This question is from by Schmitt-Groh, Uribe, Woodford

Exercise 4.5 (Oil Discovery and Extraction Costs) Consider an island populated by households with preferences given by _Cf1 _ C271, where 01 denotes consumption of food when young and 02 denotes con- sumption of food when old. Households are endowed with 8 units of food when young and 5 units when old. Households are born with assets worth 2 units of food ((1 + r0)Bo = 2), Where To = 5% denotes the interest rate in period 0 and Bo denotes the inherited stock of bonds. Suppose that house- holds have access to the international nancial market, where the interest rate, denoted r", is 10 percent. 1. Calculate the equilibrium levels of consumption, the trade balance, and the current account when young and when old. 2. Now assume that when young, each household discovers 20 barrels of oil reserves in its backyard. Households will be able to sell their oil in the international market only when they are old. The price of a barrel of oil in terms of units of food is expected to be 0.2 in period 2. Calculate the equilibrium levels of consumption, the trade balance, and the current account when young and old. 3. Now assume that extracting the oil requires investment in period 1 equal in value to 3.5 units of food. The investment must be made when young in order for the oil to be available for sale when old. Does it pay to make the investment? Calculate consumption and the trade balance when young. 4. Assume that households revise their expectations and now believe that the price of oil will be only 0.1 when old. Is it still protable to extract the oil? Show your work. . More generally, what does the intertemporal approach to the current account predict should be the effects of oil discoveries on a country's balance of payments both at the time of the discovery and at the time of actual oil production