Question

In a closed economy, people live two periods and maximize utility, U, with utility function U =C1*C2 . For this utility function, as we saw, the ratio of marginal utility of consumption in period 1 to marginal utility of consumption in period 2 - MU1/MU2 - is equal to C2/C1. The real interest rate is 4% (.04). Suppose that consumers have after-tax incomes of $10,000 in period 1 and $20,800 in period 2. Find optimal consumption in each period and saving in period 1. Suppose the government gives each a $1000 tax cut in period 1, financed by borrowing. Government spending in each period is unchanged. Find optimal consumption in both periods, as well as first-period saving. How does the tax cut affect the market for loanable funds? Will the equilibrium real interest rate rise, fall, or remain the same. Explain.

Answer 1

Optimal consumption in a two-period closed economy is determined by equating the marginal utility ratio to the consumption ratio, adjusted for the real interest rate. A $1,000 period 1 tax cut increases disposable income, affecting both consumption and savings. This can alter the equilibrium in the loanable funds market, potentially raising the real interest rate.

Step-by-step explanation:

In a closed economy where individuals live for two periods and maximize their utility with a utility function U = C1*C2, where C1 and C2 are the consumption in period 1 and period 2 respectively, the optimal consumption and saving can be calculated given their incomes and the real interest rate. The original incomes are $10,000 in period 1 and $20,800 in period 2, with a real interest rate of 4% (.04).To find the optimal consumption for each period, we need to equalize the ratio of marginal utilities (MU1/MU2) to the ratio of consumption (C2/C1), accounting for the real interest rate. Since MU1/MU2 = C2/C1, and there is a 4% interest rate, consumers will want to consume $400 less in period 1 than they would in period 2.

Without computing the full optimization, it's clear that consumers will save in period 1 to finance higher consumption in period 2.With a $1,000 tax cut in period 1 financed by borrowing, consumers will have more disposable income to either increase their current consumption or save for future consumption. This increase in disposable income leads to higher current consumption and saving, thus affecting the market for loanable funds. The equilibrium interest rate may rise due to the government's increased demand for loanable funds to finance the tax cut.