MONOPOLY: QUEATION: Bus Rides Love Sponge, Ltd. is the only bus company on St. V

Question

MONOPOLY:

QUEATION: Bus Rides

Love Sponge, Ltd. is the only bus company on St. Valentine, a small Caribbean island. Its LR total cost function is TC = .25Q2, where Q is passenger trips per hour. Its LR marginal cost function is MC = .50Q (the first derivative of the total cost function). The hourly demand function for bus rides on the island is Q = 100 - P, where P is the fare in Valentine dollars.

1.   Write the equation for the Love Sponge LR average cost function. AC =__________

2.   Write the equation for the firm’s MR function.    MR = ________________________

3.   Calculate the firm’s profit maximizing ridership.    ________________

4.   What fare will it charge?                                                                ________________

5.   What profit will it earn?                                                                   ________________

6. The St. Valentine government passes a law requiring Love Sponge to behave like a perfect competitor – i.e., provide bus service so that its fare equals marginal cost (marginal cost pricing). What will hourly ridership be in this case? ________________

7. Alternatively, the St. Valentine government passes a law requiring Love Sponge to earn only a normal (zero) profit – i.e., provide bus service so that its fare equals average cost (average cost pricing). What will hourly ridership be in this case? _______________

Explanation / Answer

1. Love Sponge LR average cost function. AC = TC/Q = 0.25Q^2/Q = 0.25Q

2. Q=100-P or P= 100-Q, TR = P*Q = 100Q-Q^2

MR=dTR/dQ = 100-2Q

3. Profit max condition MR=MC=AC=P(for long run with zero economic profits)

100-2Q = 0.50Q

2.50Q = 100

Q = 100/2.50 = 40

P = MC = 0.50*40 = 20

Profits = (P-AC)*Q

= (20-(0.25*(40)^(2))*40

= -15200 Loss

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