Consider a two-period endowment economy populated by identical house- holds with preferences defined over consumption in period
1, C1 and con- sumption in period 2, C2, and described by the utility function In C1 + E In C2, where C, denotes consumption in period 1, C2 denotes consumption in pe- riod 2, and E denotes the expected value operator. Each period, the econ- omy receives an endowment of 10 units of food. Households start period 1 carrying no assets or debts from the past (B* = 0). Financial markets are incomplete. There is a single internationally traded bond that pays the interest rate p* = 0. 1. Compute consumption, the trade balance, the current account, and national saving in period 1. 2. 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. Sup- pose that these negative events are very rare, but have catastrophic effects on the country's output. Specifically, assume that with proba- bility 0.01 the economy suffers an earthquake in period 2 that causes the endowment to drop by 90 percent with respect to period 1. With International Macroeconomics, Chapter 6, July 31, 2019 223 probability 0.99, the endowment in period 2 is 111/11. What is the expected endowment in period 2? How does it compare to that of period 1? 3. What percent of period-1 endowment will the country export? Com- pare this answer to what happens under certainty and provide intu- ition. 4. Suppose that the probability of the catastrophic event increases to 0.02, all other things equal. Compute the mean and standard deviation of the endowment in period 2. Is the change in probability mean preserving? 5. Calculate the equilibrium levels of consumption and the trade balance in period 1. 6. Compare your results with those pertaining to the case of 0.01 prob- ability for the catastrophic event. Provide interpretation.
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