Economics 101 — Fall 2009International TradeProblem Set 1September 29, 2009Due: Thu, October 15, before 12:30pInstructor: Marc-Andreas MuendlerE-mail: [email protected] Ricardian Trade Theory and SpecializationHome (no asterisk) and Foreign (asterisk) pro duce cheese and wine with thefollowing unit labor requirementsHome ForeignCheese aLC= 5 a∗LC= 6Wine aLW= 2 a∗LW= 6Home and Foreign have total labor forces of L = 100 and L∗= 200 workers.• Production possibility frontiers. Graph each country’s production possi-bility frontier and calculate the opportunity costs of cheese in terms ofwine (the amount of wine a country needs to sacrifice to obtain cheese).Which country has an absolute advantage in cheese production, which inwine production? Which country has a comparative advantage in cheeseproduction, which in wine production?• Autarky. Using the graph from your preceding answer, draw each coun-try’s consumption possibilities in the absence of trade. Calculate the rel-ative prices of cheese in terms of wine in autarky.• Free trade. Both countries open up to free trade. Graph the relativeworld supply of cheese (Q∗C+ QC)/(Q∗W+ QW) and its response to therelative world price of cheese PC/PWbased on the unit labor requirements.Provide specific values for changes to the regime of relative world supplyon the axes.World consumers’ demand for cheese relative to wine depends on the rel-ative price of the two goods:(QC+ Q∗C)/(QW+ Q∗W) = 6 − 5 · PC/PW.Graph the relative demand curve. Calculate the relative price PC/PWofcheese in world trade equilibrium. Calculate the production of QC, Q∗C,QW, and Q∗Wand explain what this pattern of production states aboutthe pattern of trade. What is the relative wage w/w∗under free trade?1• Free trade under reduced world demand. What do countries trade if rela-tive world demand changes to (QC+Q∗C)/(QW+Q∗W) = 5−5·PC/PW? Dothe countries trade if relative world demand changes to (QC+Q∗C)/(QW+Q∗W) = 4 − 5 · PC/PW? Comparing the consumption possibilities, showthat both countries gain from trade when they trade.• Free factor movements and free trade. Return to the world relative de-mand function (QC+ Q∗C)/(QW+ Q∗W) = 6 − 5 · PC/PW. Suppose thereis international migration from Foreign to Home so that L∗0= L0= 150.How do the patterns of production and trade in the world change? Why?What is the relative wage w/w∗under free trade now?2 Ricardian Trade Theory and WagesHome and Foreign invent different technologies to produce tools, beyond theirproduction of cheese and wine. The table of unit labor requirements is:Home ForeignTo ols aLT= 3 a∗LT= 6Wine aLW= 2 a∗LW= 3Cheese aLC= 5 a∗LC= 3• Comparative advantage. In which good does Home have the strongest com-parative advantage? In which go od does Home have the least comparativeadvantage?• Trade and wages. If the relative wage rate w/w∗= 1, in what goods willHome specialize? [Hint: You may neglect the relative size of the laborforces for your answer.]• Gains from trade. Do both countries benefit from trade? Present aneducated verbal argument.• Transport costs (transfer question). If transport costs add 50% to theprice of a good that is shipped from one country to another, what is thepattern of production and what is the pattern of trade? Will all goods betraded? [Hint : Calculate the total cost of each foreign good to a homeconsumer and compare it the the cost of the same good when produced athome; then calculate the total cost of a home good to a foreign consumerand compare it the the cost of the same good when produced abroad.]3 Sector-Specific Factors and TradeHome can produce machinery and flowers (in bundles of 1,000). The productionfunctions of the two industries areQM=√K · LMand QF=√T · LF,where K is capital, T is land, and L is labor. Consider goods prices PM= PF=1. Factor supply is LM+ LF= 100 and T = K = 100.2• Derive the marginal products of labor MP LM(K/LM) and M P LF(T/LF)for the two industries.• Autarky wages. Graph the labor demand curves in the machinery andflowers industries, and calculate the equilibrium wage rate in autarky.• Trade pattern. After opening up to free trade, Home faces a relative priceof PM/PF= 2. How do the allocation of labor and wages change?• Production possibility frontier. Using the general labor demand relation-ships for the two industries, show that the production possibility frontieris−MP LF/MP LM= −PM/PFin labor market equilibrium.• Gains from trade. Draw the production possibility frontier. How does thechange in relative prices after trade affect production? Depict the gainsfrom trade.4 Heckscher-Ohlin Trade Theory and Endow-mentsAt current goods and thus factor prices, cloth is produced using 20 hours oflabor for each acre of land, while food is produced using only 5 hours of laborper acre of land.• Resource allocation. The economy’s total resources are 600 hours of laborand 60 acres of land. Use an Edgeworth box to determine the allocationof resources.• Endowment changes. Labor supply increases from 600 to 900 to 1200hours. Using the Edgeworth box, trace out the changing allo cation ofresources.• Extreme endowment changes. What would happen if the labor supplyincreased beyond 1200 hours?5 Heckscher-Ohlin Trade Theory and WagesThe relationship between the wage-rental rate ratio w/r and the relative priceof cloth in terms of food PC/PFisPC/PF=pw /rin the Home economy. The optimal land-labor ratio choice is given by TF/LF=5 · w/r in food production and by TC/LC=12· w/r in cloth production.• Factor price equalization. Home opens up to free trade and experiences adoubling of the relative price of cloth. Use a goods-price-to-input-choicediagram to show how a doubling of the relative price of cloth affects wagesand the choice of land-labor ratios in both industries.3• Resource allocation. How can it happen that both industries change land-labor ratios in the same direction, although total land and labor resourcesare given? [Hint: Describe the factor flows within the Home economy.]• Relative sector size. Use an Edgeworth box to show the effect of a doublingin the relative price of cloth. [You may reuse the Edgeworth box from thepreceding question for the initial state of the