Question

I need some help on finding out the American units and Texas Air Corp units, please.

Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 40. Assume that the demand curve for the industry is given by P = 160-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? (Round all quantities and dollar amounts to two decimal places.) When competing, each firm will produce 40 units of output. In turn, each firm will earn profit of $ 1600 What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of $40? units and If Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of $40, American would produce Texas Air Corp. would produce units.

Answer 1

First case with C(q)=40q

Marginal Cost=MC=dC(q)/dq=40

Let output of Texas Air be q1 and output of American Air be q2

So, Q=q1+q2

P=(160-Q)=160-q1-q2

Total revenue of Texas air =TR1=P*q1=(16-q1-q2)*q1=160q1-q1²-q1q2

Marginal Revenue of Texas air=MR1=dTR1/dq1=160-2q1-q2

Set MR1=MC for profit maximization

160-2q1-q2=40

q2=120-2q1 -------(1)

Total revenue of American air =TR2=P*q2=(16-q1-q2)*q2=160q2-q2²-q1q2

Marginal Revenue of American air=MR2=dTR2/dq2=160-2q2-q1

Set MR2=MC for profit maximization

160-2q2-q1=40

Put q2=120-2q1 (from equation 1)

160-2*(120-2q1)-q1=40

160-240+4q1-q1=40

3q1=120

q1=40

q2=120-2q1=120-2*40=40

When competing, each firm will produce 40 units of output.

P=160-q1-q2=160-40-40=$80

Since output and cost of each firm is same,

Profit of each firm=p*q1-40q1=80*40-40*40=$1600

In turn each firm will earn a profit of $1600

Now consider the second case, where Marginal costs are different.

Put MR1=MC1

160-2q1-q2=10

q2=150-2q1 ----(2)

Put MR2=MC2

160-2q2-q1=40

Put q2=150-2q1 (from equation 2)

160-2*(150-2q1)-q1=40

160-300+4q1-q1=40

-140+3q1=40

3q1=180

q1=60

q2=150-2q1=150-2*60=30

If Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of $40, American would produce 30 units and Texas Air Corp. would produce 60 units.