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.
(a) Write down the government’s current period budget constraint
and its future period budget constraint. [10]
(b) Determine the present value budget constraint of the government. [7]
(c) Write down the lifetime budget constraint of a consumer. [7]
(d) Define the competitive equilibrium. [7]
(e) List the full set of conditions characterising the competitive equilibrium given the exogenous variables. [7]
(f) Suppose there is a change in the loan program ∆L. Argue why
or why not Ricardian equivalence holds in this setup. Provide
an intuition for your answer. [12].
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