(e) Firm 1 will behave as in( b), and reacts according to his reaction function 1 (100-12). Firm 2 will take this into consideration when maximizing his own profit max 2=P3n(32)+g2lbp=I (100-y2)y2, which implies y*=50. Then, yi=25 In summary, the competitive industry output is the highest, the Stackelberg industry output is the second, the Cournot industry output is the third, and cartel output is the lowest nswer (a) The profit maximization for firm i is max丌 ∑m)m-(k+t)m The FOc is P(Y)+P(Y)yi=k+ti (b) By summarizing (3) from i=l to n, we have nP(Y)+P()Y=mk+∑t This equation determines the industry output Y, which obviously depends on >t rather than the individual tax rates tis (c)Since the total output depends only on > ti and the latter has no change, Y doesn't change for a tax change. Then, by 3), At;= P(Y)Ayi,i.e Pr(Y determined by(4) Answer 2.5. This is from Example 12.E. 2 on page 407 of MWG(1995). Once n identi- cal firms are in the industry, they play a bertrand game. As we know, if n >0, the result he competitive outcome, i.e., P*=c and the profit without including the entry cost K is zero for all the firms. This means that each firm loses K in the long run. Knowing this, once one firm has entered the industry, all other firms will stay out. Therefore, more intense competition in stage 2 results in a less competitive industry!(e) Firm 1 will behave as in (b), and reacts according to his reaction function yˆ1 = 1 2 (100−y2). Firm 2 will take this into consideration when maximizing his own profit: max π2 ≡ P[ˆy1(y2) + y2]y2 = 1 2 (100 − y2)y2, which implies y∗ 2 = 50. Then, y∗ 1 = 25. In summary, the competitive industry output is the highest, the Stackelberg industry output is the second, the Cournot industry output is the third, and cartel output is the lowest. Answer 2.4. (a) The profit maximization for firm i is max πi = P #[n j=1 yj $ yi − (k + ti)yi. The FOC is P(Y ) + P0 (Y )yi = k + ti. (3) (b) By summarizing (3) from i = 1 to n, we have nP(Y ) + P0 (Y )Y = nk +[n j=1 ti. (4) This equation determines the industry output Y, which obviously depends on Sn j=1 ti, rather than the individual tax rates ti ’s. (c) Since the total output depends only on Sn j=1 ti and the latter has no change, Y doesn’t change for a tax change. Then, by (3), 7ti = P0 (Y )7yi, i.e., 7yi = 7ti P0 (Y ) , where Y is determined by (4). Answer 2.5. This is from Example 12.E.2 on page 407 of MWG (1995). Once n identi￾cal firms are in the industry, they play a Bertrand game. As we know, if n ≥ 0, the result is the competitive outcome, i.e., p∗ = c and the profit without including the entry cost K is zero for all the firms. This means that each firm loses K in the long run. Knowing this, once one firm has entered the industry, all other firms will stay out. Therefore, more intense competition in stage 2 results in a less competitive industry! 2—8