Problem 1

Imagine an asset that will pay $110 dollars in one year. The interest rate is 10%.

1. What is the present value of the asset’s cash flows?
2. Suppose the asset is selling for $50. Is there an arbitrage opportunity? If so, what is the arbitrage?

Problem 2: Consider the two-periods problem of the representative consumer and assume the consumer has current-period income y = 150, future income y’ = 180, current and future taxes t = 40 and t’ = 48, respectively, and faces a market real interest rate of r = 0.2 (or 20% per period). The consumer’s preferences over c and c’ are represented by the following utility function:

U(c, c’) = log c + log c’

1. What is the budget constraint of the consumer in period 1? What is the budget constraint of the consumer in period 2?
2. Combine the two period budget constraint into a lifetime budget constraint.
3. Show the consumer’s lifetime budget constraint and indifference curves on a diagram (label the axes clearly).
4. Calculate his or her lifetime wealth, optimal current-period and future-period consumption, and optimal saving. Show these values on your diagram. Is the consumer a lender or a borrower?
5. Suppose that everything remains unchanged, except that now t = 10 and t’ = 84. Calculate the effects on current and future consumption and on optimal saving and show this on your diagram. Explain your results in light of the Ricardian Equivalence Theorem.
6. If the interest rate decreases to 10 percent, by how much lifetime wealth, current consumption, future consumption and savings change?
7. Does your answer to question 7 depends on whether the consumer is a borrower or a lender? Justify.

Price: $14.32

Solution: The downloadable solution consists of 7 pages, 732 words and 2 charts.
Deliverable: Word Document