4. Consider two countries (Home and Foreign) that produce goods 1 (with labor and capital) and 2 (with labor and land) according to the production functions described in problems 2 and 3. Initially, both countries have the same supply of labor (100 units each), capital, and land. The capital stock in Home then grows. This change shifts out both the production curve for good 1 as a function of labor employed (described in problem 2) and the associated marginal product of labor CHAPTER 4 = Specific Factors and Income Distribution 109 curve (described in problem 3). Nothing happens to the production and marginal p a b. roduct curves for good 2. . Show how the increase in the supply of capital for Home affects its production possibility frontier. On the same graph, draw the relative supply curve for both the Home and the Foreign economy. . If those two economies open up to trade, what will be the pattern of trade (i.e., which country exports which good)? . Describe how opening up to trade affects all three factors (labor, capital, land) in both countries. 2. An economy can produce leather using labor and capital and wheat using labor and land. The total supply of labor is 50 units. Given the supply of capital, the outputs of the two goods depend on labor input as follows: Labor Input Output Labor Input Output ~ to Leather of Leather to Wheat of Wheat 0 0 0 0 3 27 5 19.8 10 38.5 10 31.2 15 47.3 15 42.3 20 56 20 52.1 25 65.7 25 60.6 30 74.5 30 69 35 82.4 35 77.4 40 88.2 40 85.4 45 94.1 45 93.1 50 100 50 100 a. Graph the production functions for leather and wheat. b. Graph the production possibility frontier. What will happen if more labor is employed? 3. The marginal product of labor curves corresponding to the production functions in problem 2 are as follows: 'Workers Employed ~ MPL in Sector 1 MPL in Sector 2 5 5.4 3.96 10 & 2.28 15 1.76 222 20 1.74 1.96 25 1.94 | %) 30 1.76 1.68 35 1.58 1.68 40 1.16 1.6 45 1.18 1.54 50 1.18 1.38 a. Suppose the price of wheat relative to that of leather is 5. Determine graphically the wage rate and the allocation of labor between the two sectors. b. Using the graph drawn for problem 2, determine the output of each sector. Then confirm graphically that the slope of the production possibility frontier at that point equals the relative price. . Suppose the relative price of wheat rises to 8. Repeat (a) and (b). d. Calculate the effects of the price change from 5 to 8 on the income of the spe- cific factors in sectors 1 and 2. \fProduction Possibility Frontiers (PPFs) 50 40 30 Good 2 20 10 0 0 25 50 75 100 Good 1 Home (Before) - Home (After) Foreign