Question

4. Chelsea owns the only parking garage in town (i.e., she's a monopolist). Suppose that the marginal cost of letting an additional car in the garage is zero, and that the demand for parking in the garage is known.

(a) Show how Chelsea determines how many cars she will allow in the garage and how much she will charge each car to maximize her profits. Are profit maximization and revenue maximization equivalent in this case? Why or why not?

(b) Is it always profitable for Chelsea to fill the garage to capacity? Why or why not? Assume that Chelsea does not practice price discrimination.

Answer 1

Q4 (a) The equilibrium condition that Chelsea uses to determine how many cars to allow is mearginal revenue from additional car = marginal cost from additional car

=> MR =0

yes profit maximization and revenue maximization are the same in this case

max Profit = max (Revenue - variable cost - Fixed cost)

= max(Revenue - Fixed cost) [since marginal cost = 0 => there is no variable cost]

= max Revnue - fixed cost [ as fixed cost is not depended on the number of cars and hence not affected at the equilibrium level]

Thus, max profits is the same as max revenue and both will gave the same number of cars

(b) No, it is not always profitable for Chelsea to fill the garage to capacity. This is because, if there is no price discrimination, the downward sloping demand curve means that the marginal revenue of allowing an extra car can become negative and lower than the marginal cost. In this case, the total profits will be lesser than maximum profits that can be achieved by followin MR=MC condition.