Question: So I am stuck on finding the equilibrium quantity for a typical firm as a function of the total number of firms competing in the

So I am stuck on finding the equilibrium quantity for a typical firm as a function of the total number of firms competing in the market and using N to represent the total number of firms competing. Unsure of how to approach this question, I'll send the original details and question

The airfreight market is best modelled as Cournot competition. This is because compet- ing firms must hire aircraft and establish distribution networks before offering airfreight services. Demand for airfreight services is,

P =420.2Q,

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 60,000,000 packages per year. While the firm is inefficient, it manages to return an operating profit of $180,000,000 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.

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)

I've done steps 1-3

I need help with 4 5 and 6

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