Question 2 (31 pts.) Consider a representative individual who lives for two periods with preferences U(C1,C2) = C1C2 over current consumption C1 and future consumption C2. In period 1, they face a budget constraint Cits Yi and in period 2, C2 Y, find the interest rate that will induce the representative individual to save instead of to borrow. h) (2 pts.) Is your result in g) consistent with the policy prescription of subsidized interest rates? i) (2 pts.) Convert the aggregate production in the Harrod-Domar model into the corresponding per capita production function. j) (2 pts.) Derive the growth rate of output in the Harrod-Domar model. k) (2 pts.) Briefly explain why there is an inconsistency between the predictions of the Harrod- Domar and the microeconomic optimization problem. 1) Foreign aid might be used to generate economic growth. Briefly describe Easterly's two-step procedure of testing for the causal mechanism implied by the Harrod-Domar model. i. (3 pts.) Step 1: If foreign aid is partially effective, specify the assumption to be tested, the population regression function and the statistical hypothesis. ii. (3 pts.) Step 2: If foreign aid is not effective, specify the assumption to be tested, the population regression function and the statistical hypothesis