In the city of Cornicpia, the government holds a monopoly over the provision of airport shuttle services. Both the general public and business groups regularly complain about high prices and poor quality of service from the government owned monopoly, Cornicpian Airport Shuttles (CAS).

In response to these complaints, the government commissioned the competition authority to recommend steps for improving the efficiency of the airport shuttle services market. The commission made two recommendations:

1. The airport shuttle services market should be opened up to competition from privately owned firms.

2. Each firm operating in the airport shuttle services market, including CAS, should be required to pay an annual lump-sum licence fee to the government.

The competition authority expects that the reforms will lead to a lower cost, higher quality service. The government has pledged to implement both of the commission's regulations.

2.1 Industry structure

The airport shuttle services market is best modelled as Cournot competition. This is because competing rms must lease shuttle buses and establish supporting technical infrastructure before offering airport shuttle services. Demand for airport shuttle services is,

Q = 450,000 - 5,000P;

where Q represents the total number of passengers transported per year, and P is the price per passenger.

At present, CAS charges $50 a person and transports 200,000 passengers per year, returning an operating profit of $5,000,000 per year into government revenues.

The competition authority expects that after implementing the market reforms, all firms in the market (including CAS) will be more efficient. It expects that all firms will face the same cost structure with the marginal cost of transporting a passenger being $4, and the fixed cost of operating a shuttle service being $1,000,000 per year.

Complete following questions:

Step 1: Using the information provided in the scenario, derive a total cost function for a typical firm operating in the market. Use QA to represent the number of passengers transported by the firm. (4 marks)

Step 2: Using the cost function from step 1, derive a profit function for the typical firm. Use X to represent the combined number of passengers transported by all other firms. (7marks)

Step 3: Derive the typical firm's best-response function. (7 marks)

Step 4: Find the equilibrium quantity of the typical firm as a function of the total number of firms competing in the market. Use N to represent the total number of firms competing in the market. (6 marks)

Step 5: Find the equilibrium market quantity and market price as a function of N. (8marks)

Step 6: Find the equilibrium producer surplus of the typical firm as a function of N. (8marks)

Step 7: Complete any additional calculations that you require to support your recommendation. (10 marks)