Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and retires in period 2 (and gets income Y2 < Y1). This consumer has the usual preferences over time: u(C1) + u(C2)

1. Assume this consumer cannot save. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve.

2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse of? Could the consumer be better of? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save.

3. Assume once again that a consumer cannot save, but can buy some MacGuffins, which have no consumption value, but can be transported to the next period and sold by the next period price. Assume that MacGuffin costs P1 > 0 in the first period and is expected to cost P 2 in the second period. Write down the new budget constraint. Would a consumer buy a MacGuffin? What is the condition on the P 2? Is P 2 a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?Write down the new budget constraint. Would a consumer buy a MacGuffin? What is the condition on the P 2? Is P 2 a fair price for a MacGuffin? Could the consumer be better off with a MacGuffin?