(WD) Wage-determination equation: W = P^e F(u,z)

(PD) Price-determination equation: P = (1+m) W

i. Using WD and PD, derive unemployment (u) as a function of prices, expected prices, markups and z, assuming F(u,z) = z - u.

ii. What is the relationship between prices and expected prices when the unemployment rate is at its natural level?

iii. Use the condition from (ii) to solve for the natural rate of unemployment (u_n).

iv. Let L represent the size of the labor force, and N the number of people employed. Using the production function, Y = N, write potential output (Y_n) as a function of the unemployment rate and the labor force.

v. Plot WD and PD on a graph, where the vertical axis is given by nominal wages (W), and the horizontal axis is given by the unemployment rate (u), and identify the natural rate of unemployment.

vi. Using your graph from (v), demonstrate how an increase in prices shifts PD. Label this curve PD'.

vii. Is the unemployment rate corresponding to the intersection of WD and PD' the new natural rate of unemployment? Explain.

viii. If expectations about prices are based on past values of prices, P > P^e corresponds to rising prices (i.e., inflation). Suppose P > P^e. Is the short-run unemployment rate implied by your equation from (i) greater than or less than the natural rate of unemployment?