Two-period model using math - with a borrowing constraint Consider the following two-period model with log utility functions: M axC1,C2 ln(C1) + ln(C2) s.t. C1 + C2 1 + r = Y1 + Y2 1 + r Suppose that this household faces a borrowing constraint in period 1. Because they cannot borrow in period 1, it must be the case that S 0, or in other words C1 Y1. 1. Suppose Y1 = 100, Y2 = 100, r = 0.05, and = 0.95. Determine the optimal values of C1 and C2. (Hint: First solve the problem ignoring the borrowing constraint. Then compare C1 and Y1, and think about how the borrowing constraint would affect C1 and C2.) 2. Now, suppose that r rises to r = 0.1, while we still have Y1 = 100, Y2 = 100, = 0.95. Determine the new optimal values of C1 and C2. 3. No suppose we no longer have a borrowing constraint, i.e. C1 can be larger than Y1. How does the solution change your solutions for (1) and (2). Explain your answer in words.