Question

1. 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.

2. (a) 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

Price setting

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

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 is 4.76%  

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 is 9.09%

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