1. (A Two-Sector Economy with Linear Technologies) This exer- cise combines the TNT and Balassa-Samuelson models. Consider a two-period small open economy populated by a large number of iden- tical households with preferences described by the utility function lnC'lT+51'1CJ'1N+11'14C32T+m0;r where CIT and 0%" denote consumption of tradables in periods 1 and 2, respectively, and GIN and 0? denote consumption of nontradables in periods 1 and 2. Households are born in period 1 with no debts or assets and are endowed with L1 = 1 units of labor in period 1 and L2 = 1 units of labor in period 2. Households offer their labor to rms, for which they get paid the wage rate ml in period 1 and mg in period 2. The wage rate is expressed in terms of tradable goods, that is, wt E W't/PtT . Households can borrow or lend in the international nancial market at the world interest rate r\". Let p1 and p2 denote the relative price of nontradable goods in terms of tradable goods in periods 1 and 2, respectively. Firms in the traded sector produce output with the technology Q? = (FL? in period 1 and QT = oTLg in period 2, where Q? denotes output in period t = 1, 2 and LE" denotes employment in the traded sector in period t = 1, 2. Similarly, production in the nontraded sector in periods 1 and 2 is given by Q? = oNLilr and Q? = aNLQF. (a) Write down the budget constraint of the household in periods 1 and 2. (2 marks)