Labor Market Question Part a) Let the price setting equation be given by p= (1+)

Question

Labor Market Question

Part a) Let the price setting equation be given by p= (1+)W and the wage setting equation be given by W = P^e(z/u), where z are unemployment benefits and u is the unemployment rate. Derive the real wage and unemployment consistent with equilibrium in the labor market in the medium run. Is this the natural rate of unemployment? Does the equilibrium rate of unemployment change if unemployment benefits increase?

Part b) Initially, the labor market is in equilibrium at wages Wo and prices Po with unemployment equal to uo. Suppose competition suddenly becomes less intense and firms increase their markups. In the short run, suppose P^e is fixed. What happens to the equilibrium real wage? Compare the equilibrium real wage in the short run and the medium run.

Part c) Suppose that the price setting equation also takes into account the price of energy (another input in production). In particular, P=(1+)(W)q^(1-a) where q is the price of one unit of energy. the wage setting equation is given by W=(P^e)* (z/u). Derive the real wage and unemployment consistent with equilibrium in the labor market in the medium run. Hoe does the equilibrium unemployment rate change when the price of energy increases? What is the intuition for this result?

Explanation / Answer

Part a) In the equilibrium, expected inflation (price level) should be equal to the current equilibrium (current price level). This implies P = Pe.

Real wage is adjusted for inflation so it is given by W/P = 1/(1+)

Now this implies that the new wage setting equation is W = P(z/u) or P = W(u/z).

Substitute this value of wage rate in price setting equation

P = (1+)W

W(u/z) = (1+)W

(u/z) = (1+)

u = z(1+)

Yes. This rate of unemployment is natural rate since it is the rate of unemployment that prevails in the market when the labor market is in equilibrium. When unemployment benefits, z, are increased, the natural rate of unemployment also increases, as the economic theory of labor market predicts. This is because the job finding rate decreases and job seperation rate rises when unemployment insurance increases.

Part b)

Markup is the profit percentage over and above the total cost that a particular firm desires for producing a commodity. It can be calculated by dividing the desired profits with the total cost of production. When markup is increased, the usually increases the price of its product, at the time in short run when wage contracts expects a price level to be fixed at Pe. If price level rises, real wage automatically falls in the short run.

In the medium run, however, labor contracts are revised so that the nominal wage rate acquires the same price level prevailing in the market so that real wage remains the same.

Part c)

In the equilibrium, expected inflation (price level) should be equal to the current equilibrium (current price level). This implies P = Pe.

Real wage is adjusted for inflation so it is given by W/P = 1/[(1+)*q(1-a)]

Now this implies that the new wage setting equation is W = P(z/u) or P = W(u/z).

Substitute this value of wage rate in price setting equation

P = W(u/z)

z/u = W/P

z/u = 1/(1+)*q(1-a)

u = z(1+)*q(1-a)

This is the unemployment rate that will prevail in the medium run. Increase in the energy prices, q, will increase the unemployment rate. Note that energy is an input in production so that higher energy prices simply suggests increased cost of production. Again, firm will pass on this increase in cost in the price level so, for a fixed price level, current price level rises. This reduces real wage in the short run, which means a higher unemployment rate in the short run.

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