4 Two-period model using math - with a borrowing constraint Consider the following two-period model with log utility functions: Manitoba2 111(01) + [3111(02) 02 Y2 .. :Y 3t01+1+r l+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 2 0, or in other words C] 5 Y1. 1. Suppose Y1 = 100, Y2 = 100, r = 0.05, and ,6 z 0.95. Determine the Optimal values of 01 and Oz. (Hint: First solve the problem ignoring the borrowing constraint. Then compare 01 and Y1, and think about how the borrowing constraint would afict C1 and 02.) 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 01 and CZ. 3. No suppose we no longer have a borrowing constraint, 216. C] can be larger than Y1. How does the solution change your solutions for (l) and (2). Explain your answer in words