Question

Consider a market with two firms. Suppose that that firm 2 that invests in a new technology that changes it cost structure from firm 1. Market demand is Q = 18 – P, firm 1 faces costs G; (21) = {Q}, and firm 2 has costs, Cz (22) = 3. Consider a Cournot. a. What is firm l's best response function? b. Set up firm 2's profit maximization and solve for firm 2's best response function. c. Find the equilibrium quantity for firm 1, firm 2, the market quantity, and price.

Answer 1

as For firmie Q = 18-1 p=18-0 Here, Q = 9,792 MC, dCTC ;) dq, q IMC, 2 The = Pixh (18-9-219, = 189, - q, 2-9q TRE de TRJ dh a 18-29, -22 18-29, -92 = h Reaction function 39tq2 18 - Ti firma

and price, p= 20-20 = 20-2x 4 20-8 $ 12 MC₂ = a (T(2) dqz fx 292 . 92/3 i. R2 = 1892 - 99₂ - 9 2² FR2 & CTR 22 dq2 a 18- q - 292 So, MC2 = MR2 18-9, - 292 92 3 ใน 54-39,- 692 39, +792 feaction Finction from 2 54 -- Gil

MIR2= d [TR2) dq2 = 120-29, -3492 Now MC2 = MIR2 120 - 24-492 = 2 29, + & 2 = 118 -- tin Now Solving equation ci, and is for q, and 22 by elimination method 49, t2q2 = 116 29, +492 - 118 - - X 4 X2 89, + 492 = 232 89,+ 1692 = 472 1292 = 24 (1 2 = 20 uqt 222 = 116 49, + 2x 20 = 116 and - p=120-2 (9, +22) 2120-2x 39 IP = $42