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=201-2² - L² Q=F(K,L)=4(KxL) 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 widgets, Jack's short-run profit maximization problem can be written as ४८ >(rental rate of capital) max 7=PxF(K,L)-[WL + FK] L TT-BxQ-WL-rk IT = 5(201-2²)-10L-7 =Px [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?
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=201-2² - L² Q=F(K,L)=4(KxL) 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 widgets, Jack's short-run profit maximization problem can be written as ४८ >(rental rate of capital) max 7=PxF(K,L)-[WL + FK] L TT-BxQ-WL-rk IT = 5(201-2²)-10L-7 =Px [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?
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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