Question 3 Bunter will live for two periods. His income in period 1 is denoted I. He can spend it on cake (that can only be consumed and not saved) or save it till period 2 (or any combination of the two). Any income that is saved till period 2 earns an interest rate of r. Bunter's income in period 2 is also I. All cash in period 2 will be spent on cake in period 2. The per unit price of cake in period 1 is $1 and its price in period 2 is p. Bunter derives utility from consuming cake only. If q is the amount of cake consumed by Bunter in period 1' = 1, 2, his utility function is denoted U(c1, Cg) = log (:1 + log Cg. 1. Write down the optimization problem that Bunter must solve to maximize his utility. 2. Determine the optimal amount of cake that Bunter will consume in each period as a function of I, r and p. 3. As r increases What happens to the amount of cake Bunter consumes in period 1