Consider the two-period endowment model discussed in the lectures
where the economy is populated by m consumers and a government.
The agents derive utility from consumption in the current and future
period. The utility is well behaved. Suppose 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 (denoted by
T), while government spending is zero in both periods (i.e., G =
G0 = 0). In the future period, when the government loans are
repaid by consumers, the government rebates this amount as lumpsum transfers (negative lump-sum taxes) to consumers. Finally, each
consumer shares an equal amount of the total tax burden (or of the
total transfer benefit) in the current and future period.
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