Suppose that a firm's production function is: q=10L0.5K0.5. Its marginal product functions are: MPL=5K0.5/L0.5=0.5q/L and MPK=5L0.5/K0.5=0.5q/K. The cost of a unit of labor, w, is $20 and the cost of a unit of capital, r, is $80. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 28 and 7 . respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require units of labor. (Enter your response rounded to two decimal places.) If the marginal rate of technical substitution is LK, find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is units. (Enter your responses as integers.) Plot the cost-minimizing levels of capital and labor along with the isocost lines corresponding to outputs of 140 and 280 units. 1.) Using the point-drawing tool, plot the cost-minimizing quantities of labor and capital at 28 and 7 (Suppose that the firm is producing 140 units of output.) Label this point E1. 2.) Using the line-drawing tool, draw the corresponding isocost line. Label this line C1. 3.) Using the point-drawing tool, plot the cost-minimizing quantities of labor and capital that you found earlier in the problem. (Suppose the firm increases output to 280 units.) Label this point E2. 4.) Using the line-drawing tool, draw the corresponding isocost line. Label this line C2. Carefully follow the instructions above, and only draw the required objects. Suppose that a firm's production function is: q=10L0.5K0.5. Its marginal product functions are: MPL=5K0.5/L0.5=0.5q/L and MPK=5L0.5/K0.5=0.5q/K. The cost of a unit of labor, w, is $20 and the cost of a unit of capital, r, is $80. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 28 and 7 . respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require units of labor. (Enter your response rounded to two decimal places.) If the marginal rate of technical substitution is LK, find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is units. (Enter your responses as integers.) Plot the cost-minimizing levels of capital and labor along with the isocost lines corresponding to outputs of 140 and 280 units. 1.) Using the point-drawing tool, plot the cost-minimizing quantities of labor and capital at 28 and 7 (Suppose that the firm is producing 140 units of output.) Label this point E1. 2.) Using the line-drawing tool, draw the corresponding isocost line. Label this line C1. 3.) Using the point-drawing tool, plot the cost-minimizing quantities of labor and capital that you found earlier in the problem. (Suppose the firm increases output to 280 units.) Label this point E2. 4.) Using the line-drawing tool, draw the corresponding isocost line. Label this line C2. Carefully follow the instructions above, and only draw the required objects
