Consider an asset paying 1 next period and 2 in two periods. Suppose that the one-period rate

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Question 1

Consider an asset paying 1 next period and 2 in two periods. Suppose that the one-period rate is 4% and that it will remain constant. Show that a price of 2.5 is not an equilibrium price for this asset.

Question 2

Suppose that the annual rate of interest is 4%

(a)  What is the monthly rate?

(b) Consider a 3-year lease on a car that is worth $20,000 today. The first payment on the lease is next month. After 3 years the price of the car is estimated at $15,000. What should the monthly rent be?

Question 3

Consider an economy where individuals live for 2 periods and have preferences represented by

ln(c)+0.9ln(c’)

where c and c’ represent consumption in the first and second period, respectively. Income is denoted y in the first period and y’ in the second. The real interest rate is denoted r. Compute the individual’s optimal consumption in the first period, and the second period, as well as saving (or borrowing) when r=0.1 and

(a)  y=y’=1

(b) y=0, y’=1

(c)  y=1, y’=0

(d) y=0, y’=1.1

(e)  Compare and explain your findings for the two last cases.