Question

Joan is endowed with $200 in year one and $200 in year two. She can borrow and lend at an interest rate of 5% p.a. Joan has a utility function given by U(C1,C2) = -e^-aC1C2 (a) Write down Joan’s marginal rate of inter-temporal substitution and budget constraint. (b) Find Joan’s optimal consumption bundle (C1* and C2*). Is Joan a borrower or a lender? What is the value of her utility function at the optimal bundle if a= 1/10000? (c) Suppose that the interest rate Joan faces falls to 2% p.a.? What consumption bundle will she choose under these conditions? What is the value of her utility function at the new optimum?

Answer 1

A. It won’t change your answer. You earn all your income in period 1 and have to save to consume in period 2. so only the lending rate is relevant for the analysis here and that is unchanged.

B. Period One:-C1< 100000

Period Two :- C2 < [100000-C1] 1+r)

Here period 2 budget constraint encompasses period 1 budget constraint and after reaaranging the overall budget constraint can be written as

C1+ 1/ C2< 100000

C. Budget Constraint is:-

C1+1/1.2(C2)< 100000

now UC2=1/1.2=5/6

WHICH IS LESS THAN PART b) EFFECTIVE PRICE OF UC2

SO UC2 HAS DECREASED FROM 10/11 TO 5/6

Both budget lines interest are on same axis so their interest differ accordingly.