A. 10.3 (0) Nickleby has an income of $2,000 this year, and he expects an income of $1,100 next year. He can borrow and lend money at an interest rate of 10%. Consumption goods cost $1 per unit this year and there is no inflation. (a) What is the present value of Nickleby's endowment? $3,000. What is the future value of his endowment? $3,300. (b) Suppose that Nickleby has the utility function U(C1, 02) = CiQ. Write an expression for Nickleby's marginal rate of substitution between consumption this year and consumption next year. (Your answer will be a function of the variables C1, 02.) MRS = - 02/ C1. (0) What is the slope of Nickleby's budget line? -1.1. Write an equation that states that the slope of Nickleby's indifference curve is equal to the slope of his budget line when the interest rate is 10%. 1.1 = 02/01. Also write down Nickleby's budget equation. 01 + 0/1 .1 = 3, 000. (d) Solve these two equations. Nickleby will consume 1,500 units in period 1 and 1,650 units in period 2. (a) Will he borrow or save in the first period? Save. How much? $500. (1') Solve for Nickleby's optimal choice when the interest rate is 20%. Nickleby will consume 1,458.3 units in period 1 and 1,750 units in period 2. (h) Will he borrow or save in the first period? Save. How much? $541.7