Consider a small open economy where households live for two periods and have loga- rithmic preferences InCi + InCs, where C' and (5 denote consumption of food in periods 1 and 2 and are measured in tons. The country does not produce food. Instead, households are endowed with )y and ()5 barrels of oil in periods 1 and 2. In both periods, a barrel of oil sells for one ton of food in international markets. The economy start period 1 with By = 0. The world interest rate is r* and there is free capital mobility. The government imposes tariffs on food in periods 1 and 2, denote by 7, and 75. The revenue generated by tariffs are rebated to households using lump-sum transfers, denoted by L; and L. 1. Define terms of trade. What are the terms of trade in periods 1 and 2. 2. Derive the household's intertemporal budget constraint. 3. Write down household's optimization problem. 4. Derive the first-order condition of the household's optimization problem. 5. Write down the budget constraints for government in period 1 and period 2. 6. Combine the household's intertemporal budget constraint with the government budget constraints to find economy's intertemporal resource constraint in equi- librium. Do the policy variables 74, 79, L; and L, appear in this constraint? Why? 7. Let Y =@, + f; denote the present discounted value of the endowment path. Express the equilibrium values of consumption in period 1 and 2 in terms of Y, r*, 71, and T3. 8. Write the equilibrium trade balance in period 1 in terms of Y, v*, (01, 71, and 71. Compare the trade balance under free trade (7, = 72 = 0) to that in the following cases: (1) 7y =72 >0, (ii) 7 > 0 and 75 = 0, and (iii) 7 = 0 and 75 > 0