Substitute for Q2 in the demand function and.after solving for P. substitute for Pin the profit function: mx元-(53-g-(24-g)e)-g To determine the profit-maximizing quantity,we find the change in the profit function with respect to a change in 胎-8-现-2+0-8 Set this expression equal to 0 to determine the profit-maximizing quantity 53-2Q1-24+Q1-5=0,0rQ1=24. Substituting Q1=24 into Firm 2's reaction function givesQ: 2=24-24=-12 Substituteand into the demand equation to find the price P=5324-12=$17 Profits for each firm are equal to total revenue minus total costsor 1=(1720-(6)20=$288and 2=(1712-(6(12)=$144 Total industry profit,=+=$288+$144 =$432. Compared to the Cournot equilibrium,total output has increased from 32 to 36.price has fallen from $21 to $17.and total profits have fallen from $512 to $432.Profits for Firm 1 have risen from S256 to $288.while the profits of Firm 2 have declined sharply from $256 to$144. b. How much will each firm produce,and what will its profit be? If eachfirm believes that it is the Stackelberg kader,while the other firm is the Cournot follower,they both will initially produce 24 units,so total output will be 48 units.The market price will be driven to $5.equal o marginal cost.It is impossible to specify exactly where the new equilibrium point will be,because no point is stable when both firms are trying to be the Stackelberg leader. ete in selling identical wi choose their output nd Q2 s ly and face the dem P=30-2, where Q=Qi+Qz Until recently,both firms had zero marginal costs.Recent environmental regulations have increased Firm 2's marginal cost to $15.Firm Substitute for Q2 in the demand function and, after solving for P, substitute for P in the profit function: max  1 = 53 − Q1 − 24 − Q1 2         Q1 ( ) − 5Q1 . To determine the profit-maximizing quantity, we find the change in the profit function with respect to a change in Q1 : d dQ Q Q  1 1 1 1 = 53 − 2 −24 + −5. Set this expression equal to 0 to determine the profit-maximizing quantity: 53 - 2Q1 - 24 + Q1 - 5 = 0, or Q1 = 24. Substituting Q1 = 24 into Firm 2’s reaction function gives Q2 : Q2 24 24 2 = − = 12. Substitute Q1 and Q2 into the demand equation to find the price: P = 53 - 24 - 12 = $17. Profits for each firm are equal to total revenue minus total costs, or 1 = (17)(24) - (5)(24) = $288 and 2 = (17)(12) - (5)(12) = $144. Total industry profit, T = 1 + 2 = $288 + $144 = $432. Compared to the Cournot equilibrium, total output has increased from 32 to 36, price has fallen from $21 to $17, and total profits have fallen from $512 to $432. Profits for Firm 1 have risen from $256 to $288, while the profits of Firm 2 have declined sharply from $256 to $144. b. How much will each firm produce, and what will its profit be? If each firm believes that it is the Stackelberg leader, while the other firm is the Cournot follower, they both will initially produce 24 units, so total output will be 48 units. The market price will be driven to $5, equal to marginal cost. It is impossible to specify exactly where the new equilibrium point will be, because no point is stable when both firms are trying to be the Stackelberg leader. 5. Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q, where Q = Q1 + Q2 . Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm