Problem-2 Consider a 2-sector (food and cloth) economy with three factors: labor (which is employed in both sectors and perfectly mobile across sectors), capital (which is employed only in the cloth sector) and land (which is employed only in the food sector). We denote labor by H, capital by K and land by L. The country's endowments of these factors is 300, 60, and 60 units, respectively. Suppose the unit price of food py is $1 and the unit price of cloth p, is $2. The production functions of the two sectors are given as Y/ = H,/2[1/2 (3) Y. = H1/2/1/2 (4) (i) Calculate the value of marginal product of labor in each sector (ii) What is the equilibrium wage, price of capital, and price of land? (iii) How much of labor is employed in each sector? (iv) How much is equilibrium output in each sector? (v) Suppose the price of food doubles. Calculate the effect on wage, prices of other factors, and outputs. Argue that Stolper-Samuelson theorem holds. Show your work in graph as well. (vi) Suppose now that capital stock in the economy doubles (everything else is the same as in the original question). What happens to output in each sector? Does this guarantee that Rybczynski's theorem holds