Question 3. Free Trade Equilibrium in [1-0 model (Total 36 points, 6 each} We are under the setting of HO model. Assume home and foreign have the same capital endowment (K=K*) and home has a smaller labor endowment than foreign (1.51:). So foreign is labor abundant. Both countries produce two goods: shoes and cars, and car production is capital intensive while shoe production is labor intensive. Assume home and foreign have the same preference and the preference is homothetic. (Note that homothetic preference means that given price, an increase in income will induce the same proportional increase in the consumption of each goods. Eg, if income is doubled, then the quantity consumed for each goods will be doubled.) (1) In two separate figures, show the production possibility frontiers ofhome and foreign. Also show the no-trade equilibrium points in the two countries. (2) We now allow the two countries to trade freely. The free trade equilibrium price is in-between of the no-trade equilibrium prices in the two countries. Let us focus on the factor market in Foreign. Write an equation ofthe relationship between the relative supply of capital KWL\" and the relative demand of capital in the two sectors in foreign country. (3) In a graph, draw the relative supply and relative demand of capital (in the two sectors and for the whole economy) at Foreign no-trade equilibrium. (4) Based on the graph from 3), show how free trade changes the equilibrium factor prices and factor intensity (i.e. It's/L5, Kc/L\") in production in the two sectors in Foreign. Explain how the equation in problem (2) still holds under free trade. (5) In Foreign, are workers better off from trade? Are capital owners better off from trade? Explain why