In a city, the Taxi industry is regulated by the Government Taxi Authority. A company can only supply taxi services, if it is issued a licence by the Government taxi Authority. (Note: A licence does not place a limit on the number of taxi trips a company can supply.) The market for taxi trips in City has the following characteristics: Inverse demand for taxi trips is given by the function, P = 90 − Q/ 1000 In this equation, P is the price of a taxi trip, and Q is the total quantity of taxi trips supplied by licensed shuttle taxi companies. The marginal cost, to a taxi company, of supplying a taxi trip is $18. A taxi company’s only fixed cost is the cost of purchasing a licence from the Government Taxi Authority.
Question
Suppose that the Government Taxi Authority issues two licenses, to Big Ben Taxi and Whitehall Taxi. Find the equilibrium price and quantities for the case in which the two Taxi companies engage in homogeneous goods Bertrand (price) competition. Neglecting the cost of the license, what profits will Big Ben Taxi and Whitehall Taxi earn?