5. (Appendix 11.A) Consider an economy in which all workers are covered by contracts that specify the nominal wage and give the employer the right to choose the amount of employment. The production function is Y = 201N, and the corresponding marginal product of labor is MPN =10/2N.

Suppose that the nominal wage is W = 20.

a. Derive an equation that relates the real wage to the amount of labor demanded by firms (the labor demand curve).

b. For the nominal wage of 20, what is the relationship between the price level and the amount of labor demanded by firms?

c. What is the relationship between the price level and the amount of output supplied by firms?

Graph this relationship.

Now suppose that the IS and LM curves of the economy (the goods market and asset market equilibrium conditions) are described by the following equations:

IS curve Y = 120 - 500r.

LM curve M>P = 0.5Y - 500r.

d. The money supply M is 300. Use the IS and LM equations to derive a relationship between output, Y, and the price level, P. This relationship is the equation for the aggregate demand curve.

Graph it on the same axis as the relationship between the price level and the amount of output supplied by firms (the aggregate supply curve)

from part (c).

e. What are the equilibrium values of the price level, output, employment, real wage, and real interest rate?

f. Suppose that the money supply, M, is 135. What are the equilibrium values of the price level, output, employment, real wage, and real interest rate?