Question

In: Economics

Consider a two-period small open endowment economy populated by a large number of households with preferences described by the lifetime utility function

An Anticipated Output Shock

Consider a two-period small open endowment economy populated by a large number of households with preferences described by the lifetime utility function: 11 U = C 10 C 11 (1) Suppose that households receive exogenous endowments of goods given by Q1 = Q2 = 10 in periods 1 and 2, respectively. Every household enters period 1 with some debt, denoted B0∗, inherited from the past. Let B0∗ = −5. The interest rate on these liabilities, denoted r0, is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r∗, is 10 percent.

a (14 points) Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2. Do not forget to show step by step your algebraic calculations. Explain in detail your reasoning. No credit without an explanation.

b (16 points) Assume now that the endowment in period 2 is expected to increase from 10 to 15. Calculate the effect of this anticipated output increase on consumption, the trade balance, and the current account in both periods. Provide intuition. Do not forget to show step by step your algebraic calculations. Explain in detail your reasoning. No credit without an explanation.

Expert Solution

a.The lifetime utility function is ln C1+(10 / 11)ln C2. Compute the marginal rate of substitution as MRS = MUC1 / MUC2

MRS = (1/C1)/(10/11C2) = 1.1C2/C1. Now see the intertemporal budget constraint

C1 + C2/(1+r) + B0*(1 + i) = Q1 + Q2/(1+r)................. r is the interest rate on saving and i is the interest rate on debt

C1 + C2/1.1 + 5*(1 + 0.2) = 10 + 10/1.1

C1 + C2/1.1 = 4 + 10/1.1

1.1C1 + C2 = 14.4

Utility maximization requires MRS = slope of the budget constraint

1.1C2/C1 = 1.1/1

C2 = C1

Placing this in the budget equation

1.1C1 + C1 = 14.4

C1* = 6.8571 and C2* = 6.8571

These are the current consumption levels. In period 1 when consumers receive 10, they consume 6.8571, save the remaining and invest the same at 10% so that in period 2 they have (10 - 6.8571)*(1 + 0.1) = 3.4572. In the second period, they consume 6.8571, and add the two-period savings = 3.4572 + (10 - 6.8571) = 6.6 to pay off the liability.

Rahul Sunny answered 2 years ago

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