Consider a two-period open economy in which households consume food and oil and have preferences given by Inc, + Inc; + Inc2 + Inc2, where C- and Cf denote the consumption of food and oil in period t = 1, 2. In each of the two periods, households are endowed with one unit of oil and the terms of trade equal one. There is free capital mobility and the world interest rate equals zero. (a). Find the equilibrium levels of consumption of food and oil in periods 1 and 2. Find imports and exports of each type of good in periods 1 and 2. Find the trade balance in periods 1 and 2. Find the household's level of utility. The answer to this question is a set of numbers. (b). Answer question 1 under the assumption that the government imposes a tariff of 50 percent on imports of food in both periods. Place particular emphasis on consumption of food, the trade balance, and welfare