Question

Explain and compare Cournot’s and Bertrand’s duopoly models by using graphical analyses.

Answer 1

Mount Dushely Model Markets with 2 2 finns 1) Cournet Model : Assumption in the market (E) Product is Ironingeneous (wo) Beve firmos con observe loch other (iv) binultoneous Quant duontity setting (form (in only two ferns is met in prue but competing in ouantity only) Firm - produces & firma produces > 92 Pza-be Do curve foring the firm a=qit q2 Pz 100-20 Q=%> Boekent of Mczo the In perfect confection a-buzo In Monopoly, TRE Pod= e-bay.de (Flae funta we sell in the perfect Competition in the market = aa-be? MR 2 d (TR) 2- 260 inder Monofuely Morked in Март , MR=Mch Q-260=0 26 [ Mouspaly durys 1.. d=a of the hatent of the marke sect half

Đq = 2 ( 2 / -9% 2 Profs funsion for firma Те . or [a-b.[qutq, 2) Jq Qqi - bq, ?- bajıq 2 Q-2691 091 TI dai - Dunia 2 oq => 269 2 Q. - bq 2 Iqt 28 2 kotheefanel few time bright funition for form 2 62 T2= aqz Tzz Pogza [e-b[q 189 2 3 2 2 3 - bas -bqiqz dan = 2-691-> aa-2bqz-bogo 26q2 892 q= Q 20 1 2 07 2 92 % - Bart renforse of a But his posuse funkrong 0/26 (0,2) -B.R 2 of 1 t 0 2/26 %q, qa' Cong > BR of 2' C @ (92000) (20) 97 $

Angers of them 6 % fulang raw ofre found /26 fre* q = 2/6 1 [ 2 / - 211 qui 1/20 a% 9 = 2 / - / + 1 4 Q Q => qi- 'qta G <z> 391 X 36 uo Mb futhing, que in 2 : q * = 1 / 2 - 1 2 [ 36 ] = 2 / 3 b O +82 (baoba Q * 2 a 3 b ya - G( 2 & => 139 urtessutom of en what the other io in the In love of Courmet hq m markets hem is reached through beat Gilogrome funtion of the 2 firme. Erst response function represente the set of al nosh strategies (Nash strategy is the best Strategy that one con chuose given doing market ) & intercettisin o best response function mothing noch strictures with respect to lock Wither. The rom is unique which shows that there is Enly Combination of nosh strategy which matches for with the firm Muv ,ct dieder forme have Uue

the market individ & rd of forms froduce 1/2nd of tre bcdent of the market idually (9/6 2/3 the bekent of market together output in the market is higher than monopoly but lesser kron perfect competition free charged is lesser than nonopety A higher than perfect competition. The forms priduce desser sulfut thon perfect competition which means weight that the market has dead loss.

Pure Bertrand Model 1) auopuly 2) Homogeneuses goods 3) Mc=0 9 No fired last 4) Simultonseus prie setting mudel firms All homogeneous have ne et where betch the only maximise their but Cortels do not sustain in this Cose The. firms realise that the one whhe breaks the Cortel will nece In love of pure best and mudel Commodities, observing each other in the market. This means that som takes place that price firms further possibility to increase their frufet. The forms Con lortalise & firsduce charging a nomopoly price to profits necessorely you more than the other & therefore find it profitable to compete for eg if the test mobbet hasadowsand funtimo P=30-2 4 mc=z then there Cannet be until price is above 3 this is because sus have the incentive to reduce the frice & tell more , renewing from from Competition. Therefore rom through Induction of possile free serotafy then it results in interesting there possible profet only if they charge price = prue = me this is called Bertrand forodose because even through the market hos only tuae firms, yet ferie charged in the market is competitive free evrows frofit. Bertrand forodos con dise only that ferus do not have copacity constraint. है m uther backward reach when th they of frofst of the firms is zero resumption under the

Copathy only . If there is a Constraint in the market then forms compete till the Copacity reached tare lower Syed forms & then S the form water ligner Cefacity Con charge monapely free Bertrand froduct differentiation Products are close substitutes 9,- debith ai - aplikative difference Model with of loch other 1212 92=Q2-p2 thi ñ n Ti = piq = pi [ar-p1 + b 1 = pra, = pp? + pipe dal = 2,-2 pit P2=0 al +22 opi 13. R 노 8 fann 1 w I 2 = 6292 = P2 [az-pe this ] =Qz pz - b 2 + pip- z 4 do 2 2.2 - 2 p2th co oly h saibi-p,2+P1P2 h 8 hergetelff the function of from a fuering po= alt 1/2 [ 22 + b ******** om @ I ki 49 2 6 6bli 64 Q1 +0.2 » 16 bi [ all Qi ot.Q2 고 16 J to 63

Pukking Pit in a art 1/3 [ 32 g 32 ant y az $ z * =Q2 + yaittaa 63 126 - Z 2 63 + Pz * = 69 22 hal 126 T3 fiz ai-b-t Pr ñ Generalised = 192 ja 1, 2 ifj lach other form Ana Competiture bertrand model where firms del Close substitutes of eqm force in the market is determined by ouality Cornfoment of brekin both firms att hos bargers responseness brown cony infrovement in own improving the Cefality of the form to charge regher free it hulso observed a that there is a direct relation between firm & Capobuery to charge frue by e quen form is a higher as results in higher this because aufrovence- ?, & higher as results in highere reality of procedent by suy given for to pay in the market which firms are charge are charge nuere. Budity becouse own budil uusiky necessarily results in R. kisasa, trosged by Powollty provided otcher m rend in Q thereaus rin wellsongerness enables all the