Question

Firm A and Firm B are two companies that manufacture identical prod- ucts, and are the only firms in the market for that good. The marginal cost of producing a unit of the good is $20, and there are no fixed costs. The inverse market demand for their product is P = 140 – Q, where Q is the number of units, and P is the price. (a) What is the economically efficient (ie. social welfare maximizing) price and quantity of the product? (b) If firms A and B were to collude with one another and produce the profit maximizing quantity of their product, how much would firm produce, and what price would they charge? (c) What is the welfare loss at the output level you found in (b)? (d) Suppose instead that firms A and B act as Cournot duopolists. What level of output will A produce? What level will B produce? What price will they each charge?

Please show step by step process I am confused

Answer 1

o Two froms (A ana B) = duo duo Poly identical Products = 9A + 9B = Q mai mcz marginal cost $20 inverse demand function : p= 140 a 140-9 (a) economicauy enjicient Cie socially Rad oltima l Outcome) market is at outcome of an Level conen fiome froduces at social welfare P= mc condition optimal : P= mc 140 - a = 20 g. = 120 Units Patting in P= 140- 9 p=20= mc. So Sociany efficient price = P=mc = $ 20 and quanity 9 = 120 units

(b) If from A and firm - B get collude imprinces There will be monopoly and Profit maximizing conclition for mondary firm is where MR = mc P = 140-9 TR=(140-qja MR = dTR dQ =) MR = 140-20 optimal MR & = mc 140-29 = 20 120 29 -S = 60 units 160- 9 - 140-60 = 8 Firm Produce a=60 units P= $80

(c) in order to calculate social Loss due To concesion first we will find out how much we have Social Surplus in Two different market structures P= 140 mc =$20 P, MR, MC, MR = 140-29 140 d - t C 20 mc b 70 0 9 140 120 66 il! with Socially Social Suall optimal Surhus Consumer surfius area above Price and below The Demand Curve area of tringle (abc)

(140-20) (120) 2 (120)2 = 7200 2 with collusion Social Surplus = cs + Ps Social Surplus cs + Ps - area (of tringle aed ) cs + Олесt оf tə rectangle (Ps, 1(140-80 ) (60) 2 3600 + (80-20) (60) 2 1800 + 3600 Social Sus Pius - 5400 welfare Loss - Social Surkus Surfius with Socially Social Sur with calusion efficient 7200-5400 1800 (also called dead - weight loss

which is also equals To Shaded area Dwol = Į (80-20) ( 120-60) 2 (60) (60) Carea of tringle (det, 1800 (d). Courhot Courhot luololy. Profit function of firm TA TRA - TCA P. 9A - Mc.qA (due to constant = (P-mc IqA Mc ) - (140-9-20)9A (120-(LA 198 ) ) 26 Q = q AtqB TA = (120-9A-9B) 9A Foc ITA 120-29A - q B = 0 JqA 94 120 - 9B (BRA) Best Responce of Firm 2

Due to symmetry Same That is equal mc. and demana function we have 28 IQUE AUB 120-9A (BRB) 2 Solving BRA and BRB Simualtaneously QA = 120-QB 2 =) 29A 120-QB 120- ( 120-94) ore 6.049 A 2 (120)-120+9A 2 2 29A 11 120+qA 2 498 = 1200 qA >> 39A = 120 = ) qA = 120 40 3 from BRB 98 = 120-9A 120-40 = 40 2 2

from A will produce QA = 40 units from B will produce &B = 40 units a = 9A + 9B = 40tuo = 80 = P = 140-6 = 140-80 = 60 So Price They will charge P=60
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