QuickLearn Driving School trains learner drivers. The number of candidate drivers it can train per week is given by q= 10 min (k, l )′, where k is the number of vehicles the firm hires 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-maximising model here requires 0 <><>
b. Supposing gγ= 0.5, calculate the firm’s total cost function and profit function.
c. If v= 1000, w= 500 and P= 600, how many students will QuickLearn train and what are its profits?
d. If the price candidate drivers are willing to pay rises to P= 900, how much will profits change?
e. Graph QuickLearn’s supply curve for student slots, and show that the increase in profits calculated in part (d) can be plotted on that graph.