Suppose the airline industry consisted of only two firms: American and Texas Air

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=130Q

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 produceunits 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 $.

Explanation / Answer

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=130Q. 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.

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