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 __________ ? 

What is the future value of his endowment? __________ . With blue ink, show the combinations of consumption this year and consumption next year that he can afford. Label Nickelby’s endowment with the letter E.

(b) Suppose that Nickleby has the utility functionU(C₁, C₂) = C₁/C₂. 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, C₂.)

(c) What is the slope of Nickleby’s budget line? ___________. 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%. __________. Also write down Nickleby’s budget equation _________.

(d) Solve these two equations. Nickleby will consume ________ units in period 1 and _________ units in period 2. Label this point A on your diagram. 

(e) Will he borrow or save in the first period? _________.How much ________?

(f) On your graph use red ink to show what Nickleby’s budget line would be if the interest rate rose to 20%. Knowing that Nickleby chose the point A at a 10% interest rate, even without knowing his utility function, you can determine that his new choice cannot be on certain parts of his new budget line. Draw a squiggly mark over the part of his new budget line where that choice can not be.

(g) Solve for Nickleby’s optimal choice when the interest rate is 20%. Nickleby will consume _________ units in period 1 and _________ units in period 2.

(h) Will he borrow or save in the first period? ___________.How much ________?