Question 3 Charlie has an income of 100, 000 each in both period 1 and period 2. His utility function is given by U(C1, C2) = (738635 , where Cl and 5'2 denote the amount he spends on consumption in period 1 and period 2 respectively. (a) Write an equation that describes Charlie's budget constraint when the interest rate for borrowing and lending is 2% and there is no inflation. If Charlie chooses the optimal amount of borrowing or saving, how much will he consume in each period? Show the budget constraint and indifference curve passing through his consumption choice diagrammatically with C1 on the horizontal axis. (15%) (b) Calculate and explain Charlie's optimal consumption choice in each period if the interest rate increases to 20% and show this on your diagram. (20%) (c) Calculate the interest rate that would result in Charlie choosing the same level of consumption in both periods. Provide an intuition for your answer. (15%)