Cournot's Nash equilibrium for two airline firms American and Texas Air Corp.
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. Suppose the demand curve for the industry is given by P = 100 - Q and that each firm expects the other to behave as a Cournot competitor.
a) Compute 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?
[Hint: Remember to solve this exercise that you need to make the derivative of the profits of each firm with respect to its own product (Q1) equal to zero. To find out the derivative remember that if Y=aX+bX2+cXZ, then dY/dX=a+2bX+cZ.]
b) 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?