3) Jack's Labor Demand Problem Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in the widget (output) market. His production function is as follows Q = ZOLL? Q = F(K,L) =4(KxL) – L² T-BQ - WL-rK In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he can acquire more capital by paying r for each unit of additional capital. Given a price of p for his yll widgets, Jack's short-run profit maximization problem can be written as max =Px F(K,L)-[wL +K] = P x [ 4 (5 x L) - L2 ] - [ wL + 5r ] Assume for now that Jack is a price-taker in the labor market as well. The going wage is w = $10, price for widgets P = 5, and factor price for capital r= 15 (3a) What is Jack's short-run marginal product of labor? What is Jack's short-run marginal revenue? (3b) What is Jack's short-run marginal revenue product of labor? (3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy given the prevailing prices. How much widgets does Jack make? What is Jack's profit? OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for this example? Look at Jack's profit. At the going price of widgets, is P = MC? (3d) Suppose that Jack is a monopolist in the widget market and faces the following inverse demand for widgets: P(Q) = 30 – 0.25 Q. What is Jack's marginal revenue now? marginal revenue product for labor? (3e) Sketch Jack's labor demand curve as a price-taker and as a monopolist in the widget market. (3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need to solve for the profit maximizing quantity of labor. But you can if you want (algebraically tedious).
3) Jack's Labor Demand Problem Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in the widget (output) market. His production function is as follows Q = ZOLL? Q = F(K,L) =4(KxL) – L² T-BQ - WL-rK In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he can acquire more capital by paying r for each unit of additional capital. Given a price of p for his yll widgets, Jack's short-run profit maximization problem can be written as max =Px F(K,L)-[wL +K] = P x [ 4 (5 x L) - L2 ] - [ wL + 5r ] Assume for now that Jack is a price-taker in the labor market as well. The going wage is w = $10, price for widgets P = 5, and factor price for capital r= 15 (3a) What is Jack's short-run marginal product of labor? What is Jack's short-run marginal revenue? (3b) What is Jack's short-run marginal revenue product of labor? (3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy given the prevailing prices. How much widgets does Jack make? What is Jack's profit? OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for this example? Look at Jack's profit. At the going price of widgets, is P = MC? (3d) Suppose that Jack is a monopolist in the widget market and faces the following inverse demand for widgets: P(Q) = 30 – 0.25 Q. What is Jack's marginal revenue now? marginal revenue product for labor? (3e) Sketch Jack's labor demand curve as a price-taker and as a monopolist in the widget market. (3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need to solve for the profit maximizing quantity of labor. But you can if you want (algebraically tedious).
Chapter11: The Firm: Production And Costs
Section: Chapter Questions
Problem 8P
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