There are two countries, Home (#) and Foreign (F), and two sectors, 1 and 2. Households in each country have identical preferences over consumption of goods from both sectors, which are described by a Cobb-Douglas utility function: U. = U (CI, C5) = (09) (05) 1-s where Udenotes utilityin country c and Ofdenotes consumption of good i in country c. The parameters E (0, 1) measureshow much householdslike good 1 relativeto good 2. In what follows, we will assume that the preference parameter is given by: s = which implies that households like good 2 more than good 1. We will also begin by assuming that the supply of good i in country c, denoted by X6, is fixed, with endowments given by: X! = 1, X4 =2 Xf =2, X! = 8 Demand First, we will solve for demand in each country taking as given the relative price of good 1 to good 2, P, =p1/p2. (In other words, your answers below will be functions of p,. ) Suppose that households choose consumption to maximize utility, taking goods prices and income as given. Suppose also that all endowments in each country are owned by households. (a) What is consumption of each good in each country, Cf, given p.? Closed economy Now suppose that both Home and Foreign are in autarky and hence cannot trade with each other. Market clearing then requires that consumption of each good in each country must be equal to the respective endowment. (b) What must the autarky relative price of good 1 to good 2, pf = pi/p5, be in each country c so that markets clear for both goods? Which country has a higher autarky relative price? Why? (c) In each country under autarky, what is the value of consumption of each good and the corresponding value of household utility? Open economy Now suppose that Home and Foreign open to trade with each other. This means that instead of facing their respective autarky goods prices, they can now buy and sell goods at world prices p, and p2 , with py = p, /p2 denoting the world relative price. (d) Which country has a comparative advantage in which good? Which good will each country export? Which good will each country import? e) What are exports of each good by each country, Ef = Xf -Of, given the world relative price pr ? (Note that ES > 0 indicates that country c exports good i, whereas E.