Question

Assume an oligopolistic market with one large dominant firm. The dominant firm's marginal cost is given by the following equation:

MC = 0.48 Q

The market demand is the following: QD = - 14 P + 309

The supply of the smaller firms combines is given by the following equation:

QS = 16 P + 192

What is the profit-maximizing amount of output for the dominant firm?

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Assume a duopoly market with quantity competition.

The market inverse demand is the following: P =  497 - (Q₁ + Q₂)

Where Q₁ and Q₂ represent the production of firm 1 and 2, respectively. Assume that both firms have the same ATC = MC = 21.

If this market was a competitive market rather than a duopoly how much higher would the market quantity be under a competitive marekt than under a duopoly?

Answer 1

1)

Demand for dominant firm's output is given as

QL=QD-QS=(-14P+309)-(16P+192)=117-30P

On rearranging we get

30P=117-QL

P=117-(1/30)QL

Total Revenue of dominant firm=TRL=P*Q=117QL-(1/30)QL^2

Marginal Revenue in case of dominant firm=MCL=dTRL/dQL=117-(1/15)QL

MC of dominant firm is given as

MC=0.48QL

Set MC=MRL for profit maximization

0.48QL=117-(1/15)QL

QL(0.48+1/15)=117

QL=214.02

What is the profit-maximizing amount of output for the dominant firm?

QL=214.02

ii)

Given

P=497-(Q1+Q2)

Q1+Q2=497-P

In case of perfect competition, P=MC=21

Q1+Q2=Qp=497-21=476

In case of Cournot model, combined output is given by

Qc=2/(2+1)*Qp=476*(2/3)=317.33

(Explanation : if there are n firms in Cournot model, combined output is n/(n+1) of competitive output if marginal costs of each firm is same)

Difference in output=476-317.33=158.67

Output is higher in competitive market by 158.67