BUSI681 - Managerial Economics

2. (30 points) Suppose that a firm's production function is represented in the following table (K is depicted by row, L by column): -lnllllnnn -mmm-m 0,000 0,000 -m 00 -m 00.00 -mm H a!\" 5%! 5 la 9 ' :8 ,8 3 3 O O .3 .3 --W 00,000 -m 00,000 0000 ----------- a 51' a D 3 5 a E .3 g 3 I a. Suppose that the rm currently uses 2 units of capital and 6 units of labor. How much is being produced? What is the marginal product of labor at this combination? What is the marginal product of capital? b. Suppose that r = $500 and w = $300. What are the firm's total costs currently? Is the firm minimizing its costs at the current production level? If not, at which combination of K and L will the rm minimize its production costs for this production level in the long run? c. What is a real-world situation that mirrors the one in our simple example in this problem? d. The production function represented in this table is Q = IOOOKL. What are the marginal product of labor and marginal product of capital for this production function? (Note: when taking the derivative of an expression with multiple variables, treat the \"other\" variable as a constant; so the derivative of ley with respect to x is 10y, and with respect to y, it is 10):) For w = 300 and r = 500, show mathematically the relationship between the cost-minimizing L and K. given these input prices. Does the combination of K = 2 and L = 6 satisfy this relationship? Does the combination of L and K you identied in part b satisfy this relationship? What does that say about real-world application of these methods? 3. (30 points) Suppose a rm faces the demand function depicted in the following table. Assume that only whole units can be produced and consumed Do NOT assume that the maximum number ofunits that can he produced is 10, Price Quantity Revenue Marginal Revenue 100 0 98 . 96 94 92 90 88 86 s4 82 \\DW'JthWN 80 10 a. Fill in the revenue and marginal revenue columns in the table based on the values in the price and quantity columns. Suppose the firm's cost function is portrayed in the following table: Quantity 0 'OOO-lO'U'I-ILWNin Total Cost 1 00 1 70 240 3 10 380 450 520 590 660 730 Average Cost Marginal Cost b. Fill in the table with the appropriate average and marginal costs. c. Based on the tables, will the rm produce at the price at which prot is maximized? Why or why not? (1. The demand function represented in the table is Q = 50 0.5P. The cost function is C = 100 + 70Q. Does the marginal revenue you calculate using this demand function equal the marginal revenue from the table? Why or why not? What about the marginal cost from this function compared to the table?I Use the MR and MC you get from these functions to identify the prot-maximizing price and quantity. Are they the same as what you saw in the table above? What does this tell you about real-world applications of these methods