Suppose in our two-period model of the economy that the government, instead of borrowing in the current period, runs a government loan program. That is, loans are made to consumers at the market real interest rate r, with the aggregate quantity of loans made in the current period denoted by L. Government loans are financed by lump-sum taxes on consumers in the current period, and we assume that government spending is zero in the current and future periods. In the future period, when the government loans are repaid by consumers, the government rebates this amount as lump-sum transfers (negative taxes) to consumers.

(a) Write down the government's current-period budget constraint and its future-period budget constraint.

(b) Determine the present-value budget constraint of the government.

(c) Write down the lifetime budget constraint of a consumer.

(d) Show that the size of the government loan program (i.e., the quantity L) has no effect on current consumption or future consumption for each individual consumer and that there is no effect on the equilibrium real interest rate. Explain this result.