1. (Analytical Escmtce} Suppose that the United States and Banada produce clothing {0} and food {F}. The [1.3. has an endowment of one man-hours, each of which can produce either 2 unite of clothing or 2 units of food. Canada has an endowment of 31]] man-hours, each of which can produce either 1 unit of clothing or 2 unite of food. (a) 1|Which country has an absolute advantage in each good? {b} Derive opportunity costs and examine comparative advantages. i. For each country, what is the opportunity cost of clothing? ii. For each country, what is the opportunity cost of food? iii. 1|lliihich country has a comparative advantage in each good? (c) Draw the production possibility [rontiers for both economies (draw the production of clothing on the m-avia and of food on the yavia}. Use a different graph [or each HIGH omy. {d} 0n your graphs in part [c], indicate consumption of goods in each economy. You do not need to derive exact quantities. (e) Let 13pr denote the relative price of clothing. In the following, we will derive the autarky equilibrium of each economy. i. For each country, use the production possibility frontiers above to derive the quan- tity of production of each good. ii. Put 13pr on the y-axia and ngQp on the e-axis of a graph, and draw the relative supply curves in each economy under autarky. Use a di'erent graph for each economy. iii. In each economy, the relative demand is: 1 Dd?\" W Solve the equilibrium relative prices and relative quantities in each economy. iv. Do thme curves depend on the economies endowments in terms of number of man-hours? (f) Now assume that these economies open up to international trade. i. Derive the quantity of world production for each good. ii. The world relative demand is: Do/ DF = (Po/ PF) Solve the equilibrium relative prices and relative quantities in the world economy. (g) Graphically show the changes in welfare in each economy with free trade. Does inter- national trade provide mutual benefits to both countries? (h) Now think about a scenario where the U.S. labor force increased by a factor of 1.5. i. How does this affect the production possibility frontier for the U.S.? ii. How does the trade pattern change? Make your argument using changes in com- parative advantages. iii. Discuss changes in the world equilibrium with respective to the population growth in the U.S. (i) ([Extra Credit] Challenging) Let us go back to the initial population size in the U.S. But, now assume that productivity changes in the U.S.: each field can produce the same amount of clothing and food, but this amount is now a variable > > 0 (previously x = 2). How does the equilibrium trade relative price Po/PF depend on a? Clearly indicate how to compute Po/ PF given any value of a > 0