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Economics 3563: International Trade Chapter 6: H -O Model Homework 3 – SOLUTIONS Problem 6 -4 (a) Food is labor intensive, and cars are capital intensive. Home is relatively rich in labor, and Foreign is relatively rich in capital. Thus, according to the H-O theorem, Home exports food and Foreign exports cars. (b) We can find out about production in each country using the full employment conditions. In Home, these are for labor and for capital. The solution to this system is and . In Foreign the full employment conditions are for labor and for capital. The solution is and . (c) To find the relative price in autarky in Home, we use the demand function and the relative supply found in part ii), . The price is . (d) To fi nd the price under free trade we need the world relative supply. The total amount of food produced in the world is the sum of the production of both countries, . The world supply of cars is . The relati ve world supply is . The intersection of the world relative supply and the world relative demand (given by the same equation as each country's demand in autarky since they have the same preferences), is the new equil ibrium. The relative price is . 5 4 600 FCQQ    3 4 400 FCQQ    100 FQ  25 CQ  5 4 600 FCQQ    3 4 500 FCQQ    50 FQ  87.5 CQ  QF QC = 100 25 = 4 1.1 0.075 4 0.8 F C P P     50 100 150 WFQ    87.5 25 112.5 WCQ    QFW QCW= 150 112.5 =1.333 1.1 0.075 1.333 1 F C P P     The aggregate gains from trade are shown on the graph below The dashed line is the free -trade line. The solid line is the autarky line. 25 131.5 125 100 Cars Food Home 105 125