quantity of output workers can buy with their wage. Hence, the real wage is measured in units of output.
What does “corrected for inflation” mean? A simple example helps. Suppose the nominal wage rises 20% and the price level also rises 20%. Students will immediately understand that the wage—corrected for inflation—is unchanged. Which is to say, it can buy the same quantity of output as before.
The next slide discusses relative prices, demonstrating that they, too, are measured in physical units, which makes them real variables. The following slide returns to the real wage, showing that it is a relative price, and demonstrating that it is measured in units of output.
How is it that the real interest rate is measured in output? Suppose we measure the value of a deposit in terms of how much output the deposit can buy (i.e., the purchasing power of the deposit). Then, think of the real interest rate as the rate at which the purchasing power of the deposit grows. Thinking in these terms, students should begin to grasp that the real interest rate is the amount of output earned on the deposit (as a % of the deposit).
Real vs. Nominal Variables
Prices are normally measured in terms of money.
Price of a compact disc: $15/cd
Price of a pepperoni pizza: $10/pizza
A relative price is the price of one good relative to (divided by) another:
Relative price of CDs in terms of pizza:
price of cd
price of pizza
$15/cd
$10/pizza
=
Relative prices are measured in physical units,
so they are real variables.
= 1.5 pizzas per cd
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Real vs. Nominal Wage
An important relative price is the real wage:
W = nominal wage = price of labor, e.g., $15/hour
P = price level = price of g&s, e.g., $5/unit of output
Real wage is the price of labor relative to the price
of output:
W
P
= 3 units output per hour
$15/hour
$5/unit of output
=
0
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The Classical Dichotomy
Classical dichotomy: the theoretical separation of nominal and real variables
Hume and the classical economists suggested that monetary developments affect nominal variables but not real variables.
If central bank doubles the money supply,
Hume & classical thinkers contend
all nominal variables—including prices—
will double.
all real variables—including relative prices—
will remain unchanged.
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The Neutrality of Money
Monetary neutrality: the proposition that changes
in the money supply do not affect real variables
Doubling money supply causes all nominal prices
to double; what happens to relative prices?
Initially, relative price of cd in terms of pizza is
price of cd
price of pizza
= 1.5 pizzas per cd
$15/cd
$10/pizza
=
After nominal prices double,
price of cd
price of pizza
= 1.5 pizzas per cd
$30/cd
$20/pizza
=
The relative price is unchanged.
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17
This result is important because relative prices, not nominal prices, determine the economy’s allocation of resources.
The Neutrality of Money
Similarly, the real wage W/P remains unchanged, so
quantity of labor supplied does not change
quantity of labor demanded does not change
total employment of labor does not change
The same applies to employment of capital and
other resources.
Since employment of all resources is unchanged,
total output is also unchanged by the money supply.
Monetary neutrality: the proposition that changes
in the money supply do not affect real variables
0
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18
The material on this slide does not appear explicitly in this chapter, but it helps explain how money can be neutral.
The Neutrality of Money
Most economists believe the classical dichotomy and neutrality of money describe the economy in the long run.
In later chapters, we will see that monetary changes can have important short-run effects
on real variables.
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The Velocity of Money
Velocity of money: the rate at which money changes hands
Notation:
P x Y = nominal GDP
= (price level) x (real GDP)
M = money supply
V = velocity
Velocity formula:
V =
P x Y
M
0
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20
20
The textbook’s definition of velocity appears on this slide. You may prefer a more precise definition: The number of transactions in which the average dollar is used.
The following slide provides a simple example to clarify the meaning of velocity.
The Velocity of Money
Example with one good: pizza.
In 2012,
Y = real GDP = 3000 pizzas
P = price level = price of pizza = $10
P x Y = nominal GDP = value of pizzas = $30,000
M = money supply = $10,000
V = velocity = $30,000/$10,000 = 3
The average dollar was used in 3 transactions.
Velocity formula:
V =
P x Y
M
0
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21
If $10,000 worth of money purchases $30,000 worth of pizza, it must be true that the average dollar is used three times.
ACTIVE LEARNING 1
Exercise
One good: corn.
The economy has enough labor, capital, and land to produce Y = 800 bushels of corn.
V is constant.
In 2008, MS = $2000, P = $5/bushel.
Compute nominal GDP and velocity in 2008.
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ACTIVE LEARNING 1
Answers
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Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2005.
Compute nominal GDP and velocity in 2008.
Nominal GDP = P x Y = $5 x 800 = $4000
V =
P x Y
M
=
$4000
$2000
= 2
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U.S. Nominal GDP, M2, and Velocity
1960–2012
Nominal GDP
M2
Velocity
Velocity is fairly stable over the long run.
0
1960=100
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24
24
Note: Each variable has been scaled to equal 100 to make variables comparable.
This graph replicates Figure 3 in the textbook. Its purpose is to demonstrate that velocity is fairly stable over time. This observation justifies the assumption of constant velocity in the quantity theory of money.
Original sources:
M2 is from Board of Governors, Federal Reserve Board
GDP is from U.S. Department of Commerce, Bureau of Economic Analysis.
I obtained all data from FRED database, Federal Reserve Bank of St. Louis, at:
http://research.stlouisfed.org/fred2/
M2 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 99.999999999999986 100.8034817542685 102.61131570137262 104.08436558419818 105.89219953130231 107.83394710411785 109.67525945764982 111.5835286240375 113.89353866755941 116.30398393036491 118.11181787746904 120.48878473384666 123.16705724807498 125.84532976230331 128.42316705724807 130.90056913290928 133.07666555071978 135.35319718781386 138.43321057917643 141.24539671911614 144.09106126548375 146.46802812186141 149.34717107465684 152.59457649815869 155.54067626380984 157.41546702376965 158.35286240374958 159.9263475058587 162.53766320723133 166.42115835286239 170.94074322062269 174.55641111483092 177.53598928690991 180.48208905256109 183.96384332105791 188.24907934382321 191.4630063608972 193.1369266822899 194.37562772012052 196.04954804151322 196.75259457649815 198.09173083361233 202.57783729494477 208.00133913625709 214.69702042182789 222.96618680950786 229.6283896886508 235.8218948778038 242.919317 04050887 249.01238701037829 257.38198861734179 265.95246066287245 272.24640107130904 276.73250753264142 280.61600267827254 284.23167057248077 289.48778038165386 292.96953465015065 296.11650485436894 300.63608972212921 306.36089722129225 317.60964178105121 329.15969199866089 337.12755272849012 347.84064278540342 358.28590559089389 367.79377301640437 381.11817877469036 394.0743220622698 404.68697689989955 413.99397388684292 422.56444593237364 430.46534984934715 438.5001673920321 446.66889856042854 455.00502176096415 461.70070304653495 472.6481419484432 483.82992969534649 491.02778707733512 499.63173752929362 507.06394375627713 522.36357549380648 533.478406427854 542.58453297623032 557.28155339805824 567.1576832942751 581.78774690324735 594.94476062939395 607.66655507197856 618.01138265818543 631.93839973217268 666.68898560428522 683.79645128891866 694.60997656511552 707.19785738198857 722.46401071309003 738.03146970204216 747.7736859725477 764.34549715433536 787.31168396384328 801.23870103783065 818.2792099096082 830.33143622363571 842.65148978908599 864.98158687646458 886.64211583528629 906.32741881486436 920.62269835955806 928.59055908938728 934.3823234014061 945.06193505189151 961.63374623367929 980.24774020756604 989.2869099430867 997.95781720790092 1003.448275862069 1010.3783059926348 1029.7623033143623 1049.8158687646469 1064.8476732507531 1073.6859725477066 1085.3364579846 1093.337797120857 1106.5617676598595 1119.0826916638766 1123.3009708737864 1126.7827251422832 1136.3910277 870773 1137.1275527284899 1138.3327753598928 1146.2671576832943 1142.885838634081 1147.9075995982591 1153.2976230331435 1160.1606963508536 1163.4415801807834 1166.4881151657182 1167.1576832942751 1166.8563776364244 1168.2959491128222 1179.2433880147305 1200 1211.717442249749 1226.7157683294274 1241.4462671576832 1253.1302310010042 1267.5594241714093 1283.5286240374958 1298.12520924004 1318.5135587546033 1338.9353866755941 1363.3411449614998 1389.0190826916639 1412.3200535654503 1448.3093404753934 1473.7529293605626 1495.3465015065283 1517.3083361232004 1537.3619015734853 1561.2989621694007 1587.6799464345495 1606.1935051891528 1629.7288249079343 1672.246401071309 1714.8309340475391 1753.3311014395713 1792.3669233344492 1823.7027117509206 1838.3997321727486 1872.715098761299 1911.3157013726147 1941.9819216605288 1981.3525276196854 2022.0287914295279 2019.7522597924337 2035.4871108135253 2079.4442584532976 2102.8456645463675 2130.6327418814863 2143.388014730499 2158.8215600937392 2188.9856042852361 2218.1452962838971 2247.7067291596918 2272.3803146970204 2303.7161031134915 2341.9484432541008 2376.5985939069296 2418.2457315031807 2454.0341479745562 2480.7833947104118 2530.231001004352 2574.9246735855372 2602.6113157013724 2687.6799464345499 2777.0672915969199 2809.0391697355208 2811.7509206561767 2829.3270840308005 2836.4579845999328 2863.7428858386338 2882.3903582189491 2922.2296618680953 2971.2085704720453 3022.2296618680948 3147.5058587211247 3204.6869768998995 3274.522932708403 3314.7304988282558 GDP 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 2012.25 100.00000000000001 99.848197343453521 100.37950664136623 99.373814041745746 100.18975332068312 102.27703984819735 104.26944971537003 106.7552182163188 109.31688804554081 110.66413662239091 111.95445920303607 112.58064516129032 114.32637571157497 115.97722960151805 118.38709677419355 120.20872865275143 123.26375711574954 125.02846299810247 127.22960151802657 128.19734345351046 132.011385199241 134.36432637571158 137.6091081593928 141.84060721062619 146.26185958254268 147.98861480075902 150.4933586337761 153.11195445920305 155.18026565464896 156.03415559772296 158.82352941176472 161.80265654648957 166.94497153700189 171.55597722960152 174.44022770398482 177.64705882352945 182.33396584440229 185.21821631878561 189.05123339658445 190.60721062618597 192.9981024667932 196.03415559772296 199.33586337760912 199.75332068311198 208.36812144212524 212.29601518026567 216.14800759013283 218.48197343453515 225.82542694497153 232.56166982922201 237.05882352941177 244.13662239089183 253.33965844402277 260.24667931688805 263.88994307400384 271.6888045540797 274.47817836812146 281.74573055028463 287.22960151802658 294.64895635673628 297.79886148007597 304.55407969639469 315.44592030360536 325.21821631878561 336.2239089184061 342.35294117647061 348.70967741935488 357.59013282732451 367.83681214421256 380.49335863377615 392.03036053130933 400.5313092979128 407.79886148007591 431.63187855787476 443.11195445920305 458.44402277039853 467.41935483870975 479.39278937381408 493.30170777988616 504.62998102466798 516.90702087286525 517.64705882352951 528.50094876660341 553.18785578747634 579.01328273244792 585.25616698292231 602.84629981024671 606.2049335863378 604.34535104364329 614.97153700189756 621.32827324478183 628.55787476280841 641.55597722960158 660.75901328273244 680.66413662239097 699.82922201138524 722.46679316888049 741.23339658444036 754.45920303605317 765.46489563567366 781.25237191650854 792.35294117647061 808.02656546489573 819.48766603415561 831.57495256166987 839.31688804554085 852.23908918406084 862.10626185958267 874.97153700189767 889.31688804554085 904.07969639468695 926.58444022770414 939.01328273244792 960.01897533206841 975.86337760910828 996.39468690702097 1017.1347248576851 1034.8387096774195 1049.8861480075902 1059.1461100569261 1083.1309297912715 1100.0759013282732 1110.1707779886149 1109.2979127134727 1115.7874762808349 1131.3092979127136 1144.9146110056927 1156.0721062618597 1174.7058823529412 1194.5351043643263 1212.4667931688805 1232.1821631878558 1241.8406072106263 1256.6793168880456 1269.1271347248578 1292.9411764705883 1312.3908918406073 1336.6793168880456 1353.282732447818 1375.3700189753322 1386.6603415559773 1395.7874762808351 1414.1366223908919 1431.2 144212523719 1449.3738140417458 1480.0759013282734 1497.6660341555978 1522.3908918406073 1544.0227703984822 1570.550284629981 1595.8064516129032 1613.9848197343456 1631.9924098671729 1650.5882352941178 1678.7855787476283 1712.9981024667934 1735.9772296015183 1755.7115749525619 1784.6489563567366 1823.0929791271351 1842.4098671726756 1887.8747628083493 1900.8538899430741 1922.1631878557876 1928.8614800759015 1954.7058823529412 1955.4459203036056 1968.3301707779888 1992.1631878557878 2011.7457305502846 2030.6831119544595 2043.0550284629983 2065.9203036053132 2089.4876660341556 2135.6925996204936 2165.9962049335863 2199.2220113851995 2232.0493358633776 2264.9525616698293 2300.550284629981 2345.6925996204932 2371.9165085388995 2415.294117647059 2448.0834914611005 2497.4193548387098 2529.4876660341556 2548.9184060721063 2577.6470588235297 2610.7210626185961 2652.144212523719 2680.4933586337766 2704.5920303605317 2708.5199240986717 2735.3889943074005 2731.5180265654653 2672.049335863378 2642.011385199241 2634.8007590132829 2647.4762808349151 2681.8975332068312 2707.8368121442127 2735.0094876660346 2765.84440227704 2796.1859582542697 2811.1764705882356 2846.982922201139 2877.2675521821634 2907.2106261859585 2937.0588235294117 2959.3738140417458 Velocity 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 2012.25 100.00000000000003 99.052329945166278 97.824987385892641 95.474294803053894 94.614857151084564 94.846792308775363 95.071076404093489 95.672918335476822 95.981641561443396 95.150770319827771 94.786839466969596 93.43661769846463 92.822202840574747 92.158548768218779 92.185155908372309 91.832090149812913 92.626123900564508 92.372005682743534 91.906848787024273 90.76213910775914 91.616637451239072 91.736284087828679 92.140418308026511 92.952587480943492 94.034475801346318 94.011482860456667 95.03671506111823 95.7390429076072 95.473419878565707 93.758604459947392 92.911453653141649 92.693620081389412 94.034438993216057 95.054294933188601 94.823104668207947 94.368089046039927 95.231955932370994 95.89995010300099 97.26077060 8955866 97.223998999388243 98.09176996227859 98.961301803346018 98.399640374965855 96.034632042564866 97.052171955033245 95.214444045563596 94.129479322310374 92.647026497580427 92.963140888179424 93.393614920662301 92.103889943074009 91.79709102235573 93.055282805250357 94.042684626124455 94.039520396331355 95.587097668202119 94.815117241306666 96.168951794503513 96.998849037235203 98.008511429573645 97.205245245436231 95.889431438086959 95.833702598339016 96.467409348978421 96.66032877182667 95.553002737256364 94.81119665498025 93.826574732538489 93.341989454996437 94.021646445986889 94.694702159713827 94.785851756683996 94.734422090604042 98.433686154555815 99.203673210136373 100.75581605585906 101.23860582287188 101.42699120694027 101.9576668377055 102.77014749578532 103.45760327976738 102.08713618816077 101.17492366633624 103.69451680183195 106.71393074115024 105.01983484188327 106.29253866555737 104.19692350226673 101.5800778553465 101.20213657785622 100.53670380185066 99.46505466817699 96.230174951532589 96.630950926586138 97.992277621509629 98.958051796440444 100.00038513417266 100.43384693117365 100.89405620830456 100.14645189714675 99.230379509062004 98.890997171024011 98.747048156601096 98.694043159584837 98.685513837970134 97.03291963432406 96.119851963177368 95.12084087524282 95.041273538116599 95.770614867939244 96.756934902577214 98.044837683238953 97.647704899102564 97.936361998527616 98.643110284886845 99.843367096892592 101.36394165248407 102.42091536800703 101.9542223121256 1 100.88875026277306 101.71698328313039 102.45788149005494 102.28816785995845 101.45976071024383 100.83372739693381 101.09255610330798 101.92411835227861 102.59938144826262 103.3716259305985 105.048470727676 106.512508417018 107.49519908414749 108.65832485025896 109.47565094332106 110.04333221350839 111.44500762156309 112.8024745029896 114.59005021222603 115.94686406280678 117.86969204909961 118.69084563795467 118.36296819358547 117.84471853257432 118.11453490304567 118.15074457023893 119.22190597237348 119.51399759618423 120.10410421868613 120.29515676413747 120.98603997910391 121.03071986003813 120.54239777332828 119.7053588456952 118.83121375809904 118.86721954485293 118.27570634216296 117.79296210489845 117.41168840691583 117.61939968751538 118.58580450453499 118.00493767142942 118.90776645809169 118.34526063030124 117.943743675539 115.34553035008443 113.98825642474397 111.52747582576322 109.81736747943242 109.23727727218929 109.42917883112742 108.43524000514803 106.89259900893269 106.38205642196755 105.45764253998652 105.62127545724054 107.24068728885501 108.04401559223011 107.33874335845812 107.7089298495157 107.97498036186408 109.43854232176582 109.87089217489134 110.3385108115281 110.36623685393482 111.10966223660208 111.31445074023252 110.64377258236038 110.06421026254229 109.85115741934311 109.67223793568519 109.22803828325409 109.02169194325188 107.0463496425247 106.23180640458966 104.95297588565791 99.418434825474392 95.136743470122525 93.79722388354439 94.157567848046625 94.789236223125755 95.465430013275466 95.504715216956342 95.956621364292801 95.686728347926987 94.613905550952794 94.201408917460199 91.41420798979027 90.71745999349649 89.694251159210239 89.279469781566647
The Quantity Equation
Multiply both sides of formula by M:
M x V = P x Y
Called the quantity equation
Velocity formula:
V =
P x Y
M
0
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‹#›
The Quantity Theory in 5 Steps
1. V is stable.
2. So, a change in M causes nominal GDP (P x Y)
to change by the same percentage.
3. A change in M does not affect Y:
money is neutral,
Y is determined by technology & resources
4. So, P changes by same percentage as
P x Y and M.
5. Rapid money supply growth causes rapid inflation.
Start with quantity equation: M x V = P x Y
0
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ACTIVE LEARNING 2
Exercise
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One good: corn. The economy has enough labor, capital, and land to produce Y = 800 bushels of corn. V is constant. In 2008, MS = $2000, P = $5/bushel.
For 2009, the Fed increases MS by 5%, to $2100.
a. Compute the 2009 values of nominal GDP and P. Compute the inflation rate for 2008–2009.
b. Suppose tech. progress causes Y to increase to 824 in 2009. Compute 2008–2009 inflation rate.
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‹#›
27
This exercise makes the quantity theory more concrete for students.
If you’re pressed for time, you can delete part b or ask students to do it on their own.
ACTIVE LEARNING 2
Answers
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Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2008.
For 2009, the Fed increases MS by 5%, to $2100.
a. Compute the 2009 values of nominal GDP and P. Compute the inflation rate for 2008–2009.
Nominal GDP = P x Y
= M x V (Quantity Eq’n)
P =
P x Y
Y
=
$4200
800
= $5.25
= $2100 x 2 = $4200
Inflation rate =
$5.25 – 5.00
5.00
= 5% (same as MS!)
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ACTIVE LEARNING 2
Answers
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Given: Y = 800, V is constant,
MS = $2000 and P = $5 in 2005.
For 2009, the Fed increases MS by 5%, to $2100.
b. Suppose tech. progress causes Y to increase 3% in 2009, to 824. Compute 2008–2009 inflation rate.
First, use Quantity Eq’n to compute P in 2009:
P =
M x V
Y
=
$4200
824
= $5.10
Inflation rate =
$5.10 – 5.00
5.00
= 2%
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ACTIVE LEARNING 2
Summary and Lessons about the Quantity Theory of Money
If real GDP is constant, then
inflation rate = money growth rate.
If real GDP is growing, then
inflation rate < money growth rate.
The bottom line:
Economic growth increases # of transactions.
Some money growth is needed for these extra transactions.
Excessive money growth causes inflation.
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Hyperinflation
Hyperinflation is generally defined as inflation exceeding 50% per month.
Recall one of the Ten Principles from Chapter 1:
Prices rise when the government
prints too much money.
Excessive growth in the money supply always causes hyperinflation.
0
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Sign posted in public restroom
Hyperinflation in Zimbabwe
Large govt budget deficits led to the creation of
large quantities of money and high inflation rates.
| date | Zim$ per US$ |
| Aug 2007 | 245 |
| Apr 2008 | 29,401 |
| May 2008 | 207,209,688 |
| June 2008 | 4,470,828,401 |
| July 2008 | 26,421,447,043 |
| Feb 2009 | 37,410,030 |
| Sept 2009 | 355 |
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‹#›
This slide corresponds to a new FYI box in the 6th edition.
Greg Mankiw’s blog has a nice collection of articles on this topic. To see them, visit
http://gregmankiw.blogspot.com
and enter “Zimbabwe” in the search box.
Source of exchange rate data on this slide:
http://www.oanda.com/currency/historical-rates/
32
The Inflation Tax
When tax revenue is inadequate and ability to borrow is limited, govt may print money to pay for its spending.
Almost all hyperinflations start this way.
The revenue from printing money is the
inflation tax: printing money causes inflation, which is like a tax on everyone who holds money.
In the U.S., the inflation tax today accounts for less than 3% of total revenue.
0
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The Fisher Effect
Rearrange the definition of the real interest rate:
The real interest rate is determined by saving & investment in the loanable funds market.
Money supply growth determines inflation rate.
So, this equation shows how the nominal interest rate is determined.
Real interest rate
Nominal interest rate
Inflation rate
+
=
0
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The Fisher Effect
In the long run, money is neutral,
so a change in the money growth rate affects
the inflation rate but not the real interest rate.
So, the nominal interest rate adjusts one-for-one with changes in the inflation rate.
This relationship is called the Fisher effect
after Irving Fisher, who studied it.
Real interest rate
Nominal interest rate
Inflation rate
+
=
0
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U.S. Nominal Interest & Inflation Rates, 1960–2012
The close relation between these variables is evidence for the Fisher effect.
0
Inflation rate
Nominal interest rate
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36
36
The nominal interest rate is the 3-month Treasury Bill rate. The inflation rate is calculated as the percent change in the CPI from 12 months earlier.
Mostly, these two variables move very closely together: increases in inflation correspond to similar increases in the nominal interest rate.
When the two variables are not moving precisely together, the real interest rate is changing. This would occur if, for example, there were changes in the supply and/or demand for loanable funds. Starting in the early 1980s, the emergence of huge budget deficits caused the supply of loanable funds to fall, which increased the real interest rate. On this graph, the gap between the nominal interest rate and inflation rate clearly grows in the early 1980s.
Original sources:
CPI, not seasonally adjusted: Bureau of Labor Statistics, U.S. Department of Labor
Treasury Bill rate: Board of Governors of the Federal Reserve System
Where I obtained this data:
FRED database, Federal Reserve Bank of St. Louis
http://research.stlouisfed.org/fred2/
CPI 21916 21947 21976 22007 22037 22068 22098 22129 22160 22190 22221 22251 22282 22313 22341 22372 22402 2243 3 22463 22494 22525 22555 22586 22616 22647 22678 22706 22737 22767 22798 22828 22859 22890 22920 22951 22981 23012 23043 23071 23102 23132 23163 23193 23224 23255 23285 23316 23346 23377 23408 23437 23468 23498 23529 23559 23590 23621 23651 23682 23712 23743 23774 23802 23833 23863 23894 23924 23955 23986 24016 24047 24077 24108 24139 24167 24198 24228 24259 24289 24320 24351 24381 24412 24442 24473 24504 24532 24563 24593 24624 24654 24685 24716 24746 24777 24807 24838 24869 24898 24929 24959 24990 25020 25051 25082 25112 25143 25173 25204 25235 25263 25294 25324 25355 25385 25416 25447 25477 25508 25538 25569 25600 25628 25659 25689 25720 25750 25781 25812 25842 25873 25903 25934 25965 25993 26024 26054 26085 26115 26146 26177 26207 26238 26268 26299 26330 26359 26390 26420 26451 26481 26512 26543 26573 26604 26634 26665 26696 26724 26755 26785 26816 26846 26877 26908 26938 26969 26999 27030 27061 27089 27120 27150 27181 27211 27242 27273 27303 27334 27364 27395 27426 27454 27485 27515 27546 27576 27607 27638 27668 27699 27729 27760 27791 27820 27851 27881 27912 27942 27973 28004 28034 28065 28095 28126 28157 28185 28216 28246 28277 28307 28338 28369 28399 28430 28460 28491 28522 28550 28581 28611 28642 28672 28703 28734 28764 28795 28825 28856 28887 28915 28946 28976 29007 29037 29068 29099 29129 29160 29190 29221 29252 29281 29312 29342 29373 29403 29434 29465 29495 29526 29556 29587 29618 29646 29677 29707 29738 29768 29799 29830 29860 29891 29921 29952 29983 30011 30042 30072 30103 30133 30164 30195 30225 30256 30286 30317 30348 30376 30407 30437 30468 30498 30529 30560 30590 30621 30651 30682 30713 30742 30773 30803 30834 30864 30895 30926 30956 30987 31017 31048 31079 31107 31138 31168 31199 31229 31260 31291 31321 31352 31382 31413 31444 31472 31503 31533 31564 31594 31625 31656 31686 31717 31747 31778 31809 31837 31868 31898 31929 31959 31990 32021 32051 32082 32112 32143 32174 32203 32234 32264 32295 32325 32356 32387 32417 32448 32478 32509 32540 32568 32599 32629 32660 32690 32721 32752 32782 32813 32843 32874 32905 32933 32964 32994 33025 33055 33086 33117 33147 33178 33208 33239 33270 33298 33329 33359 33390 33420 33451 33482 33512 33543 33573 33604 33635 33664 33695 33725 33756 33786 33817 33848 33878 33909 33939 33970 34001 34029 34060 34090 34121 34151 34182 34213 34243 34274 34304 34335 34366 34394 34425 34455 34486 34516 34547 34578 34608 34639 34669 34700 34731 34759 34790 34820 34851 34881 34912 34943 34973 35004 35034 35065 35096 35125 35156 35186 35217 35247 35278 35309 35339 35370 35400 35431 35462 35490 35521 35551 35582 35612 35643 35674 35704 35735 35765 35796 35827 35855 35886 35916 35947 35977 36008 36039 36069 36100 36130 36161 36192 36220 36251 36281 36312 36342 36373 36404 36434 36465 36495 36526 36557 36586 36617 36647 36678 36708 36739 36770 36800 36831 36861 36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 39142 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 40544 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 1.24095E-2 1.4137900000000002E-2 1.51881E-2 1.9323699999999999E-2 1.8250699999999998E-2 1.7176199999999999E-2 1.3722099999999999E-2 1.47361E-2 1.23077E-2 1.3628599999999999E-2 1.4650799999999999E-2 1.36008E-2 1.6002700000000002E-2 1.4620899999999999E-2 1.4620899999999999E-2 9.1401E-3 9.1308999999999991E-3 7.7676000000000004E-3 1.25212E-2 1.1144899999999999E-2 1.24958E-2 7.7310999999999994E-3 6.7159000000000003E-3 6.7091999999999994E-3 6.7023999999999999E-3 9.0483000000000004E-3 1.1059000000000001E-2 1.3418300000000001E-2 1.34048E-2 1.2399500000000001E-2 1.00267E-2 1.1356E-2 1.4676499999999999E-2 1.33422E-2 1.33422E-2 1.23292E-2 1.33156E-2 1.22883E-2 1.1269499999999998E-2 8.9373999999999999E-3 8.9286000000000001E-3 1.32406E-2 1.5552600000000001E-2 1.5521799999999999E-2 9.8618999999999998E-3 1.21791E-2 1.3166599999999999E-2 1.6458199999999999E-2 1.6425800000000001E-2 1.41076E-2 1.4093700000000001E-2 1.54199E-2 1.5404800000000001E-2 1.3067599999999999E-2 1.0752699999999999E-2 9.7561000000000002E-3 1.17188E-2 1.20325E-2 1.3970100000000001E-2 1.19819E-2 1.0989000000000001E-2 1.19702E-2 1.19586E-2 1.38934E-2 1.6139399999999998E-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 2.5575399999999998E-2 2.7786599999999998E-2 2.86807E-2 2.7636599999999997E-2 2.43594E-2 2.7549100000000003E-2 3.4865300000000002E-2 3.5736900000000002E-2 3.7914699999999996E-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 2.9275799999999998E-2 2.60337E-2 2.5954199999999997E-2 2.5875200000000001E-2 3.1021899999999998E-2 3.2806799999999997 E-2 3.6474199999999998E-2 3.6363599999999996E-2 3.9393900000000003E-2 3.9274900000000001E-2 4.2296100000000003E-2 4.2042000000000003E-2 4.4910199999999997E-2 4.4776100000000006E-2 4.4642899999999999E-2 4.7477699999999998E-2 4.4247800000000004E-2 4.7058799999999998E-2 4.6920799999999999E-2 4.6783599999999995E-2 5.24781E-2 5.5232599999999993E-2 5.5072499999999996E-2 5.4755000000000005E-2 5.4441300000000005E-2 5.4285699999999999E-2 5.6980099999999999E-2 5.6657200000000005E-2 5.9322E-2 5.8988800000000001E-2 6.1624600000000002E-2 6.4245799999999992E-2 6.0941799999999997E-2 6.0606099999999996E-2 6.0439600000000003E-2 6.0109300000000004E-2 5.7065200000000003E-2 5.6910600000000006E-2 5.6603800000000003E-2 5.6300299999999998E-2 5.5999999999999994E-2 5.57029E-2 5.2770400000000002E-2 4.724409999999 9997E-2 4.4386400000000006E-2 4.1558400000000002E-2 4.4041499999999997E-2 4.3814399999999996E-2 4.3701800000000006E-2 4.3589700000000002E-2 4.08163E-2 3.8071100000000004E-2 3.5353500000000003E-2 3.2663299999999999E-2 3.2581499999999999E-2 3.7593999999999995E-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 5.5288500000000004E-2 5.9951999999999998E-2 5.7416299999999997E-2 7.3985700000000001E-2 7.3634199999999997E-2 8.0568699999999993E-2 8.2547200000000001E-2 8.9411799999999986E-2 9.6018699999999998E-2 0.1 0.10138249999999999 0.1006865 0.10706149999999999 0.10859730000000001 0.1153846 0.1088889 0.11946899999999999 0.1184211 0.1220044 0.1209503 0.11752140000000001 0.11205069999999999 0.1046025 0.10187110000000001 9.2592599999999997E-2 9.1836699999999993E-2 9.5334699999999994E-2 8.6172299999999993E-2 7.9051400000000008E-2 7.64706E-2 7.3786400000000002E-2 7.129089999999999E-2 6.6921599999999998E-2 6.2737600000000004E-2 6.0606099999999996E-2 5.8490599999999997E-2 6.2146899999999998E-2 5.9813099999999994E-2 5.5555599999999997E-2 5.7195600000000006E-2 5.4945099999999997E-2 5.46448E-2 5.0632900000000002E-2 5.03597E-2 5.1971299999999998E-2 6.0822900000000006E-2 6.4285700000000001E-2 6.9518700000000003E-2 6.7375900000000002E-2 6.7019399999999993E-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 8.928570000000001E-2 8.8709700000000002E-2 8.9887599999999998E-2 9.2504000000000003E-2 9.8412699999999992E-2 0.10252370000000001 0.10485129999999999 0.10697670000000001 0.1107692 0.11450379999999999 0.1183612 0.118797 0.1207154 0.12592590000000001 0.1325479 0.13868610000000001 0.14161849999999998 0.14592269999999999 0.14589240000000001 0.14425769999999999 0.14265930000000002 0.13150680000000001 0.12890090000000001 0.1276882 0.12632979999999999 0.12631580000000001 0.1235371 0.11794869999999999 0.1139241 0.10611739999999999 0.1013597 9.7919199999999998E-2 9.6969700000000006E-2 0.1077482 0.10817310000000001 0.10965439999999999 0.1027155 9.5794400000000002E-2 8.9120399999999989E-2 8.2568800000000012E-2 7.6136400000000007E-2 6.8848800000000002E-2 6.621769999999999E-2 6.9119299999999995E-2 7.1823200000000004E-2 6.5573800000000002E-2 5.9652900000000002E-2 4.94092E-2 5.0321199999999996E-2 4.4776100000000006E-2 3.8257199999999998E-2 3.70763E-2 3.48469E-2 3.5902900000000001E-2 0.04 3.4410799999999998E-2 2.4742299999999998E-2 2.3589699999999998E-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 4.3086200000000005E-2 4.2957000000000002E-2 4.2828699999999997E-2 4.2658699999999994E-2 4.1543000000000004E-2 4.0433899999999995E-2 3.5259499999999999E-2 3.6062400000000001E-2 3.7900900000000001E-2 3.5817999999999996E-2 3.5748799999999997E-2 3.6644199999999995E-2 3.4582099999999998E-2 3.3524899999999996E-2 3.2473700000000001E-2 3.23501E-2 3.5137700000000001E-2 3.7914699999999996E-2 3.9735100000000002E-2 3.1984900000000004E-2 2.1535600000000002E-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 1.1872100000000002E-2 1.3648800000000001E-2 1.91431E-2 2.84143E-2 3.6798499999999998E-2 3.6697199999999999E-2 3.7477099999999999E-2 3.9269400000000003E-2 4.2883199999999996E-2 4.2727300000000003E-2 4.3557199999999997E-2 4.5289900000000001E-2 4.33213E-2 4.1292600000000006E-2 3.9356000000000002E-2 3.8324400000000002E-2 3.9928999999999999E-2 3.9822999999999997E-2 3.9647599999999998E-2 4.1300499999999997E-2 4.1119899999999994E-2 4.1848299999999998E-2 4.2608699999999999E-2 4.2460999999999999E-2 4.41176E-2 4.4827599999999995E-2 4.6471600000000002E-2 4.8926999999999998E-2 5.0341300000000005E-2 5.2766E-2 5.1694899999999995E-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 5.7028100000000005E-2 6.1698700000000002E-2 6.3795900000000003E-2 6.1953899999999999E-2 6.2549499999999994E-2 5.6470599999999996E-2 5.3124999999999999E-2 4.8211500000000004E-2 4.8099299999999998E-2 5.03486E-2 4.69592E-2 4.36782E-2 3.7993899999999997E-2 3.3962300000000001E-2 2.8485800000000002E-2 3.0665700000000001E-2 2.9806300000000001E-2 2.6726100000000003E-2 2.81899E-2 3.18991E-2 3.1828300000000004E-2 3.0235999999999999E-2 3.01471E-2 3.1571200000000001E-2 3.0746699999999998E-2 2.9927000000000002E-2 3.2798799999999996E-2 3.1204599999999999E-2 2.9667099999999998E-2 3.2537999999999997E-2 3.2467500000000003E-2 3.0194100000000001E-2 3.1563800000000003E-2 3.2211900000000002E-2 2.9978600000000001E-2 2.84698E-2 2.84091E-2 2.7639999999999998E-2 2.7522899999999999E-2 2.7445499999999998E-2 2.8109600000000002E-2 2.4509799999999998E-2 2.5157200000000001E-2 2.6517800000000001E-2 2.3643900000000002E-2 2.28849E-2 2.4948000000000001E-2 2.6989599999999999E-2 2.90055E-2 2.9655200000000003E-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 2.7170299999999998E-2 2.8439199999999998E-2 2.8326699999999996E-2 2.8270900000000002E-2 2.8215199999999999E-2 2.8833600000000001E-2 2.8122999999999999E-2 3.0045700000000002E-2 3.0618900000000001E-2 3.2530900000000001E-2 3.3788200000000004E-2 3.0381399999999999E-2 3.0322599999999998E-2 2.7652700000000002E-2 2.4343400000000001E-2 2.2378499999999999E-2 2.23357E-2 2.1656100000000001E-2 2.2900800000000002E-2 2.2193999999999998E-2 2.0859700000000002E-2 1.89036E-2 1.6970499999999999E-2 1.6311199999999998E-2 1.4402E-2 1.37672E-2 1.4383999999999999E-2 1.6885600000000001E-2 1.62297E-2 1.74564E-2 1.6169199999999998E-2 1.4268000000000001E-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 2.1446100000000003E-2 2.2643800000000002E-2 2.6299700000000002E-2 2.56254E-2 2.6203500000000001E-2 2.6764E-2 2.7929599999999999E-2 3.2179700000000006E-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 3.4441799999999995E-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 2.0270299999999998E-2 2.2535199999999998E-2 2.48027E-2 2.7574600000000001E-2 3.1460700000000001E-2 3.0252100000000001E-2 2.1751299999999998E-2 1.89415E-2 1.94878E-2 2.0555599999999997E-2 2.2160700000000002E-2 2.3783200000000001E-2 2.04 19399999999997E-2 1.9283700000000001E-2 2.0352000000000002E-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 3.6216200000000004E-2 3.34232E-2 2.8448699999999997E-2 3.05303E-2 3.2068400000000004E-2 3.3617899999999999E-2 2.86929E-2 2.54103E-2 3.06716E-2 3.6469299999999996E-2 4.7418300000000004E-2 4.3501000000000005E-2 3.3385499999999999E-2 3.3385499999999999E-2 4.0187899999999999E-2 3.6382500000000005E-2 3.41792E-2 3.6138400000000001E-2 3.9772700000000001E-2 4.1817200000000006E-2 4.1046699999999998E-2 3.9265700000000001E-2 2.0120700000000002E-2 1.4063300000000001E-2 1.9687E-2 2.52398E-2 2.07577E-2 2.42025 99999999998E-2 2.7982E-2 2.5929199999999999E-2 2.7098900000000002E-2 2.6927699999999999E-2 2.3178899999999999E-2 1.8974500000000002E-2 2.8338299999999997E-2 3.6107E-2 4.3732699999999999E-2 4.1088100000000002E-2 4.3069800000000005E-2 4.1116200000000006E-2 3.9714900000000004E-2 3.9178499999999998E-2 4.0874499999999994E-2 4.9393399999999997E-2 5.5331599999999995E-2 5.3364300000000003E-2 4.9509200000000003E-2 3.7171900000000001E-2 1.0624499999999999E-2 -2.0809999999999999E-4 -1.1168999999999999E-3 9.4060000000000009E-4 -4.1228999999999997E-3 -5.9167000000000004E-3 -1.0357499999999999E-2 -1.2535099999999999E-2 -1.99188E-2 -1.4948600000000001E-2 -1.3656399999999999E-2 -2.2584000000000003E-3 1.8955900000000001E-2 2.80462E-2 2.59811E-2 2.1492000000000001E-2 2.2953399999999999E-2 2.1945899999 999997E-2 1.9743900000000002E-2 1.1464799999999999E-2 1.36127E-2 1.19872E-2 1.14923E-2 1.1751899999999999E-2 1.0722499999999999E-2 1.4190400000000001E-2 1.6402300000000002E-2 2.121E-2 2.6457899999999999E-2 3.0624799999999997E-2 3.4312200000000001E-2 3.5132500000000004E-2 3.6140800000000001E-2 3.7622300000000004E-2 3.8953299999999996E-2 3.5540099999999998E-2 3.4510399999999997E-2 3.0029900000000002E-2 2.92667E-2 2.8940399999999998E-2 2.6456900000000002E-2 2.2974600000000001E-2 1.7330399999999999E-2 Nominal interest rate 21916 21947 21976 22007 22037 22068 22098 22129 22160 22190 22221 22251 22282 22313 22341 22372 22402 22433 22463 22494 22525 22555 22586 22616 22647 22678 22706 22737 22767 22798 22828 22859 22890 22920 22951 22981 23012 23043 23071 23102 23132 23163 23193 23224 23255 23285 23316 23346 23377 23408 23437 23468 23498 23529 23559 23590 23621 23651 23682 23712 23743 23774 23802 23833 23863 23894 23924 23955 23986 24016 24047 24077 24108 24139 24167 24198 24228 24259 24289 24320 24351 24381 24412 24442 24473 24504 24532 24563 24593 24624 24654 24685 24716 24746 24777 24807 24838 24869 24898 24929 24959 24990 25020 25051 25082 25112 25143 25173 25204 25235 25263 25294 25324 25355 25385 25416 25447 25477 25508 25538 25569 25600 25628 25659 25689 25720 25750 25781 25812 25842 25873 25903 25934 25965 25993 26024 26054 26085 26115 26146 26177 26207 26238 26268 26299 26330 26359 26390 26420 26451 26481 26512 26543 26573 26604 26634 26665 26696 26724 26755 26785 26816 26846 26877 26908 26938 26969 26999 27030 27061 27089 27120 27150 27181 27211 27242 27273 27303 27334 27364 27395 27426 27454 27485 27515 27546 27576 27607 27638 27668 27699 27729 27760 27791 27820 27851 27881 27912 27942 27973 28004 28034 28065 28095 28126 28157 28185 28216 28246 28277 28307 28338 28369 28399 28430 28460 28491 28522 28550 28581 28611 28642 28672 28703 28734 28764 28795 28825 28856 28887 28915 28946 28976 29007 29037 29068 29099 29129 29160 29190 29221 29252 29281 29312 29342 29373 29403 29434 29465 29495 29526 29556 29587 29618 29646 29677 29707 29738 29768 29799 29830 29860 29891 29921 29952 29983 30011 30042 30072 30103 30133 30164 30195 30225 30256 30286 30317 30348 30376 30407 30437 30468 30498 30529 30560 30590 30621 30651 30682 30713 30742 30773 30803 30834 30864 30895 30926 30956 30987 31017 31048 31079 31107 31138 31168 31199 31229 31260 31291 31321 31352 31382 31413 31444 31472 31503 31533 31564 31594 31625 31656 31686 31717 31747 31778 31809 31837 31868 31898 31929 31959 31990 32021 32051 32082 32112 32143 32174 32203 32234 32264 32295 32325 32356 32387 32417 32448 32478 32509 32540 32568 32599 32629 32660 32690 32721 32752 32782 32813 32843 32874 32905 32933 32964 32994 33025 33055 33086 33117 33147 33178 33208 33239 33270 33298 33329 33359 33390 33420 33451 33482 33512 33543 33573 33604 33635 33664 33695 33725 33756 33786 33817 33848 33878 33909 33939 33970 34001 34029 34060 34090 34121 34151 34182 34213 34243 34274 34304 34335 34366 34394 34425 34455 34486 34516 34547 34578 34608 34639 34669 34700 34731 34759 34790 34820 34851 34881 34912 34943 34973 35004 35034 35065 35096 35125 35156 35186 35217 35247 35278 35309 35339 35370 35400 35431 35462 35490 35521 35551 35582 35612 35643 35674 35704 35735 35765 35796 35827 35855 35886 35916 35947 35977 36008 36039 36069 36100 36130 36161 36192 36220 36251 36281 36312 36342 36373 36404 36434 36465 36495 36526 36557 36586 36617 36647 36678 36708 36739 36770 36800 36831 36861 36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 38838 38869 38899 38930 38961 38991 39022 39052 39083 39114 39142 39173 39203 39234 39264 39295 39326 39356 39387 39417 39448 39479 39508 39539 39569 39600 39630 39661 39692 39722 39753 39783 39814 39845 39873 39904 39934 39965 39995 40026 40057 40087 40118 40148 40179 40210 40238 40269 40299 40330 40360 40391 40422 40452 40483 40513 40544 40575 40603 40634 40664 40695 40725 40756 40787 40817 40848 40878 40909 40940 40969 41000 41030 4.3499999999999997E-2 3.9599999999999996E-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 2.3700000000000002E-2 2.2499999999999999E-2 2.2400000000000003E-2 2.4199999999999999E-2 2.3900000000000001E-2 2.29E-2 2.29E-2 2.3300000000000001E-2 2.2400000000000003E-2 2.3900000000000001E-2 2.2799999999999997E-2 2.3E-2 2.4799999999999999E-2 2.6000000000000002E-2 2.7200000000000002E-2 2.7300000000000001E-2 2.7200000000000002E-2 2.7300000000000001E-2 2.69E-2 2.7300000000000001E-2 2.92E-2 2.8199999999999999E-2 2.7799999999999998E-2 2.7400000000000001E-2 2.8300000000000002E-2 2.87E-2 2.9100000000000001E-2 2.92E-2 2.8900000000000002E-2 2.8999999999999998E-2 2.9300000000000003E-2 2.9900000000000003E-2 3.1800000000000002E-2 3.32E-2 3.3799999999999997E-2 3.4500000000000003E-2 3.5200000000000002E-2 3.5200000000000002E-2 3.5200000000000002E-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 3.5699999999999996E-2 3.6400000000000002E-2 3.8399999999999997E-2 3.8100000000000002E-2 3.9300000000000002E-2 3.9300000000000002E-2 3.9300000000000002E-2 3.8900000000000004E-2 3.7999999999999999E-2 3.8399999999999997E-2 3.8399999999999997E-2 3.9199999999999999E-2 4.0300000000000002E-2 4.0899999999999999E-2 4.3799999999999999E-2 4.5899999999999996E-2 4.6500000000000007E-2 4.5899999999999996E-2 4.6199999999999998E-2 4.6399999999999997E-2 4.4999999999999998E-2 4.8000000000000001E-2 4.9599999999999998E-2 5.3699999999999998E-2 5.3499999999999999E-2 5.3200000000000004E-2 4.9599999999999998E-2 4.7199999999999999E-2 4.5599999999999995E-2 4.2599999999999999E-2 3.8399999999999997E-2 3.6000000000000004E-2 3.5400000000000001E-2 4.2099999999999999E-2 4.2699999999999995E-2 4.4199999999999996E-2 4.5599999999999995E-2 4.7300000000000002E-2 4.9699999999999994E-2 0.05 4.9800000000000004E-2 5.1699999999999996E-2 5.3800000000000001E-2 5.6600000000000004E-2 5.5199999999999999E-2 5.3099999999999994E-2 5.0900000000000001E-2 5.1900000000000002E-2 5.3499999999999999E-2 5.45E-2 5.96E-2 6.1399999999999996E-2 6.1200000000000004E-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 6.5099999999999991E-2 6.8400000000000002E-2 6.6799999999999998E-2 6.4500000000000002E-2 6.4100000000000004E-2 6.1200000000000004E-2 5.91E-2 5.28E-2 4.87E-2 4.4400000000000002E-2 3.7000000000000005E-2 3.3799999999999997E-2 3.8599999999999995E-2 4.1399999999999999E-2 4.7500000000000001E-2 5.4000000000000006E-2 4.9400000000000006E-2 4.6900000000000004E-2 4.4600000000000001E-2 4.2199999999999994E-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 4.0199999999999993E-2 4.6600000000000003E-2 4.7400000000000005E-2 4.7800000000000002E-2 5.0700000000000002E-2 5.4100000000000002E-2 5.5999999999999994E-2 6.0899999999999996E-2 6.260000 0000000003E-2 6.3600000000000004E-2 7.1900000000000006E-2 8.0100000000000005E-2 8.6699999999999999E-2 8.2899999999999988E-2 7.22E-2 7.8299999999999995E-2 7.4499999999999997E-2 7.7699999999999991E-2 7.1199999999999999E-2 7.9600000000000004E-2 8.3299999999999999E-2 8.2299999999999998E-2 7.9000000000000001E-2 7.5499999999999998E-2 8.9600000000000013E-2 8.0600000000000005E-2 7.46E-2 7.4700000000000003E-2 7.1500000000000008E-2 6.2600000000000003E-2 5.5E-2 5.4900000000000004E-2 5.6100000000000004E-2 5.2300000000000006E-2 5.3399999999999996E-2 6.13E-2 6.4399999999999999E-2 6.4199999999999993E-2 5.96E-2 5.4800000000000001E-2 5.4400000000000004E-2 4.87E-2 4.8799999999999996E-2 0.05 4.8600000000000004E-2 5.2000000000000005E-2 5.4100000000000002E-2 5.23000000000 00006E-2 5.1399999999999994E-2 5.0799999999999998E-2 4.9200000000000001E-2 4.7500000000000001E-2 4.3499999999999997E-2 4.6199999999999998E-2 4.6699999999999998E-2 4.5999999999999999E-2 4.5400000000000003E-2 4.9599999999999998E-2 5.0199999999999995E-2 5.1900000000000002E-2 5.4900000000000004E-2 5.8099999999999999E-2 6.1600000000000002E-2 6.0999999999999999E-2 6.0700000000000004E-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 9.4800000000000009E-2 9.4600000000000004E-2 9.6099999999999991E-2 9.06E-2 9.2399999999999996E-2 9.5199999999999993E-2 0.1026 0.11699999999999999 0.11789999999999999 0.12039999999999999 0.12 0.12859999999999999 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 0.14730000000000001 0.14949999999999999 0.15509999999999999 0.14699999999999999 0.13539999999999999 0.10859999999999999 0.1085 0.12279999999999999 0.1348 0.1268 0.127 0.12089999999999999 0.12470000000000001 0.11349999999999999 8.6800000000000002E-2 7.9199999999999993E-2 7.7100000000000002E-2 8.0700000000000008E-2 7.9399999999999998E-2 7.8600000000000003E-2 8.1099999999999992E-2 8.3499999999999991E-2 8.2100000000000006E-2 8.1900000000000001E-2 8.7899999999999992E-2 9.0800000000000006E-2 9.3399999999999997E-2 0.09 8.6400000000000005E-2 8.7599999999999997E-2 0.09 8.900000000000001E-2 9.0899999999999995E-2 9.5199999999999993E-2 9.69E-2 9.8299999999999998E-2 9.8699999999999996E-2 0.1012 0.1047 0.10369999999999999 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 7.1399999999999991E-2 7.0999999999999994E-2 7.1599999999999997E-2 7.2400000000000006E-2 7.0999999999999994E-2 7.0699999999999999E-2 7.0599999999999996E-2 6.5599999999999992E-2 6.0599999999999994E-2 6.1500000000000006E-2 6.2100000000000002E-2 5.8299999999999998E-2 5.5300000000000002E-2 5.21E-2 5.1799999999999999E-2 5.3499999999999999E-2 5.5300000000000002E-2 5.4299999999999994E-2 5.5899999999999998E-2 5.5899999999999998E-2 5.6399999999999999E-2 5.6600000000000004E-2 5.67E-2 5.6900000000000006E-2 6.0400000000000002E-2 6.4000000000000001E-2 6.13E-2 5.6900000000000006E-2 5.7699999999999994E-2 5.8099999999999999E-2 5.6600000000000004E-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 8.0700000000000008E-2 8.2699999999999996E-2 8.5299999999999987E-2 8.8200000000000001E-2 8.6500000000000007E-2 8.43E-2 8.1500000000000003E-2 7.8799999999999995E-2 7.9000000000000001E-2 7.7499999999999999E-2 7.6399999999999996E-2 7.690000000000001E-2 7.6299999999999993E-2 7.6399999999999996E-2 7.7399999999999997E-2 7.9000000000000001E-2 7.7699999999999991E-2 7.7399999999999997E-2 7.7300000000000008E-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 5.2199999999999996E-2 4.99E-2 4.5599999999999995E-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 2.9300000000000003E-2 2.9500000000000002E-2 2.87E-2 2.9600000000000001E-2 3.0699999999999998E-2 3.04E-2 3.0200000000000001E-2 2.9500000000000002E-2 3.0200000000000001E-2 3.1E-2 3.0600000000000002E-2 2.98E-2 3.2500000000000001E-2 3.5000000000000003E-2 3.6799999999999999E-2 4.1399999999999999E-2 4.1399999999999999E-2 4.3299999999999998E-2 4.4800000000000006E-2 4.6199999999999998E-2 4.9500000000000002E-2 5.2900000000000003E-2 5.5999999999999994E-2 5.7099999999999998E-2 5.7699999999999994E-2 5.7300000000000004E-2 5.6500000000000002E-2 5.67E-2 5.4699999999999999E-2 5.4199999999999998E-2 5.4000000000000006E-2 5.28E-2 5.28E-2 5.3600000000000002E-2 5.1399999999999994E-2 0.05 4.8300000000000003E-2 4.9599999999999998E-2 4.9500000000000002E-2 5.0199999999999995E-2 5.0900000000000001E-2 5.1500000000000004E-2 5.0499999999999996E-2 5.0900000000000001E-2 4.99E-2 5.0300000000000004E-2 4.9100000000000005E-2 5.0300000000000004E-2 5.0099999999999999E-2 5.1399999999999994E-2 5.16E-2 5.0499999999999996E-2 4.9299999999999997E-2 5.0499999999999996E-2 5.1399999999999994E-2 4.9500000000000002E-2 4.9699999999999994E-2 5.1399999999999994E-2 5.16E-2 5.04E-2 5.0900000000000001E-2 5.0300000000000004E-2 4.9500000000000002E-2 0.05 4.9800000000000004E-2 4.9599999999999998E-2 4.9000000000000002E-2 4.6100000000000002E-2 3.9599999999999996E-2 4.41E-2 4.3899999999999995E-2 4.3400000000000001E-2 4.4400000000000002E-2 4.4400000000000002E-2 4.2900000000000001E-2 4.4999999999999998E -2 4.5700000000000005E-2 4.5499999999999999E-2 4.7199999999999999E-2 4.6799999999999994E-2 4.8600000000000004E-2 5.0700000000000002E-2 5.2000000000000005E-2 5.3200000000000004E-2 5.5500000000000001E-2 5.6900000000000006E-2 5.6600000000000004E-2 5.79E-2 5.6900000000000006E-2 5.96E-2 6.0899999999999996E-2 0.06 6.1100000000000002E-2 6.1699999999999998E-2 5.7699999999999994E-2 5.1500000000000004E-2 4.8799999999999996E-2 4.4199999999999996E-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 1.6200000 000000003E-2 1.6299999999999999E-2 1.5800000000000002E-2 1.23E-2 1.1899999999999999E-2 1.1699999999999999E-2 1.1699999999999999E-2 1.1299999999999999E-2 1.1299999999999999E-2 1.0700000000000001E-2 9.1999999999999998E-3 9.0000000000000011E-3 9.4999999999999998E-3 9.3999999999999986E-3 9.1999999999999998E-3 9.300000000000001E-3 9.0000000000000011E-3 8.8000000000000005E-3 9.300000000000001E-3 9.3999999999999986E-3 9.3999999999999986E-3 1.0200000000000001E-2 1.2699999999999999E-2 1.3300000000000001E-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 2.8399999999999998E-2 2.9700000000000001E-2 3.2199999999999999E-2 3.44E-2 3.4200000000000001E-2 3.710000000 0000001E-2 3.8800000000000001E-2 3.8900000000000004E-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 4.9400000000000006E-2 4.8499999999999995E-2 4.9800000000000004E-2 5.0300000000000004E-2 4.9400000000000006E-2 4.87E-2 4.7300000000000002E-2 4.6100000000000002E-2 4.82E-2 4.2000000000000003E-2 3.8900000000000004E-2 3.9E-2 3.27E-2 0.03 2.75E-2 2.12E-2 1.26E-2 1.29E-2 1.7299999999999999E-2 1.8600000000000002E-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 1.7000000000000001E-3 1.1999999999999999E-3 7.000000000000001E-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 1.4000000000000002E-3 1.4000000000000002E-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
The Fisher Effect & the Inflation Tax
The inflation tax applies to people’s holdings of money, not their holdings of wealth.
The Fisher effect: an increase in inflation causes an equal increase in the nominal interest rate,
so the real interest rate (on wealth) is unchanged.
Real interest rate
Nominal interest rate
Inflation rate
+
=
0
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‹#›
The Costs of Inflation
The inflation fallacy: most people think inflation erodes real incomes.
But inflation is a general increase in prices
of the things people buy and the things they sell (e.g., their labor).
In the long run, real incomes are determined by real variables, not the inflation rate.
0
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
‹#›
U.S. Average Hourly Earnings & the CPI
CPI
Nominal wage
Inflation causes
the CPI and
nominal wages
to rise together over the long run.
0
39
1965 = 100
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‹#›
39
39
This graph is not in the textbook, but it helps expose the inflation fallacy.
Both series are normalized to equal 100 in 1965. The graph shows that the cost of living has risen dramatically since 1965—but the nominal wage has kept up with inflation. If the inflation fallacy were true, the nominal wage would have risen at a slower rate than the CPI.
Source: The nominal wage is average hourly earnings, total for private sector, seasonally adjusted, from the Bureau of Labor Statistics, U.S. Department of Labor. The CPI in this graph is seasonally adjusted, also from the BLS.
CPI (1965 = 100) 23743 23774 23802 23833 23863 23894 23924 23955 23986 24016 24047 24077 24108 24139 24167 24198 24228 24259 24289 24320 24351 24381 24412 24442 24473 24504 24532 24563 24593 24624 24654 24685 24716 24746 24777 24807 24838 24869 24898 24929 24959 24990 25020 25051 25082 25112 25143 25173 25204 25235 25263 25294 25324 25355 25385 25416 25447 25477 25508 25538 25569 25600 25628 25659 25689 25720 25750 25781 25812 25842 25873 25903 25934 25965 25993 26024 26054 26085 26115 26146 26177 26207 26238 26268 26299 26330 26359 26390 26420 26451 26481 26512 26543 26573 26604 26634 26665 26696 26724 26755 26785 26816 26846 26877 26908 26938 26969 26999 27030 27061 27089 27120 27150 27181 27211 27242 27273 27303 27334 27364 27395 27426 27454 27485 27515 27546 27576 27607 27638 27668 27699 27729 27760 27791 27820 27851 27881 27912 27942 27973 28004 28034 28065 28095 28126 28157 28185 28216 28246 28277 28307 28338 28369 28399 28430 28460 28491 28522 28550 28581 28611 28642 28672 28703 28734 28764 28795 28825 28856 28887 28915 28946 28976 29007 29037 29068 29099 29129 29160 29190 29221 29252 29281 29312 29342 29373 29403 29434 29465 29495 29526 29556 29587 29618 29646 29677 29707 29738 29768 29799 29830 29860 29891 29921 29952 29983 30011 30042 30072 30103 30133 30164 30195 30225 30256 30286 30317 30348 30376 30407 30437 30468 30498 30529 30560 30590 30621 30651 30682 30713 30742 30773 30803 30834 30864 30895 30926 30956 30987 31017 31048 31079 31107 31138 31168 31199 31229 31260 31291 31321 31352 31382 31413 31444 31472 31503 31533 31564 31594 31625 31656 31686 31717 31747 31778 31809 31837 31868 31898 31929 31959 31990 32021 32051 32082 32112 32143 32174 32203 32234 32264 32295 32325 32356 32387 32417 32448 32478 32509 32540 32568 32599 32629 32660 32690 32721 32752 32782 32813 32843 32874 32905 32933 32964 32994 33025 33055 33086 33117 33147 33178 33208 33239 33270 33298 33329 33359 33390 33420 33451 33482 33512 33543 33573 33604 33635 33664 33695 33725 33756 33786 33817 33848 33878 33909 33939 33970 34001 34029 34060 34090 34121 34151 34182 34213 34243 34274 34304 34335 34366 34394 34425 34455 34486 34516 34547 34578 34608 34639 34669 34700 34731 34759 34790 34820 34851 34881 34912 34943 34973 35004 35034 35065 35096 35125 35156 35186 35217 35247 35278 35309 35339 35370 35400 35431 35462 35490 35521 35551 35582 35612 35643 35674 35704 35735 35765 35796 35827 35855 35886 35916 35947 35977 36008 36039 36069 36100 36130 36161 36192 36220 36251 36281 36312 36342 36373 36404 36434 36465 36495 36526 36557 36586 36617 36647 36678 36708 36739 36770 36800 36831 36861 36892 36923 36951 36982 37012 37043 37073 37104 37135 37165 37196 37226 37257 37288 37316 37347 37377 37408 37438 37469 37500 37530 37561 37591 37622 37653 37681 37712 37742 37773 37803 37834 37865 37895 37926 37956 37987 38018 38047 38078 38108 38139 38169 38200 38231 38261 38292 38322 38353 38384 38412 38443 38473 38504 38534 38565 38596 38626 38657 38687 38718 38749 38777 38808 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107.09718670076725 107.41687979539641 107.73657289002557 108.37595907928387 108.69565217391303 109.01534526854219 109.33503836317135 109.65473145780049 109.97442455242965 110.29411764705881 110.93350383631713 111.57289002557543 111.89258312020459 112.21227621483375 112.85166240409205 113.17135549872121 113.81074168797953 114.13043478260869 114.45012787723783 115.40920716112531 116.04859335038361 116.36828644501277 117.00767263427109 117.64705882352939 117.96675191815855 118.60613810741687 119.24552429667517 119.88491048593349 120.5 2429667519182 121.16368286445011 121.80306905370844 122.44245524296673 123.08184143222505 123.40153452685422 124.04092071611251 124.36061381074167 124.68030690537083 125.31969309462916 125.95907928388745 126.59846547314578 127.23785166240407 127.55754475703323 127.55754475703323 127.87723785166239 128.19693094629156 128.83631713554985 129.47570332480817 129.79539641943734 130.11508951406648 130.43478260869563 130.7544757033248 131.07416879795394 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The Costs of Inflation
Shoeleather costs: the resources wasted when inflation encourages people to reduce their money holdings
Includes the time and transactions costs of more frequent bank withdrawals
Menu costs: the costs of changing prices
Printing new menus, mailing new catalogs, etc.
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The Costs of Inflation
Misallocation of resources from relative-price variability: Firms don’t all raise prices at the same time, so relative prices can vary…
which distorts the allocation of resources.
Confusion & inconvenience: Inflation changes the yardstick we use to measure transactions.
Complicates long-range planning and the comparison of dollar amounts over time.
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The Costs of Inflation
Tax distortions:
Inflation makes nominal income grow faster than real income.
Taxes are based on nominal income,
and some are not adjusted for inflation.
So, inflation causes people to pay more taxes even when their real incomes don’t increase.
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ACTIVE LEARNING 3
Tax distortions
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You deposit $1000 in the bank for one year.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
a. In which case does the real value of your deposit grow the most?
Assume the tax rate is 25%.
b. In which case do you pay the most taxes?
c. Compute the after-tax nominal interest rate,
then subtract inflation to get the
after-tax real interest rate for both cases.
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Most principles-level students have difficulty the first time they are asked to calculate the after-tax real interest rate because the calculation involves several intermediate steps. The intermediate steps are, at first, not obvious to most students. This exercise walks students through these steps.
The exercise leads students to see for themselves that inflation reduces the after-tax real interest rate.
Suggestion: Display this slide, and give students 3-4 minutes to work the problem on their own.
ACTIVE LEARNING 3
Answers
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a. In which case does the real value of your deposit grow the most?
In both cases, the real interest rate is 10%,
so the real value of the deposit grows 10% (before taxes).
Deposit = $1000.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
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44
Suggestion: If you can spare the class time, ask students for the answers before you display them.
ACTIVE LEARNING 3
Answers
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b. In which case do you pay the most taxes?
CASE 1: interest income = $100,
so you pay $25 in taxes.
CASE 2: interest income = $200,
so you pay $50 in taxes.
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
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ACTIVE LEARNING 3
Answers
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c. Compute the after-tax nominal interest rate,
then subtract inflation to get the
after-tax real interest rate for both cases.
CASE 1: nominal = 0.75 x 10% = 7.5%
real = 7.5% – 0% = 7.5%
CASE 2: nominal = 0.75 x 20% = 15%
real = 15% – 10% = 5%
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
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ACTIVE LEARNING 3
Summary and lessons
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Inflation…
raises nominal interest rates (Fisher effect) but not real interest rates
increases savers’ tax burdens
lowers the after-tax real interest rate
Deposit = $1000. Tax rate = 25%.
CASE 1: inflation = 0%, nom. interest rate = 10%
CASE 2: inflation = 10%, nom. interest rate = 20%
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47
By lowering the after-tax interest rate, inflation reduces the incentive to save. Recall that saving is critically important for future productivity and living standards.
A Special Cost of Unexpected Inflation
Arbitrary redistributions of wealth
Higher-than-expected inflation transfers purchasing power from creditors to debtors: Debtors get to repay their debt with dollars that aren’t worth as much.
Lower-than-expected inflation transfers purchasing power from debtors to creditors.
High inflation is more variable and less predictable than low inflation.
So, these arbitrary redistributions are frequent when inflation is high.
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For many students, this is one of the harder concepts of the chapter. You might consider asking students to work through Problem 10 in the “Problems and Applications” at the end of this chapter for practice with this concept.
The Costs of Inflation
All these costs are quite high for economies experiencing hyperinflation.
For economies with low inflation (< 10% per year),
these costs are probably much smaller,
though their exact size is open to debate.
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CONCLUSION
This chapter explains one of the Ten Principles of economics:
Prices rise when the govt prints
too much money.
We saw that money is neutral in the long run, affecting only nominal variables.
In later chapters, we will see that money has important effects in the short run on real variables like output and employment.
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SUMMARY
To explain inflation in the long run, economists use
the quantity theory of money. According to this theory, the price level depends on the quantity of money, and the inflation rate depends on the money growth rate.
The classical dichotomy is the division of variables
into real and nominal. The neutrality of money is the idea that changes in the money supply affect nominal variables but not real ones. Most economists believe these ideas describe the economy in the long run.
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SUMMARY
The inflation tax is the loss in the real value of people’s money holdings when the government causes inflation by printing money.
The Fisher effect is the one-for-one relation between changes in the inflation rate and changes in the nominal interest rate.
The costs of inflation include menu costs, shoeleather costs, confusion and inconvenience, distortions in relative prices and the allocation of resources, tax distortions, and arbitrary redistributions of wealth.
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
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aa.2015
brief-ch12-presentation6e2012.pptx
