Exercise 9.31. Consider an economy with aggregate production function Y (t) = AK (t) 1 L(t)

Exercise 9.31. Consider an economy with aggregate production function Y (t) = AK (t) 1−α L(t) α . All markets are competitive, the labor supply is normalized to 1, capital fully depreciates after use, and the government imposes a linear tax on capital income at the rate τ , and uses the proceeds for government consumption. Consider two specifications of preferences:

• All agents are infinitely lived, with preferences X∞ t=0 βt ln c (t) • An overlapping generations model where agents work in the first period, and consume the capital income from their savings in the second period. The preferences of a generation born at time t, defined over consumption when young and old, are given by ln cy (t) + β ln c0 (t) (1) Characterize the equilibria in these two economies, and show that in the first economy, taxation reduces output, while in the second, it does not. (2) Interpret this result, and in the light of this result discuss the applicability of models which try to explain income differences across countries with differences in the rates of capital income taxation.