Suppose you now own a taxi company in Aberdeen and you are the sole producer of

Question

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%u2019ve 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%u2019s total profit. What is the monopolist%u2019s 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?

Explanation / Answer

a) Profit maximising condition for the taxi company is MC=MR

MR=d(TR)/dQ=105-0.5Q

MC=dC/dQ= 1.5Q+15

equating both we get

1.5Q+15=105-0.5Q

2Q=90

therefore profit maximising output level Q=45

b) Monopolistic total profit= TR-C

TR=105*45-0.25*Q^2=4218.75

C=160+15*45+0.75*45^2=2353.75

Therefore Total Monopolistic profit=1865

Average profit=41.44

c) i) P=ATC

therefore PQ=TC gives us the output level

105Q-0.25Q^2=160+15Q+0.75Q^2

we get a quadratic equation

Q^2-90Q+160=0

Hence we get Q=88.18 and Q=1.82 which will be round off to 88 units and 2 units respectively

Profit for both cases will be

for 88 units of production

TR-C=16

for 2 units of production

TR-C= 16

Hence the firm can produce 2 units when P=ATC because the average profit=16/2=8 units greater than that of producing 88 units.

ii) now we equate P=MC

hence 105-0.25Q=15+1.5Q

1.75Q=90

therefore output level=51.42 or round off to 51 units

Profit=TR-C=1829

Average profit=35.86

iii) Aberdeen City commission would suggest Equating P=ATC coz the Taxi Company is reaping lesser profit in that situation but this regulation has a negative impact on the production of output by the taxi company which reduces Q to 2 hence from the welfare point of view the commission should regulate P=MC

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