M & B 4th Edition by Dean Croushore

Exercise 2

An economy has 75 households, all of which have incomes of $25,000 each in period 1, 50 of which have incomes of $40,000 each in period 2, and 25 of which have incomes of $20,000 each in period 2. Assume that the price of the good is $1 in both periods. Suppose that each household decides that its consumption in period 1 will equal 50 percent of the present value of its income from both periods.
a Find the equilibrium value of the interest rate.
b Now suppose instead that each household will consume 60 percent of the present value of its income from both periods in period 1. Now what is the equilibrium value of the interest rate?
c Finally, suppose that each household's period 1 consumption equals one-half the present value of its income from both periods, but everyone's income in period 1 is lower: just $20,000. What is the equilibrium value of the interest rate now?