**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-U^{vol})

where RP_{-1} is the past year’s rate of
change in prices, U, is total unemployment, and U^{vol} 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-U^{vol})

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=U^{vol}=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.