Suppose a closed economy has reached its steady state, with a constant growth rate of real production per capita equal to the technological growth rate g. The first order condition (Euler equation) for the representative households optimal consumption is U (Ct) U (Ct+1)/(1 + ) = 1 + rt+1 where the period utility function U is the natural logarithm function U(Ct) = ln(Ct), Ct is consumption in period t, rt+1 is the real interest rate between period t and t + 1, and the subjective discount rate is = 0.02.

(a) What is the long run real interest rate r if g = 0?

(b) What is the marginal rate of substitution MRS of future consumption for current consumption?

(c) What is the long run real interest rate r if g = 0.01?

(d) Suppose that the real return is taxed at the rate = 0.5, and that g = 0.01, What is the long run real interest rate r?

(e) Suppose instead that the mafia extracts a fraction per year on all savings and its return, i.e. the mafia takes (1 + r). There are no taxes ( = 0), g = 0.01 and = 0.08. What is the long run real interest rate r?