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ECON 7520

SEMESTER 1, 2023

Tutorial 6

Problem 1 (The Current Account As Insurance Against Catastrophic Events)

Consider a two-period small open endowment economy with a single good that is populated by a representative household with preferences deined over consumption in period 1, C1 , and consumption in period 2, C2 . The household’s preferences are described by the utility function

U = ln C1 + E[ln C2],

where E denotes the expected value operator. Each period, the household receives an endowment of 10 units of the good. The household starts period 1 carrying no assets or debts from the past. The interest rate on inancial assets held between periods 1 and 2 is zero.

(a) Assume that there is no uncertainty (U = ln C1 + ln C2). Compute the house- hold’s consumption, the trade balance, the current account, and national sav- ings in period 1.

(b) Assume now that the endowment in period 1 continues to be 10, but that the economy is prone to severe natural disasters in period 2. Suppose that these negative events have catastrophic effects on the country’s output. Speciically, assume that with probability 12  the economy suffers an earthquake in period 2 that causes the endowment to drop by 50 percent with respect to period 1. Without an earthquake, the endowment in period 2 increases to 15.

(i) What is the expected endowment in period 2? How does it compare to that of period 1?

(ii) What portion of the period-1 endowment will the country export? Com- pare your answer to what happens under certainty and provide intuition.

(c) Suppose that the endowment for the good state increases to 19 and the one for the bad state decreases to 1, all other things equal.

(i) Calculate the optimal level of consumption and the trade balance in pe- riod 1.

(ii) Compare your results with the previous case. Provide interpretation.