Question

The natural rate of unemployment and the natural level of output.

Suppose that the firms’ mark-up over costs is 5% and the wage-setting equation is W = P (1 − u) where u is the unemployment rate.

(a) What is the real wage as determined by the price-setting relationship?

(b) Solve for the natural rate of unemployment, that is, the rate of unemployment at the real wage determined by the price-setting relationship.

(c) Assume the production function is Y = N, and the total labour force is equal to When employment equals N, solve for the natural level of output. In = N where employment is at the natural rate (1 − un)L.

(d) Suppose the mark-up of prices over costs increases to 10%. What happens to the natural rate of unemployment? Explain the logic behind the answer and the sense in which there is nothing “natural” about the natural rate of unemployment.

Answer 1

a)

Price setting relationship or equation is

P = (1 + )W  

= mark-up of prices over cost

= 5% = 0.05  

P = (1 + 0.05)W

P = 1.05W

P/W = 1.05

W/P = 1/1.05  

W/P = 100/105

W/P = 20/21

So real wage determined by price setting relationship is 20/21

b)

Wage setting equation

W = P(1 - u)  

W/P = 1 - u  

In equilibrium

(W/P)_WS = (W/P)_PS  

1 - u = 20/21

1 - 20/21 = u  

1/21 = u  

u = 0.0476 or 4.76%

therefore natural rate of unemployment (u_n) is 4.76%  

c)

Y = N  

N = (1 - u_n)L  

= (1 - 0.0476)L

= 0.9524L

Y = N  

Y = 0.9524L  

Natural level of output is Y = 0.9524L

d)

Now mark-up of prices over cost increases from 5% to 10%  

So price setting equation would be

P = (1 + )W  

P = (1 + 0.10)W

P = 1.1W

W/P = 1/1.1

W/P = 10/11

Wage setting equation

W = P(1 - u)  

W/P = 1 - u  

In equilibrium

(W/P)_WS = (W/P)_PS  

1 - u = 10/11

1 - 10/11 = u  

1/11 = u  

u = 0.0909 or 9.09%  

Natural rate of unemployment (u_n) is 9.09%

Thus as mark-up of prices over cost increases from 5% to 10% , natural rate of unemployment increases or goes up from 4.76% to 9.09%