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 5 10 min 1k, l2r

, where k is the number of backhoes the firm rents per week, l is the number of instructors hired each week, and γ is a parameter indicating the returns to scale in this production function.

a. Explain why development of a profit-maximizing model here requires 0 , γ , 1.

b. Supposing γ 5 0.5, calculate the firm’s total cost function and profit function.

c. If v 5 1000, w 5 500, and P 5 600, how many students will Acme serve and what are its profits?

d. If the price students are willing to pay rises to P 5 900, 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.