Exercise 4.7 (Import Tariffs] Consider a two-period open economy in which households have preferences given by lnCl+lnf32, where 01 and 02 denote consumption of food in periods 1 and 2, measured in tons. The country.r does not produce food. Households are endowed 1avith Q1 and Q9 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 starts period 1 with no assets, Bu = I]. The world interest rate is r'\" and there is free capital mobility. The government impose: tariffs on food imports in periods 1 and 2, denoted 1'1 and T2, and rebates the revenue generated by the tari's to the public using lump-sum transfers, denoted L1 and L2. 1. 1'What are the terms of trade in periods 1 and 2'? 2. Derive the household's intertemporal budget constraint. 3. Write down the optimization problem of the household. 4. Derive the rst-order conditions of the household's optimisation prob- lem