An Economy Has Fifty Households, All of Which Have Incomes

Essay

An economy has fifty households, all of which have incomes of $25,000 each in period 2.The twenty-five poor households have incomes of $10,000 each in period 1, while the twenty-five rich households have incomes of $20,000 each in period 1.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.Calculate the present value of income for poor households as a function of the interest rate.
Calculate the amount that poor households will spend on consumption, as a function of the interest rate.Calculate the amount that poor households will save as a function of the real interest rate.Show your work.

b.Calculate the present value of income for rich households as a function of the interest rate.
Calculate the amount that rich households will spend on consumption, as a function of the interest rate.Calculate the amount that rich households will save as a function of the real interest rate.Show your work.

c.Given the equations you calculated for savings for each type of household and assuming that the households borrow from each other, find the equilibrium value of the interest rate.Show your work.