Suppose two countries, Oceania (denoted O) and Eastasia (denoted E), each with one citizen. Denote by 2:0 the amount of Brawndo consumed, by the citizen of Oceania. Her utility is U (170) = ln(zo). Similarly, the utility function of the citizen of Eurasia as a function of the quantity of Brawndo consumed, 22E, is U(zE) = ln(zE). Each citizen, no matter the country, is endowed with one unit of time. Citizens of each country can spend all their time in the home country (i.e. work and consume there) or migrate to the foreign country (if this is allowed). Denote the amount of time a citizen of country 1' chooses to work in country j by El}, where i E {0, E} and j E {0, E}. For example, 6% is the amount of time the citizen of Oceania works in Eastasia. Denote the wage per unit time paid in Oceania by too and the wage paid per unit time in Eastasia by 10E. There is one factory in Oceania which converts labor into Brawndo. Its production function is o E 1 o l 1 E l 2 F0(Lo= Lo) 2 5(L0)2 + (LO)2 a where L8 is the amount of labor acquired from the citizen of Oceania and L5 is the labor acquired from the citizen of Eastasia. The amount of Brawndo produced by this rm is denoted yo. The rm sells it at price pa per unit. The prot of the rm, TI'O, goes to the citizen of Oceania. The factory in Eastasia has the following production function 2 a l g 1 s owing) = [5015 + Easy] . where LE is the labor acquired from the citizen of Eastasia and LE is the labor acquired from the citizen of Oceania. Notice that L; E [0, 00). The amount of Brawndo produced by this rm is yE . The rm sells it at price pE per unit. The prot of the rm, :rrE, goes to the citizen of Eastasia. Note, ff, need not equal L: except at equilibrium. The rst is what a citizen is willing to supply while the second is what the rm demands. 1. Initially, the Ministry of Plenty in Oceania forbids all trade in Brawndo between countries, so all Brawndo produced in Oceania is consumed in Oceania and all Brawndo produced in Eastasia is consumed in Eastasia. Also, it prohibits any immigration, so the citizen of Eastasia cannot supply labor to the factory in Oceania and citizen of Oceania cannot supply labor to the factory in Eastasia. Find a Walrasian equilibrium allocation and prices in Oceania. That is, compute the wage, how much time the Oceania citizen spends working, and the amount of Brawndo produced and consumed in this country. For convenience treat the price of labor, wo, as the numeraire. (a) Set up the prot maximization problem for the Oceania factory. Find the amount of Brawndo produced, labor demand and prot as function of prices and wages. (b) Set up the utility maximization problem for Oceania's citizen. Find the demand for Brawndo and labor supply as a function of prices, wages and factory prots. (c) Use the market clearing conditions to compute the Walrasian equilibrium
