Consider twocountries whose representative consumers have the same preferences given by U(CC;CF)= CC CFand U* (CC*;CF*_)= CC*CF*_.The two countries share the same production technologies which are given byQC=Lc2/3 Kc1/3 , QF=LF1/3 KF2/3The home country isendowed with 400 units of capital and 300 units of labor, while the foreigncountry isendowed with 100units of capital and 50 units of labor.1. Answer thefollowing questions for the home country, then for the foreign country:(a) It turns out that in autarky equilibrium the wage-rent ratio is 1.333 forthe home country and 2 for the foreign country. Find the capital-labor ratioused in each industry.(b) Calculate the number of workers employed and the amountof capital used in each industry in autarky equilibrium (find LcA;LFA ;KcA ;KFA) where A means under Autarky.(c) Calculate the autarky production (= consumption) foreach industry (QcA and QFA).(d) Derive the autarky price ratio, (Pc/ PF)A,and the real value of production in autarky.(e) Calculate the real wage rate ( w/PF) and the real rate of returnoncapital ( r/PF) in autarky.(f) Calculate real total factor income. Is it equal to thereal value of production that you derived in question 2d?2. It turns out that in the free-tradeequilibrium the wage-rent ratio for both countries is 1.4287. Find thecapital-labor ratio used in each industry.3. Calculate the number of workersemployed and the amount of capital used in each industry in free trade for eachcountry.4. What are the quantities produced ofclothing and food in the home and in the foreign country?5. Calculate the price ratio in freetrade as well as free trade consumption in each country (Find (Pc/ PF)T , CcT, CFT, CC*T,CF*T).6. Determine real GDP in each country.7. Determine the real interest rate andreal wage rate in each country.8. Calculate real total factor incomefor each country.9. Calculate each country’s exports and imports.10. Calculate the autarky and free trade utility for each country.11. Has each country benefited from trade?12. Does the Heckscher-Ohlin theorem hold? Explain briefly13. Does the Factor-Price Equalization Theorem hold? Explain briefly14. Does the Stolper-Samuelson Theorem hold? Explain briefly
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