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3 Manager, of two competing oligopoly firms. Al's elk. din' rick.cs simultaneously. Al (A) and I. (ft) lace the following dernond Ind loos., cow condltleat, lebldt at common knowledge to the managen Q...

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3 Manager, of two competing oligopoly firms. Al's elk. din' rick.cs simultaneously. Al (A) and I. (ft) lace the following dernond Ind loos., cow condltleat, lebldt at common knowledge to the managen Q XXXXXXXXXX, slat LACA 13* XXXXXXXXXX', 1PA and LAW.. LAC.. VS.67 The prices, PA and are the prices cheesed by Mood Itert respectively Tbe Qa Ors, the respective daily quonthies sold by each firm. lhe figure below allows Thett's best-evapaewe ctArYc, DR. ()My one 'mint on Ars best•response curve, point le shown la the nista
a. When Al believes licit is going to dungy a pf iee of $50, Al's best response i, to charge a peice of S Plot this price par on the graph, label it J, end then .w the best-response cure far A; (label this boo b. Given the best.msponse curves for Al cunt Bert, you would predict that Al will choose price of and Bert will choose e price of S Label thie polM N in the figure below. c. At the prices associated with polio N (see part 1,, Al can expect to earn daily profit of S mot Rat can expect to mini a deity profit of S At point C in the figure, Al piens to price ut Scli and Hat et S60. d. At point C, Al earns dully profit of S whkh is (imre, lass) than it would earn at point N. Bert enm. titoly profit of _ , which Is (more, las) than would ram at point N. e Point C is na likely to he the decision outcome because it is not and either flmt could unil.temlly °wrens°, decrease) Its price end earn grader daily Profit.
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Answered Same Day Dec 21, 2021

Solution

Robert answered on Dec 21 2021
128 Votes
Answer to 3:
Al: QA = 72-4pA+4pB and LMCA = LMCA = $2
Bert: QB = 100-3pB+3pA and LMCB = LMCB = LACB = $6.67
Al would maximize:
A = pAQA – 2QA = 72pA – 4pA^2 + 4pBpA – 2*72 +2*4pA -2*4pB
At maximum d A/dpA = 0 implies
72 – 8pA + 4pB +8 = 0, simplifying this we get reaction function for Al as;
BRA: pA = (10 + 0.5pB) ………………….. (1)
Similarly Bert would maximize
B = pBQB – 6.67QB = 100pB – 3pB^2 + 3pApB – 6.67(100-3pB+3pA)
At maximum d B/dpB = 0 implies
100 – 6pB + 3pA +20 = 0, simplifying this we get reaction function for Al as;
BRB: pB = (20 + 0.5pA)...
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