Suppose that an economy consists of 100 households, 50 of which have no income i

Question

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 no income of $40,000 in period 1 and no income in perod 2. Assume that the price of the good in $1 in both periods. Suppose that each household decides that its consumption in period 1 will equal one-half that 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?

Explanation / Answer

present value for first 50persons = 0 + 50000/(1+r) PV of 2nd 50 persons = 40000 + 0/(1+r) for equilibrium value of interest rate 50000/(1+r) = 40000 r= 25% in period 1 consumption 0-50 : 50000/(1.25*2) = 20000 saving = 0 as no income in period 1 50-100 : 20000 saving = 30000 (50000 in period 1)

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