Problem 8.6: Borrowing Constraints. {25 points) Consider a consumer who has preferences given by U{c1._ r32) = ln(c1) + [3111(62) The consumer starts life with no wealth. receives nominal wage income yl and yg in the two periods in which they live and can save (but not borrow) an amount I); at a nominal interest rate 2'. Let P1 and P2 denote the price levels in the two periods. (a) 1Write down the consumer's problem (this should now have three constraints). (b) Take the three rst-order conditions. (c) Suppose y1 = 100. gm = 100. 33 = 0.9, P1 = 1 and P2 = 1. What is the minimum real interest rate r such that the consumer's borrowing constraint is not binding? [Ilintz Find the optimal consumption (:1 as a function of 7' assuming that the borrowing constraint does not bind. Then, nd 3" such that indeed. b2 3: 0 or (:1 g yl] (d) Suppose the real interest rate is 0 (1 + \"r = 1). Find the optimal consumption (:1 and (:2. (e) Suppose the consumer's income in period 1 goes 11p by $1, i.e. y1 = 101. How does con- sumption change in the two periods? 'What is the slope of the consumption function at these parameters, i.e. what is 5