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Sociology

1. {Speci?c Factor Model. Chapter 3} In the "simple" version of the specific factor model, there are two sectors {goods}, one factor {labor} that is perfectly mobile between the two sectors, and onefuced — or speci?c — factor in each sector. To be concrete, suppose the two goods are food and clothing, the speci?c factor in food is "land" — represented by "T", and the specific factor in clothing is "capital", represented by "K". The production functions for each sector are given by: C=1(K)?{£.c)?; F=H{T)1F(LJ)"2; Eel}; reenurceconstraint: .|'_'.L.+JLJr 2L where C, F are the outputs of clothing and food, that:r are labor employed in clothing and food, respectively, and "I." is the total available labor available in the economy. "3 "" and " 21 " are productivity factors, so an increase in H {in it. } represents an increase in productivity in food {clothing} production. a} Derive the production possibility frontier for this economy {that is, express C as a function of F , and also of the resources available: If, IL, and productivity variables, 3 and ii }. b) Consider a market economy with labor mobility so that wages are equalised across the twosectors. Let PE, Pf represent output prices and Wthe wage rate. Labor demand in each sector comes from pro?t maximiziation — which entails equating the marginal value product of labor to the wage: iv Given output prices, show graphically how the equilibrium wage rate and the allocation of labor between the two sectors is determined. Using the production functions, show mathematically how the equilibrium wage rate and the supply curve for each good (C, F) is determined {as a ftmction of output prices}. Also, discuss how the returns to land and capital are determined. Using your result in part ii, givll output prices, show how an increase in the amount ofcapital {K} available for production affects: [1}the quantity supplied of each good; {2}the real return to capital; {3}the real return to land; and {4}the real wage rate. Given output prices, show how an increase in food productivity {"3 "} affects the supply {output} of each good and the real return to each input. Given output prices, what happens to the supply of each good, and the real return to each factor, if productivity in both sectors {i.e., 2i and t9 ] doubles? Now assume there are two countries, Jamaica and Barbados, that are almost identical. They have the same tastes {the same demand curves], the same technology, and the same amount of land and labor; however, Jamaica has more capital than Barbados. Based upon your results ?'om part {b}, what predictions would you make concerning the autarky {no trade] relative price of food in EarbMos as compared to Jamaica? {a verbal answersuffices) lftrade is allowed between the two countries, what will the pattern of trade be and how willthe relative price of clothing change in each country?

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