Question

(30 marks) Jane lives for two periods. In the first period of her life she earns income Y1. The value of Y1 was determined by your student number. In the second period of her life, Jane is retired and does not earn any income. Jane’s decision is how much of her period one income should she save (S) in order to consume in period two. For every dollar that Jane saves in period one she has (1 + r) dollars available to spend in period two, where r is the interest rate?

Jane gets utility from consumption in period one (given by C1) and in period two (given by C2) according to the following utility function:

U(C1, C2) = ln(C1) + β ln(C2)
where the value of β ws determined by your student number. Given this utility function

Jane’s marginal utility from consumption in period one is given by: MUC1 = ∂U = 1

∂C1 C1
and her marginal utility from consumption in period two is given by:

MUC2 = ∂U = β ∂C2 C2

The parameter β describes how impatient Jane is. The lower the value of β the more she prefers consumption in the present (period one) to consumption when retired (period two).

1. (a) What is Jane’s budget constraint in period one? What is her budget constraint in period two?

2. (b) Combine these two budget constraints in order to have a single budget constraint that relates C1 and C2 to Jane’s income and the interest rate.

3. (c) Assume Jane is currently saving exactly 40% of her income in period one. Could she increase her utility by increasing or decreasing the amount she saves? Carefully explain your answer.

4. (d) Solve for Jane’s optimal choice of savings, and how much to consume in periods one and two.

Answer 1