Question

In the labor market the wage rate requested by workers will generally depend on workers’ expected price P^e which is to prevail in the future, the current unemployment rate u, and a variable z that represents the unemployment benefits package. This defines the wage-setting relationship: W = P^eF(u,z). At the same time, firms define the price-setting relationship: P = (1+m)W, where m is the markup of goods prices over wage rate.

(1) Suppose we know the functional form F(u,z) = z(1-u) and z = 1; and the markup m = 5%. Calculate the natural rate of unemployment, i.e., the unemployment rate when the economy is at the medium-run equilibrium.

(2) Assume everything given in part (1) but now z = 1.05. That is to say, the government increases the unemployment benefits package. Calculate the natural rate of unemployment again.

(3) Assume everything given in part (1) but with a new markup m = 10%. Calculate the natural rate of unemployment again.

(4) Suppose that the unemployment benefits z = 1. Also assume the production function is Y = N and we know the definition of unemployment gives u = (L- N)/L, where N is the number of employed workers and L is the labor force. Also assume that the markup m = 10%, labor force L = 880 and the expected price P^e = 1. Derive the aggregate supply (AS) relationship, i.e. a relationship between the current price P and the output Y. How will current price P change if the output Y increases? Explain why in economic words.

(5) Place price P on the vertical axes and output Y on the horizontal axes. Draw the aggregate supply (AS) curve. Explain and illustrate on the graph what will happen to the AS curve if the expected price Pe increases.

(6) Suppose the goods market in a closed economy can be represented by the following equations:

C = 100 + .5YD
I = 200 + .1Y – 800i T = 200
G = 200
YD = Y – T

Also suppose in the money market of this closed economy, the real money demand is (M^d/P) = Y – 3,000i; and the nominal money supply is set by the FED at M^s = $500.

Derive the aggregate demand (AD) equation for this economy.

(7) Put AD and AS curve together to solve for the equilibrium output and price for this economy. Is this economy at the medium-run equilibrium?

Answer 1

Ans(1) Wage setting relation :

Price setting relation :

  

In the medium run, equilibrium is attained such that nominal wages depend on the actual price level, i.e., P = P^e .

From Wage setting relation,

(substituting P=P^e and value of F(z,u))

(z=1) (1)

From Price setting relation,

(m=0.05) (2)

Substituting eq(1) in eq(2) :-

This gives natural rate of unempoyment u = 0.05 or 5%.

Ans(2) Following the same procedure as in subpart (1), and replacing the vaue of z as z = 1.05, then the value of natura rate of unemployment is :-

With z = 1.05, the Wage setting relation becomes:

(3)

And, Price setting remains same as :-

(4)

So, by substituting expression (3) in eq(4), gives :-

u = 0.1 or 10%

Thus, natural rate of unemployment increases to 10% with the increase in unemployment benefits.

Ans(3) Again, folowing the same procedure as in subpart (1), replacing markup as m=10%

Price setting relation becomes :-

(5)

Wage setting remains same :-

(6)

From eq(4) and eq(5),

That gives, natural rate of unemployment as u = 0.09 or 9.09%.

Ans(4) To find the aggregate supply relation, lets modify the given equation by using the given expression Y = N.

or    (7)

The Wage setting relation is:

Substituting expression (7) in the above equation

(8)

Putting this value in price setting relation equation as:

(9)

or, or for z=1 & P^e =1   

The above equation represent the reationship between the output and the price level, i,e the aggregate supply function. As output increases, number of employed workers (N) increases, that reduces the unemployment rate (u), and thus increases the wages as more number of people are employed. As wages increases, the price increases.

Hence, as output increases,the price also increases.  

Ans(5) The following figure shows curve AS₁ that represents the relation between the price and output. Now as expected price increases from P^e to P^e* as shown in the diagram , nominal wages increases, which in turn increases the price level, and finally lead to leftward shift in the Aggregate Supply curve i.e AS₁ to AS₂

Ans (6) When both IS and LM curve attains the equilibrium, one can find the expression for Aggregate demand.

That is by , AD=C+I+G and where Money demand equals Money suppply.

Ans(7) Medium run equilibrium is the one in which AS curve shifts in such a way that natural level of output is attained. So, as AS adjusts gradually, firms increases their expected prices tp a level at which natural evel of output is achieved. Hence, in this subpart, one can draw an upward sloping AS curve as drawn in subpart (5) and downward sloping AD curve by using expression in subpart (6). And, the intersection point od two curves will determine the equiibrium level of output and equilibrium level of prices and if expected price is equal to th eactual prices, then one can say that economy is in medium run equilibrium.