– Question:Consider asmall economy producing two goods, clothing and food. The clothing industry usescapital (K) and labor (LC) as inputs, while the food industry usesland (La) and labor (LF) as factors of production.The production technologies for the two industries are given by: QC =K1/4 Lc3/4 ; QF =La1/2 LF1/2Also, thecountry is endowed with 216 units of capital, 1822 units oflabor, and 9units of land. Finally, the utility function of the representativeconsumer isgiven by U(CC;CF )= Cc1/2 CF1/21. Calculatethe autarky production (= consumption) for the two industries.2. Derive theautarky price ratio ( [img width=’13’ height=’22’ id=’ i1025′ src=’file://localhost/Users/lolwah/Library/Caches/TemporaryItems/msoclip/0clip_image001.png’>A,and the real value of production(i.e.real GDP) in autarky.3. Determinethe autarky utility level.4. Determine LC and LF inautarky.5. Calculatethe real wage rate ([img width=’21’ height=’21’ id=’ i1025′ src=’file://localhost/Users/lolwah/Library/Caches/TemporaryItems/msoclip/0clip_image002.png’>[img width=’21’ height=’21’ id=’ i1025′ src=’file://localhost/Users/lolwah/Library/Caches/TemporaryItems/msoclip/0clip_image003.png’>realreturn on land ([img width=’21’ height=’23’ id=’ i1025′ src=’file://localhost/Users/lolwah/Library/Caches/TemporaryItems/msoclip/0clip_image004.png’>6. Calculatereal total factor income in autarky. Is it equal to the real value ofproduction that you calculated previously?7. Now, assumethat the country is allowed to trade with the rest of theworld at thefree trade price ratio, ([img width=’18’ height=’22’ id=’ i1025′ src=’file://localhost/Users/lolwah/Library/Caches/TemporaryItems/msoclip/0clip_image005.png’>equal to 0:1244.8. Determinethe pattern of trade for the home country. Briefly explain the possible causesfor the HC’s comparative advantage.9. Determine LC and LF infree trade.10. DetermineQC and QF infree trade.11. Calculatethe real wage rate, the real interest rate, and the real return on land in freetrade.12. Who arethe home country’s winners and losers of the move from autarky to trade?13. Calculatereal total factor income in free trade.14. Calculatefree trade consumption of food and clothing.15. Calculateexports and imports.16. Determinethe level of utility with free trade. Is the country better off due tointernational trade?
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