Question

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 Wt 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).

Answer 1

Assumption taken: Inflation, Expected inflation and Markup are not too large.

Since, the derivation involves use of subscripts and superscripts simultaneously, I am attaching a picture for clarity.

In Continuation, the concluding steps

Lastly, the value of Natural Rate of Unemployment Un is derived as follows