Specific-Factor Model, see Part 1 and Part 3.

Part 1

1. {Specic Factor Modal. 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 onefixed or specic factor in each sector. To be concreteI suppose the two goods are food and clothing, the specic factor in food is \"land" represented by \"T". and the specic factor in clothing is \"capital", represented by \"K\". The production functions for each sector are given by: c=s(s){sc)l1; F=H{T)IF(LJ)\"2; 3H}; mmurcecunsimint: int; :1. where C, F are the outputs of clothing and food, 11.6.11:Ir are lab-or employed in clothing and food, respectively. and \"I.\" is the total available labor avaiIahle in the economy. \"a "' and \" 21 \" are productivity factorsI so an increase in H (in El 1| represents an increase in productivity in food [clothing] production. Consider a market economy with labor mobility so that wages are equalized across the two sectors. Let PE, PJr represent output prices and Wthe wage rate. Lab-or demand in each sector comes from prot maximiziation which entails equating the marginal value product of labor to the wage: i Given output prices, show graphically how the equilibrium wage rate and le allocation of labor between the two sectors is determined. ii Using the production functions, show mathematically how the equilibrium wage rate and the supply curve for each good (C, F} is determined {as a function of output prices). Also, discuss 1101!! the returns to land and capital are determined. iii Using your result in part ii, given output prices, show how an increase in the amount ofcapital (K) available for production affects: (\"the quantity supplied of each good; (2 }the real rettu'n to capital; (3}the real return to land; and (4}the real wage rate. iv Given output prices, show how an increase in food productivity (\"45" "} a'ects the supply {output} of each good and the real return to each input. v Given output prices. what happens to the supply of each good.' and the real return to each factorI if productivity in both sectors {i.e., A and I9] doubles