Question

Suppose the economy is characterised by the following equations: Price setting: P = (1+m) (W/A) Wage setting: W = Ae P e (1-u) where A is the unobserved and difficult to estimate technology parameter in the production function Y=AN, and Ae is its expected value. First suppose that expectations of both prices and technology are accurate.

Solve for the natural rate of unemployment and medium-run real wage rate if the mark-up, m, is equal to 10 per cent and A = 4.

Answer 1

Price setting P = (1 + m)(W/A)  

P/(1 +m) = W/A  

A/(1 + m) = W/P

  W/P = A/(1 + m)

wage setting W = AePe(1 - u)  

since expectations of both prices and technology are accurate therefore A = Ae and P = Pe  

W = AP(1 - u)

W/P = A(1 - u)  

In Equilibrium (W/P)PS = (W/P)ws  

A/(1 + m) = A(1 - u)

A/A(1 + m) = 1 - u  

1/(1 + m) = 1 - u  

u = 1 - 1/(1 + m)  

= (1 + m - 1)/(1+m)

= m/(1+m)  

m = 0.10  

u = 0.10(1 + 0.10)

= 0.10/1.1

= 0.09

natural rate of unemployment is 0.90

real wage W/P = A(1 - u)

= 4(1 - 0.09)

= 3.64