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? To determine the Cournot-Nash equilibrium,we first calculate the reaction function for each firm,then solve for price,quantity,and profit.Profit for Texas Air,is equal to total revenue minus total cost: 元1=(100.Q1-Q2)Q1·40Q1,or 元1=1009-Q-Q2-402,or元=60-Q-4Q2 The change in with respect to is 8-0-20-0 Setting the derivative to zero and solving for in terms of 2 will give Texas Air's reaction function: Q1=30-0.5Q2 Because American has the same cost structure,American's reaction function is Q2=30.0.5Q1. Substituting for Q2 in the reaction function for Texas Air, Q1=30.0.5(30.0.5Q1)=20. By symmetry,Q2=20.Industry output,r,is Q plus Q2,or 2r=20+20=40 Substituting industry output into the demand equation,we find P =60.Substituting Q1,Q2,and Pinto the profit function,we find 1=2=60(20)-202.(20)(20)=$400 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? To determine the Cournot-Nash equilibrium, we first calculate the reaction function for each firm, then solve for price, quantity, and profit. Profit for Texas Air, 1, is equal to total revenue minus total cost: 1 = (100 - Q1 - Q2)Q1 - 40Q1, or   1 1 1 2 1 2 1 1 1 1 2 1 2 =100Q −Q −Q Q − 40Q , or = 60Q −Q −Q Q . The change in 1 with respect to Q1 is   = − − 1 1 1 2 60 2  Q Q Q . Setting the derivative to zero and solving for Q1 in terms of Q2 will give Texas Air’s reaction function: Q1 = 30 - 0.5Q2. Because American has the same cost structure, American’s reaction function is Q2 = 30 - 0.5Q1. Substituting for Q2 in the reaction function for Texas Air, Q1 = 30 - 0.5(30 - 0.5Q1) = 20. By symmetry, Q2 = 20. Industry output, QT, is Q1 plus Q2, or QT = 20 + 20 = 40. Substituting industry output into the demand equation, we find P = 60. Substituting Q1, Q2, and P into the profit function, we find 1 = 2 = 60(20) -202 - (20)(20) = $400