Background Info

In the island nation of Autarka, the government holds a monopoly over the provision of airfreight services. Both the general public and business groups regularly complain about high prices and poor quality of service from the government owned monopoly, Autarka Airfreight Services (AAS). In response to these complaints, the national government commissioned the competition authority to recommend steps for improving the efficiency of the airfreight market. The commission made two recommendations: 1. The airfreight services market should be opened up to competition from privately owned firms. 2. Each firm operating in the airfreight market, including AAS, 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 national government of Autarka has pledged to implement all of the commission's regulations.

Question

The airfreight market is best modelled as Cournot competition. This is because competing firms must hire aircraft and establish distribution networks before offering airfreight services. Demand for airfreight services is, P = 42 0.1Q, where P represents the price of transporting a package, and Q is the total number of packages transported per year, measured in millions of packages. At present, AAS charges $30 a package and transports 120,000,000 packages per year. While the firm is inefficient, it manages to return an operating profit of $360,000,000 per year into government revenues. The competition authority expects that after implementing the market reforms, all firms in the market (includeing AAS) will be more efficient. Each firm in the market will be able to transport a package at a marginal cost of $6 per package, and face fixed costs of $100,000,000 per year.

The Minister for Transport has instructed you to recommend an appropriate licence fee for the airfreight market. The minister has three objectives:

1. Maximise government revenues from the licence fee

2. Minimise the cost of airfreight services to consumers, and

3. Increase the number of packages transported per year to at least 250,000,000.

Note that competition policy prevents the government from imposing any other form of market regulation, including price controls or quotas.

Required Steps:

When completing the industry analysis you should assume that firms are engaged in Cournot Competition.

Step 1: Using the information provided in the scenario, derive a total cost function for a typical firm. Use QA to indicate the number of packages transported by the firm (measured in millions of packages). (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 packages transported by all other firms (measured in millions of packages). (7 marks)

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. (8 marks)

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

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