Question

In the market of cournot competition, the aggregate market demand is P 100 4Q a. There exists two firms in the market, with identical production technology, i.e. mci = m2-20. Calculate the cournot equilibrium in this case. Also, draw the best response functions for firm 1 and firm 2 in the((2) plane b. There exists two firms in the market, with different production technology, i.e. mci = 10 and m2-30. Calculate the cournot equilibrium in this case. Also, draw the best response functions for firm 1 and firm 2 in the (1,2) plane c. There exists two firms in the market, with different production technology, i.e. mci = 40 and m2 = 20, Calculate the cournot equilibrium in this case. Also, draw the best response functions for firm 1 and firm 2 in the (1,2) plane d. There exists 50 firms in the market, with identical production technology, ie. mci = mc50-20. Calculate the cournot equilibrium in this case. e. Among the 50 firms, two firms decides to merge with keeping the same production technolgoy as before. After the merger, there are 49 firms in the market, with identical production technology, mci - - mc49. Recalculate the cournot equilibrium in this case. Argue how the merger affects the market equilibrium

Answer 1

The aggregate market demand in P = 100 - 4(q_1 + q_2) MR_1 = 100 - 8q_1 - 4q_2 MR_2 = 100 - 4q_1 - 8q_2 At equilibrium: MR_1 = MR_2 = MC therefore 100 - 8q_1 - 4q_2 = 20 8q_1 = 80 - 4 q_2 therefore q_1 = 10 - 0.5q_2.....BR_1 Again 100 - 8q_2 - 4q_1 = 20 therefore q_2 = 10 - 0.5q_1....BR_2 By symmetry of BR_1 and BR_2: q_1 = 10 - 0.5q_1 and 1.5q_1 = 10 therefore q_1 = q_2 = 6 10/15 = 6 2/3 At equilibrium MR_1 = MC_1 = 10 MR_2 = MC_2 = 30 Therefore100 - 8q_1 - 4q_2 = 10 therefore q_1 = 90/8 - 0.5q_2....BR_1 Again, 100 - 4q_1 - 8q_2 = 30 on, 8q_2 = 70 - 4q_1 therefore q_2 = 70/8 - 0.5q_2.....BR_2 solving BR_1 and BR_2 BR_1 times 1 8q_1 + 4q_2 = 90 BR_2 times 2 8q_1 + 16q_2 = 140 12q_2 = 50 Therefore q_2 = 4 1/6 therefore q_1 = 9 1/6