Consider a world with two countries, Home and Foreign, both able to produce two goods: cloth and food. The production of both goods uses capital and labor in fixed proportions, with the food industry using more capital per worker than the cloth industry. The units of each input needed to produce one unit output are given by:

	capital	labor
cloth	1	2
food	2	1

Home has 6 units of capital and 10 units of labor, whereas Foreign has 12 units of capital and 16 units of labor. Consumers like to consume both goods and have the same preferences in both countries. Assume that the countries are closed to international trade. The relative demand of cloth relative to food is given by

a) Compute algebraically the quantity of each good produced in each country.

b) Compute algebraically the quantities of labor and capital employed in each country in the production of each of the goods at the output levels in a), as well as the equilibrium relative price of cloth in autarky.

c) Indicate the range of prices of cloth relative to food at which the Home country will produce both goods. Which good would be produced if the relative price was outside of this range? Explain.

d) Compute algebraically the equilibrium world relative price of cloth. Which country would export which good? Explain.