†† Problem Set 7 Solutions

††

†† 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.

 

False.The natural rate of unemployment depends on labour market institutions (captured in z) and the markup rate, both of which may change.

 

†† 2. If the price level rises more than expected, workers receive lower

†† real wages than they expected to have.

 

True.Real wages are W/P.If the denominator is larger than expected, the real wage is lower than expected.

 

†† 3. The unemployment rate is the percentage of adults without a job and

†† thus is the best indicator of available workers in the economy.

 

False.It is the percentage of people in the labour force without a job.It may not be the best indicator of available workers since it does not count discouraged workers (the unemployed who want to work, but are not actively looking for a job and so are not included in the labour force).

 

†† 4. In the absence of fiscal or monetary policy changes, the economy

†† will always remain at the natural level of output.

 

False.Due to shocks (e.g. the oil price shocks of the 1970's) the economy does not remain at the natural level of output even in the absence of policy changes.

 

 

†† 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/A,

†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††

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.

 

u=1-1/[(1+m)z], W/P=A/(1+m), Y=A(1-u)L=AL/[(1+m)z].

 

(Or, using the incorrect price setting equation, P = (1 + m )W, you would get:

u=1-1/[(1+m)zA], W/P=1/(1+m), Y=A(1-u)L=L/[(1+m)z].)

 

†† 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?

 

You could argue many ways of modeling this. Since itís an increase in benefits, we could model this as an increase in z.If you think of it as similar to the increase in the price of oil, i.e. an increase in non-wage costs of producers, then you model it as a rise in the markup.Finally, you might think that now that workers are receiving health care from their employers they are willing to work for a lower wage, so it is best modeled by a decrease in z.

 

From the formulas in question 1 we can see:

An increase in z results in an increase in u andno change in W/P.

††††††††††††††† A decrease in z results in a decrease in u and no change in W/P

††††††††††††††† An increase in the markup results in an increase in u and a decrease in W/P.

In all cases, prices are not determined in the labour market, so we can not specify an effect on the price level.

 

(The answer is the same with the incorrect price setting equation.)

 

†† 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?

 

An increase in the markup causes u and W/P fall, we can not specify an effect on prices.

 

(The answer is the same with the incorrect price setting equation.)

 

†† 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?

 

This has no effect on unemployment, but both output and real wages rise.

 

(With the incorrect price setting equation, this would have no effect on the real wage or output, but would cause unemployment to rise.)

 

†† 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/A

†††††††††††††††††††††††††††††††††† 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 it has the slopes in the correct

†† direction.

 

Note that the labour market equations are the same as in Part 2: so un=1-1/[(1+m)z], Yn=A/[(1+m)z].

Actual output is Y=A(1-u)=AP/[(1+m)Pez] and actual unemployment is u=1-Y/A=1-P/[(1+m)Pez].

The AS curve is P=Pe(1+m)z(1-u)=Pe(1+m)zY/A, which is clearly upward sloping.

 

(With the incorrect price setting equation: un=1-1/[(1+m)zA], Yn=1/[(1+m)z].

Actual output is Y=A(1-u)=AP/[(1+m)Pez] and actual unemployment is u=1-Y/A=1-P/[(1+m)Pez].

The AS curve is P=Pe(1+m)Az(1-u)=Pe(1+m)zY, which is clearly upward sloping.)

 

†† 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.

 

Goods market equilibrium yields: Y=(B-I1i)/(1-c1) where B=c0-c1T+I0+G

Financial market equilibrium yields: M=PY/i

Combining these we get: Y=B/(1-c1+I1P/M), which is downward sloping in Y,P space.

 

†† 3. Graph your results (and the equilibria) in (i,Y) space and in (P,Y) space.

 

You do not need to solve for the expression for the equilibrium, but you should show that Yn,Pe is a point on the AS curve.

 

†† 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?

 

This is the same as in Part 2: the natural rate of unemployment rises and the natural level of output falls.For given Pe, Y falls so the AS curve shifts to the left.The dynamics are those shown on page 142 of the text in figure 7-11.In the long run, the AS curve passes through the AD curve at the natural level of output, so output has fallen and prices have risen.Note that the AD curve does not move.Also note that in equilibrium the real wage is unchanged (it still equals A/(1+m)).

 

5. How do these changes compare to the effect of an increase in

†† A? Which would workers prefer?

 

An increase in A shifts the AS curve to the right and leaves the AD curve unchanged.Unemployment is unchanged, prices fall, and output increases.Note that workers are receiving a higher real wage.So workers would definitely prefer an increase in A over an increase in z.

 

(However, if you used the incorrect price setting equation you would have gotten that A is not in the AS curve (or the AD curve), so a change in technology does not move output or prices.Note that, as in part 2, real wages are unchanged but unemployment is higher.So it is not clear what workers would prefer, it depends on which case has the smaller increase in unemployment.Note that output is higher in the technology case, but leaving A out of the price setting equation means that the change is like an increase in the markup: firms get all of the benefits from the improvement in technology.)

 

†† 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?

 

If the central bank is concerned with price stability then it must accommodate money supply in such a way that the AD schedule shifts and intersects the new AS schedule at the old price level.Thus we need an expansionary monetary policy in order not to have deflation as in part 5.Since prices don't change the new price level is at the level of expectations and we thus know that the equilibrium is already at the natural level of output and thus the AS curve will no longer shift.There are no further pressures on prices and price stability is maintained in the long run (actually there is no difference between long and short run in this case).

 

(With the incorrect price setting curve, prices havenít moved so the question is pretty meaningless.If you answer it for a change like in 4, however, you get a very similar answer to the one given above.)