If both firms must announce output at the same time,both firms believe that the otherfirm is behaving rationally,and each firm treats the output of the other firm as a fixed number,a Cournot equilibrium will result For Firm 1.total revenue will be TR=(30-(Q:+Q))Q.or TR,=30Q,-Q-QQ Marginal revenue for Firm 1 will be the derivative of total revenue with respect to. OTR =30-2Q-Q. Because the firms share identical demand curves the solution for Firm 2 will be symmetric to that of Firm 1: aR=30-20-Qr 80. To find the profit-maxir venueomng level of output br both firms set markina 0=15-g and 02=15-号 With two equations and two unknowns,we may solve for Q and g=15-o515-9 .0rQ,=10 By symmetry,Q2=10. Substitute and into the demand equation to determine price P=30-(10+10.orP=$10 Since no costs are given,profits for each firm will be equal to total revenue: 1=TR1=(1010)=$100 and xg=1R2=(10X10)=$100 Thus,the equilibrium occurs when both firms produce 10 units ofoutput and both firms earn $100.Looking back at the payoff matrix,note that the neither firm will have an ntive to deviate,given the other firm's choic b. Suppose you are told that you must announce your output before your competitor does.How much will you produce in this case,and how much do you think your competitor will produce?What do you expect your profit to be?Is announcing first an advantage or disadvantage?ExplainIf both firms must announce output at the same time, both firms believe that the other firm is behaving rationally, and each firm treats the output of the other firm as a fixed number, a Cournot equilibrium will result. For Firm 1, total revenue will be TR1 = (30 - (Q1 + Q2 ))Q1 , or TR1 Q1 Q1 Q Q 2 1 2 = 30 − − . Marginal revenue for Firm 1 will be the derivative of total revenue with respect to Q1 ,   TR Q Q Q 1 = 30 − 2 1 − 2 . Because the firms share identical demand curves, the solution for Firm 2 will be symmetric to that of Firm 1:   TR Q Q Q 2 = 30 − 2 2 − 1 . To find the profit-maximizing level of output for both firms, set marginal revenue equal to marginal cost, which is zero: Q Q 1 2 15 2 = − and Q Q 2 1 15 2 = − . With two equations and two unknowns, we may solve for Q1 and Q2 : Q1 =15 − (0.5) 15 − Q1 2     , or Q1 = 10. By symmetry, Q2 = 10. Substitute Q1 and Q2 into the demand equation to determine price: P = 30 - (10 + 10), or P = $10. Since no costs are given, profits for each firm will be equal to total revenue: 1 = TR1 = (10)(10) = $100 and 2 = TR2 = (10)(10) = $100. Thus, the equilibrium occurs when both firms produce 10 units of output and both firms earn $100. Looking back at the payoff matrix, note that the outcome (100, 100) is indeed a Nash equilibrium: neither firm will have an incentive to deviate, given the other firm’s choice. b. Suppose you are told that you must announce your output before your competitor does. How much will you produce in this case, and how much do you think your competitor will produce? What do you expect your profit to be? Is announcing first an advantage or disadvantage? Explain