14.02    Principles of Macroeconomics

Problem Set 7

Due:  Wednesday, November 15, 2000

Part 1.  True/False/Uncertain.  Explain your answer carefully.  (12 points, 3 points each.)

1. The Natural Rate of Unemployment is fixed and cannot be changed.
2. If the price level rises more than expected, workers receive lower real wages than they expected to have.
3. The unemployment rate is the percentage of adults without a job, and thus is the best indicator of available workers in the economy.
4. In the absence of fiscal or monetary policy changes, the economy will always remain at the natural level of output.

Part 2.  Labor Market Equilibrium (28 points)

In a certain economy, wages are set according to the following equation:

W = APz(1 – u),

where W is wages, P is prices, u is the unemployment rate, and z captures other factors involved in wage setting.  Prices are set:

P = (1 + m)W,

where m is the markup of price over cost.  Output is Y = AN.  The labor force is L.

1. Solve for the equilibrium unemployment rate, real wage, and output.
2. Suppose that the government mandates that all employers provide their workers with health insurance.  Assuming they weren’t already doing so, what parameter should this change?  What will be the direction of the effect on unemployment?  On real wages?  On prices?
3. A more laissez-faire government is elected.  This government has a much more lax anti-trust policy than the old one, and the price markup rises as a result.  What will be the direction of the effect on unemployment?  On real wages?  On prices?
4. There is a technological innovation that makes workers more productive.  As a result, A rises.  What will be the direction of the effect on unemployment?  On real wages?  On prices?

Part 3.  Aggregate Supply – Aggregate Demand (30 points)

An economy is described by the following equations:

Y = C + I + G

C = c0 + c1(Y – T)

I = I0 – I1i

M = PY(1/i)

Y = AN

W = PeAz(1-u)

P = (1 + m)W

L = 1

1. Find the natural level of unemployment, the natural level of output, the actual output and the actual unemployment.  Derive the Aggregate Supply curve, and show that the AS curve slopes in the correct direction.
2. Derive the Aggregate Demand curve as a function of G, T, M, and the price level.  Show that it slopes in the correct direction.
3. Graph your results (and the equilibria) in (i,Y) space and in (P,Y) space.
4. A change in federal labor law gives unions greater bargaining power with employers.  This raises z.  What are the new natural rates of unemployment and output?  Assume that Pet+1 = Pt.  Show the changes in (i,Y) space and in (P,Y) space.  What happens in the long run?
5. How do these changes compare to the effect of an increase in A?  Which would workers prefer?
6. The Central Bank is worried about inflation and is determined to keep the price level constant.  What should it do in the short run?  Can it continue this in the long run?