Question

Assume that there are two firms competing in the market for taxi services, Company U and Company G. Company U has a marginal cost MC_UB = $6 per trip, and a fixed cost FC_UB = $2,500,000; while Company G has a marginal cost MC_GC = $12 per trip, and a fixed cost FC_GC = $1,500,000.

The inverse demand for taxi trips in the market is given by the function: ?=60−?/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 firms, i.e. Q = Q_UB + Q_GC.

(a) If the taxi firms engage in Cournot (quantity) competition as they take the taxi fleet of the rival firms as given, derive each firm’s best response function and then solve for the equilibrium quantities (i.e. profit-maximizing taxi trips of each firm) and the market price. [Hints: You could consider the following steps to derive the best-response function of each firm:

a. Find the firm’s residual demand function.

b. Derive its MR function by either (i) finding the first derivative of the total revenue (TR) function; or (ii) using two-times the slope rule if the demand function is linear.

c. In Cournot competition, the firm’s “best-response” is its profit-maximising quantity holding the other firm’s quantity unchanged. This can be derived as either (i) MR = MC, or (ii) via the first-order condition: ??/??=0, where π = (TR – TC).

d. The best-response function of the firm is expressed as the profit-maximising quantity of the firm as a function of the quantity of the other firm.]

(b) What profits will Company U and Company G earn? (c) 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 license, if the government wants both Company U and Company G to operate in the market? (Note: A license does not place a limit on the number of taxi trips a firm can supply. You should assume that both firms are charged the same license fee.)

Answer 1

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