The airport shuttle services market is best modelled as Cournot competition. This is because competing firms must lease shuttle buses and establish supporting technical in- frastructure 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. The Minister for Transport has instructed you to recommend an appropriate licence fee for the airport shuttle market. The minister has three objectives: 

1. Maximise government revenues from the licence fee; 

2. Minimise the cost of airport shuttle services to consumers, and; 

3. Increase the number of people using the shuttle services to at least 300,000. Note that competition policy prevents the government from imposing any other form of market regulation, including price controls or quotas. 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.