M & B 4th Edition by Dean Croushore

Exercise 9

Suppose that the demand for and supply of bonds both change with the state of the business cycle. In economic expansions, the demand for bonds is given by the equation

and the supply of bonds is

where r is the expected real interest rate. In recessions, however, both the demand for and supply of bonds is lower:

a Given these equations, what is the equilibrium expected real interest rate in economic expansions?
b Given these equations, what is the equilibrium expected real interest rate in recessions?
c If the expected infl ation rate is 4 percent in economic expansions, what is the equilibrium nominal interest rate in economic expansions?
d If the expected infl ation rate is 2 percent in recessions, what is the equilibrium nominal interest rate in recessions?