The Phillips curve, supply shocks, and wage flexibility

Suppose that the Phillips curve is given by = ( ) (1)

where the natural rate of unemployment, = (+) / .

[Recall that this Phillips curve was derived under price-setting and wage-setting:

= (1 + ) (2)

= (1 + ) (3)

where m is the mark up over marginal cost, which is just the wage rate when output is assumed to simply equal employment: =

We can think of as a measure of wage flexibility---the higher is , the greater is the response of the wage to a change in the unemployment rate, . z represents other factors affecting wage bargains.]

a. Explain how you obtain (1) from (2) and (3).

b. Suppose = 0.5 and z = 0.01. What is the natural rate of unemployment if m = 0.05? If m = 0.06? What is the relation between m and the natural rate of unemployment, and explain why?