Solve natural rate of unemployment-natural level of output

Question

Assignment:

AS-AD Model

Consider the following extension to the problem above. All the information in the previous problem will hold here so that the AD curve will be your answer from Question 2.3. However, the following information relevant to aggregate supply is given below:

Production function:            Y = N

Wage Setting relationship:   w = p^e z/u

                                       z = 1 /16

Price setting relationship:     P = (1 +m)w

                                       m = 0.6

Unemployment rate:            u = U/L

Unemployment level:           U = L - N

                                      L = 20

where Y is real output, N is the number of employed workers, to is the nominal wage, Pe is the expected price level, P is the price level, u is the unemployment rate, U is the number of unemployed workers, L is the size of the labor force, and z is our catch-all variable for other labor market conditions.

1. Solve for the natural rate of unemployment and the natural level of output.

2. Derive the AS curve; this should be an equation with P, Y, and P^e in it.

3. Suppose P^e - 72, what are P and Y? Is this a medium run equilibrium?

4. Given your answers above, do you expect P^e to rise or fall? Explain.

5. Suppose P^e = 12, what are P and Y? Is this a medium run equilibrium?

6. Given your answers above, do you expect P^e to rise or fall? Explain.

7. Solve price level P that corresponds to the medium-run AS-AD equilibrium:

8. Provide an AS-AD graph showing the above changes in P^e.