Assumptions: Pip=s income in the current Year 1 is $500, but after he comes into his inheritance his income in Year 2 will be $5,000. This is a two-period problem, so you do not need to assume anything about his income in future years after Year 2. (If you want to be morbid about it, assume he dies after Year 2.) Pip can borrow and lend (save) money at an interest rate = 0.2.
a) What is the present discounted value of Pip=s income? If he decides to consume nothing in Year 2, what is the maximum amount that Pip can consume in Year 1? Explain how he can consume that amount; i.e., explain how much he has to borrow and how much he pays back in principal and in interest in Year 2.
b) If Pip decides to consume nothing in Year 1, what is the maximum amount he can consume in Year 2? Explain how he can consume that amount; i.e., explain how much he has to save (lend) and how much he receives in principal and interest in Year 2.
c) Draw Pip=s budget line showing his opportunities to consume C1 in Year 1 (on the horizontal axis) and C2 in Year 2 (on the vertical axis). On your budget line, show the Polonius point (where Pip is neither a borrower nor a lender) and the points you calculated in a) and b).
d) Suppose Pip=s optimal choice of consumption in Year 1 is $2,545.45. Explain how much he borrows in Year 1 and how much he has to pay back in principal and interest in Year 2. How much does he consume in Year 2?
e) Draw an indifference curve consistent with the facts in d). What do we know about Pip=s marginal rate of time preference at his optimal choice? What do we know about Pip=s marginal rate of time preference at his Polonius point?