The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that the school can educate per week is given by q ¼ 10 min(k, l) r , where k is the number of backhoes the firm rents per week, l is the number of instructors hired each week, and g is a parameter indicating the returns to scale in this production function. a. Explain why development of a profit-maximizing model here requires 0 < g < 1. b. Supposing g ¼ 0.5, calculate the firm’s total cost function and profit function. c. If v ¼ 1000, w ¼ 500, and P ¼ 600, how many students will Acme serve and what are its profits? d. If the price students are willing to pay rises to P ¼ 900, how much will profits change? e. Graph Acme’s supply curve for student slots, and show that the increase in profits calculated in part (d) can be plotted on that graph.
