Question

Suppose we have two firms with the same cost C(q) = {Q2 in a market which demand is Q 18 – P, the two firms compete in the Cournot Model. a. Set up firm 1's profit maximization and best response function. b. Solve for firm 1's quantity, firm 2's quantity, the equilibrium market quantity, and price. Please show your work. c. Is this a Nash equilibrium?

Answer 1

TR1 = (1B- Q-Q) a 2 TR, - 188, Q Q,Q2 ITRI = 18(1) - 20 Qy (1) da, MR = 18 -29, - P2 Profita maximizing Condition MR,=MC, 18-20, -Q2 = 0 = 18 20,ta taa 3Q, & Q = 18 (BRI) رف Firma Best response function TR2 = POL (18-Q, -Q₂JQ 1802 2 ♡ ar MR₂ dTR2 T20

MR2 = 18 (1) Q (1) -20% MR₂=18 - Q - 2P2 profit-maximizing MR₂=MC condition 18-01-2% az - 18 Q,+20 +22 ait 3 Q₂ 18 Multiplying by (3) 3Q, ta Q2 =su (BR₂ Solvin ing BRI and BR2 30, +9Q -S4 3Q, & Q2 Tlf 8 Q2 = 36 Q2 = 36

Q 4.s unite substitu using Qq into BR, 30, +4.5 =18 32 cl8-4.5 13.5 3 २ =his mit substitut uting Q and a into P P=18 - us-4.5 = 18-9 = $9 occurs (c) This is Wash Equilibrium because Nash equilibrium at the utrusection of BRI and BR₂. Q, 2 und has been calculated at the autresection of BR, and BR.2