Consider a consumer who has preferences given by U(c1, C2) = In(c1) + BIn(c2)The consumer starts life with no wealth, receives nominal wage income y1 and y2 in the two periods in which they live and can save (but not borrow) an amount b2 at a nominal interest rate i. Let P1 and P2 denote the price levels in the two periods. (a) Write down the consumer's problem (this should now have three constraints). (b) Take the three first-order conditions. (c) Suppose y1 = 100, y2 = 100, B = 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? [Hint: Find the optimal consumption c1 as a function of r assuming that the borrowing constraint does not bind. Then, find r such that indeed, b2 2 0 or c1