14.02 Principles of Macroeconomics

Problem Set 1

Posted: Wednesday, February 14, 2001

Due: Friday, February 23, 2001

Part 1:  True/False Questions: Decide whether each statement is true or false and justify your answer with a short argument.  (5 points each, 35 points total)

1.  The higher the share of youth in the population, the lower the non-accelerating inflation rate of unemployment.

2.  The full employment unemployment rate has typically been about 4% in the post-war period.

3.  As a rule of thumb, current conditions suggest that for every point that unemployment is below the full employment level, inflation will increase by 0.5 percentage points per year.

4.  The Federal Reserve’s only priority is attaining full employment in the economy.

5.  Exports can be larger than GDP.

6.  If the government cuts spending to reduce the deficit, the Fed will most likely raise interest rates to make sure the cut in spending doesn’t lead to inflation.

7.  Fiscal policy is more effective when consumers’ marginal propensity to consume is higher.

Part 2: Unemployment vs. Changes in Inflation (10 points each, 30 points total)

1.  Assume that the rate of change of wages, RW, follows the following equation:

RW = RP-1 + 2 - 1.5(U-Uvol)

where RP-1 is the past year’s rate of change in prices, U, is total unemployment, and Uvol is voluntary unemployment (all of the variables are measured in percentage points, i.e. U=6, not 0.06 for a six percent unemployment rate).

Why does the rate of change of wages depend on changes in the price level?  Why is there a constant in the equation?  Explain why the rate of change in wages depends on the difference between the unemployment rate and the voluntary unemployment rate.

2.  Assume that prices are set by firms according to the following equation:

P = K(W/A)

RK = - 0.5(U-Uvol)

RA = 2

where K is the markup.

What is W/A?  Is it a realistic assumption to assume that prices are a markup over only labor costs?  Why or why not?  Is the markup pro-cyclical or counter-cyclical?  Why might this be the case?

3.  Solve for the change in price inflation as a function of involuntary unemployment.  Is inflation in this economy more or less sensitive to excess demand than the U.S.?  If RP=12 and U=Uvol=5, what will the total unemployment rate have to be in the next year to get inflation down to 4% (recall, all of the variables are measured in percentage points)?  What unemployment rate is needed to achieve the inflation target in two years instead of one?  Do you think it would be better to reduce inflation in one year or two?

Part 3.  Fiscal Policy (Parts 1,  2, and 3, 5 points each; parts 4 and 5, 10 points each; 35 points total) (Chapter 3 of the textbook may be helpful in answering this question.)

Consider the following model of the economy:

C = 50 + 0.6(Y-T)

I = 10 +0.1Y - i

G = 100

X = M = 0

where C is consumption, Y is income, T is taxes, I is investment, i is the interest rate (measured in percentage points, i.e. an interest rate of five percent is i=5 instead of i=0.05), G is government spending, X is exports and M is imports.

1.      State the equilibrium condition for GNP (national income) and give a brief explanation of what it means.  Solve for national income as a function of the unknown variables, i and T.

2.      Now assume that the government budget is balanced, and write income as a function of the interest rate.  Plot this curve in i-Y space.  State and interpret the slope of this curve.

3.      Assume that i=10.  What is the value of autonomous spending?  What is the value of the multiplier?  Interpret the multiplier.

4.      The government decides to increase spending by 10.  If it doesn’t raise taxes, what will the new values of autonomous spending, the multiplier, and equilibrium income be?  Give a brief explanation of why income changed by as much or as little as it did.  If the government raises taxes at the same time to maintain a balanced budget, what will the new values of autonomous spending, the multiplier, and equilibrium income be?  Give a brief explanation of why income changed by as much or as little as it did.

5.      Now, instead of assuming that the government collects a fixed amount of taxes, assume that it collects a fixed percentage of national income: T=tY.  Assuming the tax rate, t, is one-third, solve for equilibrium income, autonomous spending, and the multiplier.  Explain any differences with your answers to part 2.  Is the government budget balanced?  What happens now if the government increases spending by 10?  State and briefly explain the changes in equilibrium income and the government budget deficit.