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 eciency of the airfreight market.

The commission made two recommendations:

1. The airfreight services market should be opened up to competition from privately owned rms.

2. Each rm 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.

The airfreight market is best modelled as Cournot competition. This is because competing rms 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 ineffcient, it manages to return an operating prot of $360,000,000 per year into government revenues. The competition authority expects that after implementing the market reforms, all firms in the market (including 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 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.

So far, this is what i have,

Total-Cost Function

TC(Qa) = 6Qa+ 100,000,000

Profit Function (Since Q=Qa+X)

A = -0.1Q²a+0.1QaX + 36Qa - 100,000,000

Best-Response Function

d/dQa = 0.2Qa + 0.1x + 36

Qa = -0.5x - 180

Equilibrium quantity of the typical firm as a function of the total number of firms competing in the market, replacing x with (N-1)Qa

Qa = - (N-1)Qa/2 -180 or (N+1)Qa = 360

Equilibrium Market Quantity and Market Price

Q* = 360N/(N+1)

P* = 42-36N/(N+1)

Equilibrium Producer Surplus

PS = Q* (P* - MC)

PS = 12960N/(N+1)²

^{Need to find}

a. Maximise government revenues from the license fee

b. Minimise the cost of airfreight services to consumers and;

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