7.) Market demand is given by P = 140 -Q. There are two firms, each with unit co

Question

7.) Market demand is given by P = 140 -Q. There are two firms, each with unit costs = $20. Firms can choose any quantity. Find the Cournot equilibrium and compare it to the monopoly outcome and to the perfectly competitive outcome. Why aren't the latter equilibria of the market game?

8.) What is the outcome of the oligopoly in number 7 as the number of firms grows large? Why will this number of firms grow large? Is this outcome a tradgedy?

9.) Suppose that two firms both have AVC = $50. Market demand is given by Q = 100 - P. Find the Bertrand Equilibrium. Would your answer be different if there were three firms?

Explanation / Answer

(7)

P = 140 - Q = 140 - (QA + QB) [Q = QA + QB]

MCA = MCB = 20

(a)

TRA = P x QA = 140QA - QA2 - QAQB

MRA = dTRA / dQA = 140 - 2QA - QB

Equating MRA = MC,

140 - 2QA - QB = 20

2QA + QB = 120 ......(1) [Firm A's response function]

TRB = P x QB = 140QB - QAQB - QB2

MRB = dTRB / dQB = 140 - QA - 2QB

Equating with MC:

140 - QA - 2QB = 20

QA + 2QB = 120........ (2) [Firm B's response function]

Cournot-Nash equlibrium is obtainde by solving for the response functions of both firms.

2QA + QB = 120 ......(1)

QA + 2QB = 120 ........ (2)

(2) x 2 gives:

2QA + 4QB = 240 ..... (3)

(3) - (1) Gives:

3QB = 120

QB = 40

QA = 120 - 2QB [From (2)]

= 120 - 80 = 40

(b)

In perfect competition, there are numerous buyers and sellers, and

P = MC

140 - Q = 20

Q = 120

P = 140 - 120 = 20

(c)

In monopoly, MR = MC

P = 140 - Q

TR = P x Q = 140Q - Q2

MR = dTR / dQ = 140 - 2Q

Equating with MC:

140 - 2Q = 20

2Q = 120

Q = 60

P = 140 - Q = 80

(d)

In monopoly market, the monopolist is the sole seller who can set price as per his choice, since no substitutes to his product exists. Therefore, monopoly output is lower and price higher than those in perfect competition. This results in inefficiency, resulting in deadweight loss. There is no market competition, so the monopolist chooses his own market equilibrium.

NOTE: Out of 3 questions, the first question is answered with all sub-parts.

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