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An individual lives for two periods. She receives income yl in period and y2 in period 2. Her period utility function is: u(c) = In C She discounts the future at the rate [3 and can save/ borrow at the rate R. If she saves in the rst period, her consumption in period 2, 02, will be a sum of her income in period 2 and the return on her savings. Assume there are no restrictions on savings. (a) What are the budget constraints for period 1 and period 2? (b) What is the intertemporal budget constraint? Interpret. (0) Write down the consumer's optimization problem. ((1) Solve for optimal c1 and (:2 assuming 5(1 + R) = 1. (e) Assume y1 = 100, y2 = 200, and R = 0.10. What is the value of c1 and C2. What is 31? (f) Suppose the government gives the consumer $40 in period 1 and nances it by taking away $40(1 + 0.10) in period 2. How does it affect consumption period 1 and 2? (g) Now assume that the consumer can not borrow, i.e., 31 2 0. Solve for the optimal consumption in two periods. (h) How does your answer to part (f) change? (i) How would your answer to part (g) change if :91 = 200 and y2 = 100? (Think about whether the borrowing constraint binds)