Question

The price in a market is dominated by two firms is affected by the quantities supplied by both firms, Q1 and Q2: P = 150 - (Q1 + Q2). The marginal cost for the two firms is identical and constant and equal to 20.

a. Derive the equations for total revenue for the two firms.
b. Compute the profit-maximizing levels of output and prices for the firms.
c. Compute the profit-maximizing level of output and price for the industry if the duopolists merged and formed a monopoly.
d. Compare and contrast the results from b. and c.

Answer 1

The prices in a market is two firms ii affected by both | Q2; p= 150-(Qc+Q2] les in a market is dominated by o e affected by both firms Q1 and = 2 . Marginal cost for both tims ie me, = 20 Me2 = 20 a Now total revene for first fiams: Trio par = [150- (QutadQ1 - 150 Q, - Q1 == 'Q, Q2 Total reve me for second firmst. TR2=PQ2 = (150-(Q1 +92)] Q2 = 150 Q 27 Q1 Q2-22 20cm 2Q1 be Now Total reve me for firm 1: TRI= 150Q; -Q, ²-Q, Q2 Marginal revenue for füm 1 . MR. = 2(TR) - 150 - 2Q1-Q2 Marginal cost for firm 1. Mc1=20. Prosit maimising condition for fim 1: . MRI = MC, 3) 150 - 20,-Q2 = 20 -) .221.782 = 130 Q2 = (130-201) ----). 1. cs Scar =) Scanned with CamScanner

Veu Total revenue for firm 2 TR2 = 150 Q2 - Q1 Q2 - Q2 Marginal reve me for füm 2. MR2 = a (TR2) = 150-Q1-2Q2 Now, Marginal cost for firm 2: MC2 = 20 Profit manmising condition for firma? MR2 e Mez 150- Q,- 2Q1 = 20 => Ql+242 = 130 ---liv =). Now substituting Q2 = (130-201) from egnation (i in equation (i) we gee! ا ل ا ا Q1 +2 Q2 = 130 Q1 + 2(130- 2Q1 = 130 =) Q, + 260 - 4Q1 - 130 - 3Q1 =- 130 =) Q1 = 43,33 — 43.3 from equation (U). We gut! Q2= (130 - 2Q1) - 130-12X43.33), and = 43.3 Now puce charged by both tims. : P = 150-(Q1+Q2) = 150- (43.37 43.3) CS Scanned with CamScanner. = $63.9 = yo

level of output for at manimising : 43.3 and Hnce profit manimising lead of both tims Q = 43.3 and Q2²4 Prices for both firms p = $63.4 - formed a duo bolists merged and ei wareed and demand function e of the mono paly, then Industry will be p= 150-Q zovem Now. To tal revenue (PQ) = TR = 13 Marginal revence (MR) _d (TR) 150-20 Now, Marginal cost me 20 condition will i Now, monopolist's probis bei MR = MC monopolist's profit main mising 3) : 150-2Q = 20 130 = 2Q.. =) Q = 65 and Price changed by monopolist .. . .P= 150-Q = (150-65) 58 85 d) Now comparing both (b) and (e) we can see - that when there were two firms to tal industry out but was Q = Q1tQ2 1: 43.3 + 43.3) ... 86.6 hits which was higher than the industry. Output CS When the with dao polist's merged and formed monopoly ler

je 65 units. Also, in duopoly case, Price charged by both birms were much lown (ie $63.4) than the price charged by the .. mono polist le $85. Hunce As market pown increasn and mono poly is formed. Market becomes - more in efficient than the case when there were two firms in the market. 2 cs Scanned with CamScanner