Question 3. The Current Account As Insurance Against Catastrophic Events (30 marks)

Consider a two-period endowment economy populated by a representative household with preferences defined over consumption in period 1, C1 and consumption in period 2, C2, described by the following utility function

U = ln C1 + E[ln C2]

where E denotes the expected value operator. In period 1, the household receives an endowment of 10 units of food (Q1 = 10). In period 2, the household receives an endwoment of 20 units of food (Q2 = 20). The household starts period 1 carrying no assets or debts from the past. The interest rate on financial assets held between periods 1 and 2 is zero. Based on the above information, answer the following questions.

1. (1) [5 marks] Assume no uncertainty (U = ln C1 + ln C2), compute consumption, the trade balance, the current account in periods 1 and 2.

2. (2) [25 marks] 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 events happen by chance, but have severe negative effects on the countrys

   output. Specifically, assume that with probability 1 the economy suffers an 2

   earthquake in period 2 that causes the endowment to decrease to 15. With probability 1 , the endowment in period 2 increases to 25. Using this information,

   2

   compute consumption, the trade balance, the current account in periods 1 and 2.