Problem set 2: Factor-endowment trade models Problem-1 Consider a perfectly competitive small open economy with two goods, food (f) and cloth (c), and two factors, labor (1) and capital (k). The technology for production of both goods is given by Leontief and given as follows: Y. = min{ Lc, As] (1) Yf = mint 7 - (2) Suppose the country takes international prices of cloth and food, which are $10 and $12 per unit, respectively. The country's labor and capital endowments are 100 and 80 units respectively. Suppose the unit prices of labor and capital are denoted by w and r respectively. (i) Determine the factor intensity of the goods. (ii) Write down the unit cost functions for each good. (iii) Can we have a Factor Intensity Reversal in this economy? Explain. (iv) Write down the equilibrium conditions (Note: you have four equations with four unknowns). (v) What is the equilibrium wage and rental rate? (vi) What is the equilibrium output levels? (vii) How much of labor is used to produce clothes? (vili) Suppose the unit price of food increases to $16 while the unit price of cloth remains the same. Solve for the new equilibrium factor prices. Comparing with the initial equilibrium in (v), show that the Stolper-Samuelson theorem holds. (ix) Suppose now that the country's capital stock doubles to 160 units (all else the same as in the original problem). Solve for the new equilibrium output. Comparing with your answers in (vi), show that Rybczynski's theorem holds