13 Suppose that an economy consists of 100 households, 50 of which have no income in period 1 and income of $50,000 in period 2 and 50 of which have income of $40,000 in period 1 and no income 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 one-half the present value of its income from both periods. Find the equilibrium value of the interest rate. How much does each household save in period 1 and consume in each period?