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.

1.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.

2.Find the equilibrium market quantity and market price as a function of N.

3.Find the equilibrium producer surplus of the typical firm as a function of N.

Answer 1

Given demand for airfreight services

P = 42 - 0.1Q

Here,

P -> Price for transportation

Q -> Total packages per year

AAS = $30 per package

Number of packages transported = 120,000,000/Year

Profit after government revenue = $360,000,000

Hence demand is

1. P = 42 - 0.1(120000000*3N)

360000000 = 42 - 36000000N

36000000(10+N) = 42

N+10 = 42/36000000

i.e., N+10 = |42/36000000)

N+10 = 116

N = 106

2. Market Quantity = 42 - 0.1(N+10)

Market Price = 6*(42 - 0.1(N+10)

3. Given Demand

P = 42 - 0.1Q

P = 42 - 0.1(N+10)

P = 42 - (N/10 + 1)

(N+10)/10 = 42 - P

Hence, P = 42 - (N+10)/10