M&B3 3rd Edition by Dean Croushore

Exercise 4

Suppose that conditions in the economy are such that the after-tax expected real interest rate is described by the equation

where a is a number that depends on how people value their consumption in one period compared with another period, and g is the growth rate of the economy. The number a equals 1 when people prefer consumption to be balanced, with the same amount of consumption each period; a may be bigger than 1 when people prefer consumption today over consumption in the future, with a being larger and larger the more impatient people are.
a Suppose that a _ 2, g _ 0.02, the infl ation rate is expected to be steady at _ 0.03, and the tax rate is 0.40. What are the values of the equilibrium nominal interest rate and the before-tax expected real interest rate
b Beginning with the situation in part a, if the growth rate of the economy increases to 0.04, what are the new values of the equilibrium nominal interest rate and the before-tax expected real interest rate
c Beginning with the situation in part a, if the tax rate in the economy is reduced to 0.25, what are the new values of the equilibrium nominal interest rate and the before-tax expected real interest rate
d Beginning with the situation in part a, if the expected infl ation rate declines to 0.01, what are the new values of the equilibrium nominal interest rate and the before-tax expected real interest rate
e From these results, what general conclusions can you draw about the relationship between the nominal interest rate and the rate of economic growth, the tax rate, and the infl ation rate What about the relationship between the before-tax expected real interest rate and the rate of economic growth, the tax rate, and the infl ation rate