Question

Suppose the airline industry consisted of only two​ firms: American and Texas Air Corp. Let the two firms have identical cost​ functions,

​C(q)=40q.

Assume that the demand curve for the industry is given by

P=130−Q

and that each firm expects the other to behave as a Cournot competitor.

Calculate the​ Cournot-Nash equilibrium for each​ firm, assuming that each chooses the output level that maximizes its profits when taking its​ rival's output as given. What are the profits of each​ firm? ​(For all of the​ following, enter a numeric response rounded to two decimal​ places.)

When​ competing, each firm will produce？units of output.

In​ turn, each firm will earn profit of $？.

What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of

​$40​?

If Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of $40​,

American would produce ？units and Texas Air Corp. would produce ？units.

In​ turn, American's will earn profit of $？ and Texas Air Corp. will earn profit of $？.

Answer 1

From the cost function ​C(q)=40q, we have the marginal cost of $40 for both firms.

The demand curve for the industry is given by P=130−Q. This implies the total revenue function is TR1 = 130Q1 - Q1^2 - Q1Q2 and TR2 = 130Q2 - Q2^2 - Q1Q2.............Q1 is the quantity by American and Q2 is the quantity by Texas Air Corp

This also gives the marginal revenue functions as MR1 = 130 - 2Q1 - Q2 and MR2 = 130 - 2Q2 - Q1.

Find the reaction functions as

MR1 = MC1 and MR2 = MC2

130 - 2Q1 - Q2 = 40 and 130 - 2Q2 - Q1 = 40

We have the reaction functions as

Q1 = 45 - 0.5Q2 and Q2 = 45 - 0.5Q1. Solve them to get Q1 = Q2 = 30 units. Price is 130 - 60 = $70 and each firm earns a profit of TR - TC = (70*30 - 40*30) = $900.

When​ competing, each firm will produce 30 units of output. In​ turn, each firm will earn profit of $900

Now that Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of ​$40​, we have the following reaction functions

130 - 2Q1 - Q2 = 40 and 130 - 2Q2 - Q1 = 25

We have the reaction functions as

Q1 = 45 - 0.5Q2 and Q2 = 52.5 - 0.5Q1. Solve them to get Q1 = 25 and Q2 = 40 units. Price is 130 - 65 = $65 and the profit are

American = (25*65 - 40*25) = $625

Texas Air corp = (40*65 - 25*40) = 1600

If Texas Air had constant marginal and average costs of $25 and American had constant marginal and average costs of $40​, American would produce 25 units and Texas Air Corp. would produce 40 units. In​ turn, American's will earn profit of $625 and Texas Air Corp. will earn profit of $1600.