Question

You are asked to perform a merger simulation. Suppose inverse demand is P=360-Q. a) There are three firms in the industry: A, B and C. The firms have costs of zero. Suppose the three firms pick quantities simultaneously. That is, they play a Cournot game. What quantities do the firms choose? What is the price? Hint: In this case, Q=QA+QB+Qc. Compute MR for each of the three firms, and then derive three best response functions, and then solve the three functions simultaneously to get quantities. Now firms B and C merge. The market is a duopoly. What is the new quantity and b) price? c) Recall that the Department of Justice is particularly concerned about price increases of 5% or more. Would the DOJ oppose this merger?

Answer 1

classmate Date 2 c = 360-1360-QB QC -QB 2 P = 360-8. 8 = QAT QB+Qc p= 360-(Q At Q B t Qc) for from A. _TRA = P QA = (360-QA-QB-8c) &A TRA = 360 8A 8A-QA QB - Q&A TCA =0 TTA - TRATCA ac = 720 - 300 t QB tac - 29B O c = 360-QB toc 4 QC = 360-QBtQc 3 QC + QB = 360 - 300-2QA-QB - Qc = 0 360 - QB- Qc = 2 QA QA = 360-QB-QC Best response 2 - function of A. Similarly QB - 360-QA - QC 4 QB = 360 +QB-QC 3QB tac =360 306 +QB = 360 2QA-2QB: 360 2QB-2Qc =0 388 +QB3340 7 QB = QC - 4 Of 360 p=360-280 QA = 360-QB-QB 2B = 360 | 2 Rultino & c = 360-QA-QB = 360 - 201T 90 QB = 360-1360-QB - QC)-oc 9 B=50 fan so A B - 90 tor-go QA = 90 720-3 to to Blac-206 EQAD288 = 360 QA = 360-180 the 350 2

classmate with duopoly Date Page on = 120 QA =120 If both merge market duopoly a las P = 360-/GA TOB) P = 300-QA - QB P = 360-240 20 seher yes, DoJ oppose as merger. Beause, n merger, duopologs Price has risen from go to 120 for firm A. TA - TRA - TCA = Boo-QA - Qn) QA - 0 TTA = 360 QA-QA - QA QB Отр - 0 o change in price = 120-90 100 360 - 29A - QG = 300-QB-QA - ooo - 333.33% QB -QA Best response - of firma Similarly TQ R = 360-QA QB = 300 (360-03 DB 720-360+03 4 4 QB = 360tQB SOB = 360
Please see the above picture attached .With three firms ,Quantity produced by each firm=90 and price charged=90

But with mergers ,only two firms ,Quantity charged by each firm=120 and price charged=120.

DOJ is concerned with price increses, which is 33.33% and thus oppose the merger.