Suppose that there are two firms competing in the market for taxi services. Big Ben Taxis has the marginal cost MCB = $\$9$ per trip, and the fixed cost FCB = $\$3,000,000$, while Whitehall Taxis has the marginal cost MCB = $\$15$ per trip and the fixed cost FCW = $\$1,000,000.$

Inverse demand for taxi trips in the market is given by $$P = 75 − \frac {Q}{10,000}$$

In this equation, $P$ is the price of a taxi trip, and $Q$ is the total quantity of taxi trips supplied by the two taxi companies.

Question 1: Find the equilibrium price and quantities for the case in which the two taxi companies engage in Cournot (quantity) competition. What profits will Big Ben Taxis and Whitehall Taxis earn.

Question 2: Using your answers to question 1, determine which firm has the greater market power.

Question 3: Now suppose that a firm can only supply taxi services if it purchases a license from the government. What is the highest fee that the government can charge for a licence, if the government wants both Big Ben Taxis and Whitehall Taxis to purchase a license? (Note: A licence does not place a limit on the number of taxi trips a company can supply. You should assume that both firms are charged the same fee.)

Question 4: If, instead, the government wants to maximise the revenue it receives from taxi license fees, how many licenses should it sell, and what fee should it charge?

After doing up the questions For question 1, I found the equilibrium price is $33.

For question 2, Big Ben has more market power

For question 3, I subsitute Q=0 to find the price. Then I pick the next best answer by deducting 1 cent from the answer which is 74.99. But I do not know if this is correct.

For question 4, the main part for this question. I do not know how to start, could someone guide me please.

  • $\begingroup$ What is Whitehall's marginal cost? $\endgroup$ – Doug M Sep 21 '16 at 16:38
  • $\begingroup$ Hi Doug, Whitehall's marginal cost is $15. I have added it in $\endgroup$ – Badatit Sep 22 '16 at 6:03
  • $\begingroup$ For Q4) Using the demand function I got R'(Q)=75-(2Q/10,000) in which I got the quantity to maximize revenue is 375,000 in which the price is $37.5. Is it correct? Should I do anything to the price like deducting the equilibrium price or just leave it as that? For Q3, I am unsure if I should I should also deduct the equilibrium price or leave it at the maximum price the price can go up to in order for Q not to be 0. $\endgroup$ – Badatit Sep 22 '16 at 16:40
  • $\begingroup$ Is there anyone who can help me with this? I could show u my workings thru another platform if you would like $\endgroup$ – Badatit Sep 24 '16 at 4:24

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