Question

Suppose there are only two firms in the marker, firm A and firm B. They produce identical products. Firm A and firm B have the same constant marginal cost, MCA = MCB = ACA = ACB = 25. The market demand function is given by Q = 400 – 4P. a. If the firms practice under the Bertrand model, what will be the Nash equilibrium market price and output level? b. If these two firms practice under the Cournot model. Write the best response functions for firm A and firm B. c. What are the Cournot output level for each firm? What is the market output level? What is the market price? d. Graph the best response functions of firm A and B. and label the Cournot Nash equilibrium in the graph. e. Calculate the profits for each firm in the Cournot model. f. If these two firms cooperate and act as a monopolist. What is the monopoly price and monopoly output level

please answer all 10 questions
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Answer 1

under Bertrand comletition folccs are cquals To marginal costs. So bA=bB = 25 (Nash eam Prices) a = 400-4P - up= 400- = P = 100- 0.259 = Q = 400-4(25) - 400 - 100 9=300 Therefore P= 25 9=300 (6 9= 400-up = Up= 400- - P= 100- 0.259 G = 9 A+QB -> PE 100 -0.25 9A + 0.2598 for from To A TA TRA-TCA - P. QA - Mc QA TA ² (100 -0.259A-0.25 QB - 25) QA

TA=175-0.25 QA -0.25 QB) QA F.o.c ITA = 75-0.5 9 A-0.25 QB = 0 IGA =) 75-0.25 QB -= 9A 0.5 = 150 - 0.5 QB = QA BRASA BRA By symmetry BR-B 196= 150 - 0.594 For tournot Level There Yose BRA: QA = 150-0.5QB BRB : QB - 150 - 0.5Q A Ans-s for couronot level of out fut, Solving BRA and BRB, QA = 150-0.5 GB

QA = 150-0.5. (150-0.5 AA) QA = 150- 75+ 0.259 A 0.75 QA = 75 - QA = 75 0.75 = 100 By Symmetry PA = Q8=100 mastect out put Level (QATQB = 200 | market price 9 = 400-up =) 200 - 400 - up = up = 20.0 - p= 50 Ans-4 QB 3oo1 BRA 50 150 - BRA 50 QA 0 50 100 150 200 250 300

Ans-5 Profit of from A TA= TRA-TCA = PA. QA - Mc.qA = (pa-mc) IA = (50-25, 100 TTA = 2500 14 = 8 = 25 00

monopoly from maxi its fooyit as TI TR- TC - p. - mc.ca = (P-mc la - (P- 25 ) (40o-up) (noo-up) 1 = P(noo-up) - 25 F.o.c IT = noo-8 P + 100 = 0 - 500 = 8P P= 500 - 62.5 therefore &- noo-up - 40o- u (62.5) - 400- 250 = 150 G21 9 = 150, P= 62.5 Ans-1 No this monolooy out come is not Stable if from. A operates in monopoly outcome that is want to produce d = 150 =15

why QA = 75 Because they produce half-half of monopoly quantity, so from B will froauce, 9 B = 150 - 0.59A = 150 - 0.5 (75) = 150 - ses 37.5 QB = 112.5 Ans-8 monopoly Price = 62.5 a = 150 Cournot po 50 9 = 200 Perfect com feriti8n p=25, Q = 300 com P = mc 100- 0.250 = 25 75= 0.250 - 9 = 300 P= 100-0.259 = 100 -0.25 (300) = 100-75 P = 25

100 80 monopoly monopoly 62.50 - Price 60 Cournot = 50 Cournot price. --- no - Perfect me=24 + Perfect 25- Price 20 - - 40 80 120 200 280 360 400 Cournot 300 = Perfect a monopoly Ans-9 Firm- A is deader and from-2 is followor, So frost Calculating BR-B TTB = TRB - TCB which gives. 96 = 150-0.5 QA Now at stage- I from A will incorporate this into his

poogit maximization Behaviour. TA=TRA - TCA = (100 - 0.259A - 0.25QB - 25 )GA (75-0.25 PA -0.2506) PA TA = (15-0.25 QA - 0.25/150 - 0.5QA)) QA = (15-0.250A - 37.5+ 0.125 QA ) QA TA= ( 37.5 - 0.125 QA ) QA roc OTA = 37.5 -0.25 QA = 0 dQA - QA = 150 there zore B = = GB - 150- 0.5(150) 150 - 75 75 QA= 150 ,9B=75 Ans-10 - a= 400-Up => 225= 400-up =) upo 400 - 225 - up= 175 - P= 175/4 = 43.75

Profit of From I (Frast mover) TA= TRA - TCA = p. 9A - mc. QA = (b-mc )qA = (43.75-25 150 TA = 2812.5 Profit of from B TIB = TRB - TCB = b. q B - Mc.qB = (4.3-75-25) 75 TIB. = 1406. 25 Frost mover advantage is calculced as how much fim- A earn more profit Than firm- B. THA - TIA = 2812.5 - 1488.25 = 1409.25