3. Suppose that there are two periods, today and tomorrow, and that there is only one good, whose price is 2 per unit that is same for both today and tomorrow. Let m be the amount of consumption of the good today, and y be the amount of consumption of the good tomorrow. The utility function Ma}, y) of the consumer is given by the following: u(m,y) : lnm+6lny Fix the income of the consumer to be 100 for both time periods so that using the notation in the lecture, I : I' : 100. Let 1" : 0.5 be the interest rate that applies when the consumer either borrows or saves money. (a) Let 6 : 0.5. Write down the intertemporal budget constraint. (b) Let 6 : 0.5. Find m and y that maximize the utility function given the intertemporal budget constraint in (a). (c) Based on the answers in (b), is the consumer borrowing or saving money today? ((1) There is a cutoff value of (3* such that if 6 6*, the utility maximizing m and y imply that the consumer is saving money today. Find such 6*. (Hint: Think about the utility maximization condition. Because the prices are the same today and tomorrow, how should :1: and y be related when the consumer is borrowing?)