1. (50 points) Consider the two-period endowment model discussed in class where theeconomy is populated by m consumers and a government. The agents derive utilityfrom consumption in current and future period. The utility is well behaved. Supposethat the government, instead of borrowing in the current period, runs a governmentloan program. That is, loans are made to consumers at the market real interest rater, 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), and we assume that government spending is zero in the current andfuture periods (i.e., G = G0 = 0). In the future period, when the government loansare repaid by consumers, the government rebates this amount as lump-sum transfers(negative taxes) to consumers. Hence, if we call T r0the lump sum transfers in thefuture period, then T r0 = −T0 > 0.(a) (10 points) Write down the government’s current period budget constraint andits future period budget constraint.(b) (8 points) Determine the present value budget constraint of the government.(c) (8 points) Write down the lifetime budget constraint of a consumer.(d) (10 points) Define the competitive equilibrium.(e) (14 points) Argue why or why not Ricardian equivalence holds in this setup.
1. (50 points) Consider the two-period endowment model discussed in class where the
economy is populated by m consumers and a government. The agents derive utility
from consumption in 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), and we assume that government spending is zero in the current and
future periods (i.e., G = G0 = 0). 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. Hence, if we call T r0
the lump sum transfers in the
future period, then T r0 = −T
0 > 0.
(a) (10 points) Write down the government’s current period budget constraint and
its future period budget constraint.
(b) (8 points) Determine the present value budget constraint of the government.
(c) (8 points) Write down the lifetime budget constraint of a consumer.
(d) (10 points) Define the competitive equilibrium.
(e) (14 points) Argue why or why not Ricardian equivalence holds in this setup.
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