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

Ra = a X g

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 a equals 1 when people prefer consumption to be balanced, with the same amount of consumption each period; a may be bigger than the one 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 inflation rate is expected to be steady at pi = 0.03, and the tax rate is .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 .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 inflation rate declings 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 inflation rate? what about the relationship between the before tax expected real interest rate and the rate of economic growth, the tax rate, and the inflation rate?