Question

(16 points) Cournot Duopoly. Market demand is p(Q) = 50 – 4Q, where Q = 4+ 42. Firm 1's cost function is C (91) = 0, and firm 2 has a cost function C2(92) = 1092- The two firms engage in Cournot competition; they simultaneously choose a quantity and the price adjusts so that the market clears. (a) Formally write firm 1's profit maximization problem (b) Find firm l's best response function. (c) Take as given that firm 2's best response function is 42 = 5 - 591. Find the equilibrium quantities. 91 = ------------- 42 = ----- (a) When the market is at the equilibrium you found in part c., find the elasticity of demand. dQ(p) E = dp 26) = ----------

Answer 1

Both the firm will try to maximize their profit and choose quantities simultaneously.

Profit = Revenue - Cost

Ans a) Market demand, PC) - 50 - 49. Firme's cost function, G (01) - 0 Firm 2's cost function Co (Ve) : 10V Iwo firms engage in couenot competition from a's Revenue, Ri= P(Q), 9/1 = 150 - 4 (+/)) V cost, a (0) = 0 Firm is profit maximization probleem is, mase Rice (ai). et, mase [50 - 4 (v +212) 00, -0. om max. (50 - 4 (0, +0,2)] WV To find out the best response function, we need to manimire ...(as e (961) = 0] 29 proget w.pt. a → - π = Ri-a (011). en TT,= (50 -4 (91, +962)79 = 50 -89,- 422 F.O.C. for profit mazémization orequires, JM 20. 50-800,-40V2 -0. eu 891, -50 - 4010 om, avi - so - į V2 09, av, a 25- avg → Best Response function of pisem 1. Firma's best response function is al = 5-1291 Putting 92 en firm 1's best response function, we get a V = 25 -Ź 15 - Qi] on, gizarte +40v. e)

导 : 号 We = 6 - Axs -s - 2 " a's S , 03::s} | A 1 20zilibsituw, g* * * -5+2" Se 1 P*:0-49 2 SO - 4x1's 20-30 *20 elasticity of demands P20-4g. 49 - P. | 91 Q = 1's - FA : 最 “是25] : - - At egna - 1 2 * :