To determine Q substitute for in the reaction function for American: 02=30-(0.537.5.0.5Q2=15. American has cut back slightly in its output in response to the increase in output by Texas Air. Total quantity.Or is+Qa.or Qr=30+15=45. Compared to 8 the equilibrium quantity has risenslightly. =404,how $40 to $25,assuming that American will not follow suit?How much should American be willing to spend to reduce its marginal cost to $25, assumingthat Texas Air will have marginal costs of regardless of American's actions? $400 under the original cost structun (65)80).(25)30)=8900 The difference in profit is $500.Therefore.Texas Air should be willing to invest up to $500 to lower costs from 40 to 25 per unit (assuming American does not follow suit). To determine how much American would be willing to spend to reduce its average wp.myst calculate the difrenee in profite exas Air's average First,without investment,American's profits would be (65)(15)·(40(15)=$225 Second,with investment by both firms,the reaction functions would be 1=37.5.0.502 and Q2=37.5.0.50. To determine substitute forin the first reaction function and solve for 21=37.5-(0.5037.5.0.5Q)=25 Substitutingfor in the second reaction function to find Q2=37.5.0.537.5.0.5Q2)=25 Substituting industry output into the demand equation to determine price: P=100.50=$50. Therefore,American's profits if Q=Q2=25(when both firms have MC =AC 25) are 2=(100.25.2525)·(25)(25)=$625. To determine Q2 , substitute for Q1 in the reaction function for American: Q2 = 30 - (0.5)(37.5 - 0.5Q2 ) = 15. American has cut back slightly in its output in response to the increase in output by Texas Air. Total quantity, QT, is Q1 + Q2 , or QT = 30 + 15 = 45. Compared to 8a, the equilibrium quantity has risen slightly. c. Assuming that both firms have the original cost function, C(q) = 40q, how much should Texas Air be willing to invest to lower its marginal cost from $40 to $25, assuming that American will not follow suit? How much should American be willing to spend to reduce its marginal cost to $25, assuming that Texas Air will have marginal costs of $25 regardless of American’s actions? Recall that profits for both firms were $400 under the original cost structure. With constant average and marginal costs of 25, Texas Air’s profits will be (55)(30) - (25)(30) = $900. The difference in profit is $500. Therefore, Texas Air should be willing to invest up to $500 to lower costs from 40 to 25 per unit (assuming American does not follow suit). To determine how much American would be willing to spend to reduce its average costs, we must calculate the difference in profits, assuming Texas Air’s average cost is 25. First, without investment, American’s profits would be: (55)(15) - (40)(15) = $225. Second, with investment by both firms, the reaction functions would be: Q1 = 37.5 - 0.5Q2 and Q2 = 37.5 - 0.5Q1 . To determine Q1 , substitute for Q2 in the first reaction function and solve for Q1 : Q1 = 37.5 - (0.5)(37.5 - 0.5Q1 ) = 25. Substituting for Q1 in the second reaction function to find Q2 : Q2 = 37.5 - 0.5(37.5 - 0.5Q2 ) = 25. Substituting industry output into the demand equation to determine price: P = 100 - 50 = $50. Therefore, American’s profits if Q1 = Q2 = 25 (when both firms have MC = AC = 25) are 2 = (100 - 25 - 25)(25) - (25)(25) = $625