Suppose you now own a taxi company in Aberdeen and you are the sole producer of this service. You have a taxi monopoly in Aberdeen. Yes, you have cornered the market in the Aberdeen Taxi Cab industry. Your cost structure is described by the following equation:
C = 160 + 15 Q + .75 Q2
Additionally you face the following inverse demand curve:
P = 105 - .25 Q
Where TR = P*Q = (105 - .25Q)*Q
a. Find the taxi firms profit maximizing or loss minimizing output level, Q.
b. Calculate the monopolist's total profit. What is the monopolist's average profit?
c. Suppose the Aberdeen City Commission feels that the taxi monopolistic taxi company is reaping excessive profits. They ask you to calculate a regulated quantity, price, and profit/loss under two different regulatory schemes. You suggest two different regulations. The taxi company will set price equal to average total cost of production and the taxi company will set price equal to marginal cost.
i. Using the information above calculate the output level, price, and average profit/loss (ie compare AR with ATC) if you set the regulatory price at average total cost of production. That is P = ATC.
ii. Second, calculate the output level, price, and average profit/loss (compare average revenue with average total cost) if you set the regulatory price at marginal cost of production. That is P = MC.
iii. Which regulatory price (P) and quantity (Q) would you suggest the Aberdeen City Commission enforce?