Explain why the Government Taxi Authority has an incentive to only issue one licence.

In Lumino City, the taxi industry is regulated by the Government Taxi Authority. A company can only supply taxi services, in Lumino City, 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 Lumino 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 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 1: Suppose that the Government Taxi Authority issues only one license, to Big Ben Taxis. Assuming uniform pricing, find the quantity of taxi trips that Big Ben Taxis will choose to supply, and the price at which these trips will be sold. Neglecting the cost of the license, what profit will Big Ben Taxis earn. (8 Marks)
Question 2: Now suppose that the Government Taxi Authority issues two licenses, to Big Ben Taxis and Whitehall Taxis. Find the equilibrium price and quantities for the case in which the two taxi companies engage in Cournot (quantity) competition. Neglecting the cost of the license, what profits will Big Ben Taxis and Whitehall Taxis earn. (8 Marks)
Question 3: Now suppose that the Government Taxi Authority offers an unlimited number of licences for sale at a price of $600,000 per license. How many companies will purchase a license? Briefly explain. (You should assume that, if more than one firm is present in the market, firms engage in Cournot competition.) (4 Marks)
Question 4: Repeat question 2 for the case in which the two firms engage in homogeneous goods Bertrand (price) competition. (3 Marks)
Question 5: Explain why the Government Taxi Authority has an incentive to only issue one licence. What problem does the Government Taxi Authority create if it only issues one licence? (2 Marks)

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