homework - MACROECONOMIC ANALYSIS

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ECON3353 Macroeconomic Analysis

Assignment 3

Instruction: Here is a study guide to assist you in this assignment (tips are in blue color).

For short-answer questions, you need to show the instructor your work. When working on a

calculation, an equation or a formula, you should write down the process for your solution and

then show each step on a separate line below. If you need more steps, write down each one on a

separate line. If you just write bare answers (final answers), only partial credits will be given to

them even they are correct. Your homework will be graded for content and neatness.

Question 1.

The Table below shows us percentage changes of annual unemployment rate (UNemp) and real

gross domestic product growth rate (GDP) after WWII in the United States.

Year UNemp GDP Year UNemp GDP Year UNemp GDP

1949 2.3 -0.6 1973 -0.7 5.6 1997 -0.5 4.4

1950 -0.9 8.7 1974 0.8 -0.5 1998 -0.5 4.5

1951 -1.9 8.0 1975 2.9 -0.2 1999 -0.3 4.8

1952 -0.3 4.1 1976 -0.8 5.4 2000 -0.3 4.1

1953 -0.1 4.7 1977 -0.7 4.6 2001 0.8 1.0

1954 2.7 -0.6 1978 -1.0 5.5 2002 1.0 1.7

1955 -1.3 7.1 1979 -0.2 3.2 2003 0.3 2.9

1956 -0.3 2.1 1980 1.3 -0.3 2004 -0.5 3.8

1957 0.2 2.1 1981 0.4 2.5 2005 -0.4 3.5

1958 2.6 -0.7 1982 2.1 -1.8 2006 -0.5 2.9

1959 -1.4 6.9 1983 -0.1 4.6 2007 0.0 1.9

1960 0.1 2.6 1984 -2.1 7.2 2008 1.2 -0.1

1961 1.1 2.6 1985 -0.3 4.2 2009 3.5 -2.5

1962 -1.2 6.1 1986 -0.2 3.5 2010 0.4 2.6

1963 0.1 4.4 1987 -0.8 3.5 2011 -0.7 1.6

1964 -0.5 5.8 1988 -0.7 4.2 2012 -0.9 2.2

1965 -0.6 6.5 1989 -0.2 3.7 2013 -0.7 1.8

1966 -0.7 6.6 1990 0.3 1.9 2014 -1.2 2.5

1967 0.0 2.7 1991 1.3 -0.1 2015 -0.9 3.1

1968 -0.3 4.9 1992 0.7 3.5 2016 -0.4 1.7

1969 0.0 3.1 1993 -0.6 2.8 2017 -0.5 2.3

1970 1.5 0.2 1994 -0.8 4.0 2018 -0.4 3.0

1971 1.0 3.3 1995 -0.5 2.7 2019 -0.3 2.2

1972 -0.4 5.3 1996 -0.2 3.8

(1) Recall in the unit of Economic Fluctuations, we introduced the concept of Okun’s Law. What

is the Okun’s Law about? Please use your own language to explain it.

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Answer: see our lecture notes or your textbook.

(2) Use data in the attached spreadsheet (xlsx.), which is the same as data in the table. Now plot

change of real GDP growth rate with respect to change of unemployment rate from 1949 to 2019

(the full sample). Open the spreadsheet, plot the two columns, “UNemp” and “GDP”. Right click

any plot and choose “Add Trendline”. In “Trendline Options”, select “Linear”. Also select

“Display equation on chart” and “Display R-squared on chart”.

Answer: see the spreadsheet document attached.

(3) How to interpret relationship between changes of GDP growth rate and unemployment rate?

Now go to your notes (slides). Is the relationship you plotted similar as the Okun’s Law predicts?

Suppose you got a relation as GDP = a + b * UNemp. Are the coefficients of a and b are close to

the value of Okun’s Law?

Answer: see the spreadsheet document attached.

(4) Now repeat the plot you did in part (2) above. However, this time you use the sample only

from 2000 to 2019. Any change to the relationship? How is the value of a and b in this sample?

Answer: see the spreadsheet document attached.

Question 2.

Recall the Keynesian cross is foundation to derive the IS curve. The cross of planned expenditure

(PE) and the equilibrium condition (PE = Y) shows us the equilibrium level of national output in

the goods market. Now we assume the consumption (C) is a function of

 C = 120 + 0.8(Y-T); note here MPC is 0.8. Planned investment (I) is 200; government purchases (G) and taxes (T) are both 400. Use the

conditions given as above, finish the following part.

(1) What is the equilibrium level of income? You need to show your work step by step.

Tip: recall the definition of planned expenditure (PE). At equilibrium, actual expenditure (Y)

equals planned expenditure.

Answer:

PE = C + I + G. At equilibrium in Keynesian cross, planned expenditure = actual expenditure or

PE = Y; Note, C is a function of (Y-T) as above.

(2) If government purchases increase to 420, what is the new equilibrium income? What is the

multiplier for government purchases?

Tip: recall the multiplier for government purchase in your notes (slides).

Answer: after G increases from 400 to 420, we have

Government spending multiplier = 1 / (1 – MPC)

(3) If government cut tax to 380, what is the new equilibrium income? What is the multiplier for

government tax policy?

Tip: recall the multiplier for tax policy in your notes (slides).

Answer: after G increases from 400 to 420, we have

Government spending multiplier = - MPC/(1 – MPC)

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Question 3.

Suppose in a country A, its economy can be described as the following equations,

 Y = C + I + G; national output or GDP.

 C = 100 + 0.5 (Y-T); consumption, marginal propensity to consume MPC = 0.75.

 I = 150 – 10 * r; investment which is a negative function of real interest rate (r).

 (M/P)d = Y - 30 * r; real money demand which is adjusted by price level (inflation).

 G = 200; government spending.

 T = 200; tax.

 M = 2,400; money supply.

 P = 4; price level.

(1) With the equations above, try to derive the IS curve.

Tip: recall IS curve represent the relation between national output (Y) and real interest rate (r) in

goods market. So to derive IS curve, you need to put all components of Y together and find its

connection with r.

Answer:

Y = C + I + G. Here C = 100 + 0.5 (Y-T); I = 150 – 10 * r; G = 200 and T = 200.

(2) Use the same equations, now try to derive the LM curve.

Tip: recall LM curve represent the relation between national output (Y) and real interest rate (r)

in money market. So to derive LM curve, you need to consider money supply and demand.

Answer:

(M/P)d = Y - 30 * r and M = 2,400 and P = 4.

(3) What are the equilibrium level of national output (Y) and the equilibrium interest rate (r)?

Tip: recall the IS-LM model represent the short-run equilibrium in both goods market and money

market. The intersection of the IS curve and the LM curve satisfy conditions for equilibrium in

the two markets. You can get equilibrium interest rate (r) and equilibrium level of output (Y).

Answer:

At equilibrium, IS = LM.

(4) If price level (P) increases from 4 to 6, which curve would shift in this case, the IS curve or

the LM curve? What would happen to the new equilibrium interest rate (r) and equilibrium level

of output (Y)?

Tip: this question practices how to derive aggregate demand (AD) curve, which presents a

negative relationship between price level (P) and national output (Y).

Answer:

In this question, the only change comes from price level (P). So the IS curve remains the same.