The equilibrium output at B is lower than the output at the competitive solution and the output at the Cournot equilibrium The equilibrium price at B is higher than the price at thecompetitive solutionand the price at the Cournot equilibrium Answer 2.3 (a) For competitive output, firms take price as given in maximizing their own profits P which implies if P>0 0,+∞)ifP=0 That is, the firms supply curve is the horizontal line at P=0. So is the industry The equilibrium industry supply is thus y*= 100 and the equilibrium ce Is (b) Firm 1 maximizes his own profit, given any y maxr;≡P(1+y2)h=(100--v)h, which gives the foc 100-2 Firm 1's reaction function is thus 3n=2(100-y2) (c) By symmetry, the outputs for the two firms should be the same in equilibrium. By the reaction function in(b), we hence have y1 =5(100-1), which gives y1 Therefore, the Cournot equilibrium is 1=y (d)Suppose the two firms collude. They form a monopoly and maximizes their total max≡P(Y)Y=(100-Y)Y, which gives the cartel output: Y*= 50• The equilibrium output at B is lower than the output at the ‘competitive solution’ and the output at the Cournot equilibrium. • The equilibrium price at B is higher than the price at the ‘competitive solution’ and the price at the Cournot equilibrium. Answer 2.3. (a) For competitive output, firms take price as given in maximizing their own profits: max πi ≡ P yi, which implies y∗ i = ⎧ ⎪⎨ ⎪⎩ +∞ if P > 0 [0, +∞) if P = 0. That is, the firms’ supply curve is the horizontal line at P = 0. So is the industry supply curve. The equilibrium industry supply is thus Y ∗ = 100 and the equilibrium price is P∗ = 0. (b) Firm 1 maximizes his own profit, given any y2 : max πi ≡ P(y1 + y2)y1 = (100 − y1 − y2)y1, which gives the FOC: 100 − 2y1 − y2 = 0. Firm 1’s reaction function is thus yˆ1 = 1 2 (100 − y2). (c) By symmetry, the outputs for the two firms should be the same in equilibrium. By the reaction function in (b), we hence have y1 = 1 2 (100 − y1), which gives y1 = 100 3 . Therefore, the Cournot equilibrium is y∗ 1 = y∗ 2 = 100 3 . (d) Suppose the two firms collude. They form a monopoly and maximizes their total profit: max π ≡ P(Y )Y = (100 − Y )Y, which gives the cartel output: Y ∗ = 50. 2—7