Consumption, Production, Welfare B:Monopoly and Oligopoly (partial eq)

Univ. Prof. dr. Maarten JanssenUniversity of Vienna

Winter semester 2013

2

Profit maximisation MonopolistP

Q

ATCMC

D

MRQM

PM

Profit

ATC

MCPdQdP

PQ )1(Pricing rule

Profit π = P(Q)Q – C(Q)

)1

1/(

MCP

When is monopoly outcome Pareto inefficient?

3

On which part of demand curve is the monopolist’s price?

P

Q

Q

Demand

Elastic

Inelastic

MRTotal

Revenue(€)

Total revenue=PQ

Marginal revenue =

dQdPQP

Demand curve is elastic where or elasticity is larger than 1.

Oligopoly: between monopoly and perfect competition

• On demand side always many consumers who take prices as given

• On supply side– Under perfect competition, firms take prices as given (problems

with increasing returns to scale)– Under monopoly, one firm takes effect on price into account (look

at previous formulaes)– Middle ground: what if there are some firms (more than one, not

many)• Have to take actions, reactions into account (game theory)• Subtleties important, for example, what are the decision variables (price or

quantity) of the firms• Here, two basic models: Cournot (quantity) and Bertrand (price)

5

Cournot Model• 2 (or more) firms

• Market demand is P(Q)• Firm i cost is C(q)• Firm i acts in the belief that all other firms will put some amount

Q-i in the market. • Then firm i maximizes profits obtained from serving residual

demand: P’ = P(Q) - Q-i • For each output produced by the others, firm is the monopolist

for the residual demand

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Demand and Residual Demand

Market demand P(Q)=P(q1,Q-1=0)

q1

P(q1)

P(q1, Q-1 =10)

P(q1, Q–1 =20)

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Cournot Reaction Functions

• Firm 1’s reaction (or best-response) function is a schedule summarizing the quantity q1 firm 1 should produce in order to maximize its profits for each quantity Q-1 produced by all other firms.

• Since the products are (perfect) substitutes, an increase in competitors’ output leads to a decrease in the profit-maximizing amount of firm 1’s product ( reaction functions are downward sloping).

• Check for monopoly

8

Profit maximisation Monopolist for different demands

P

Q

ATCMC

D

MRQM

PM

Profit

ATC

MCPdQdP

PQ )1(Pricing rule

Profit π = P(Q)Q – C(Q)

)1

1/(

MCP

When is monopoly outcome Pareto inefficient?

D‘MR’

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Cournot Model• A firm can only decide bout what it will produce. It has to take as given what others produce. What others produce is, however, relevant.• The problem

Max{(P(qi+Q-i) qi – C(qi)}

defines the best-response (or reaction) function of firm i to a conjecture Q-i as follows:

P’(qi+Q-i)qi + P(qi+Q-i) – C’(qi) = 0

Linear case on blackboard

Q-i

qiqiM

qj

r1

qi*(qj)

Firm i’s reaction Function

Q-i=0

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Cournot Equilibrium

• Situation where each firm produces the output that maximizes its profits, given a conjecture about the output of rival firms

• Conjectures about what the others produce are correct

• No firm can gain by unilaterally changing its own output

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Cournot Equilibriumq2

q1q1

M

r1

r2

q2M Cournot equilibrium

• q1* maximizes firm 1’s

profits, given that firm 2 produces q2

*

• q2* maximizes firm 2’s

profits, given firm 1’s output q1

*

• No firm wants to change its output, given the rival’s

• Beliefs are consistent: each firm “thinks” rivals will stick to their current output, and they do so!

Rewriting optimal decision rule

• Can we detect monopoly pricing rule as a special case?

• Is perfect competition another special case?

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Properties of Cournot equilibrium• The pricing rule of a Cournot oligopolist satisifes:

• Cournot oligopolists exercise market power:– Cournot mark-ups are lower than monopoly markups– Market power is limited by the elasticity of demand

• More efficient firms will have a larger market share.• The more firms, the lower will be each firm’s individual

market share and market power.

i

ij ji

iiij ji s

qqP

qMCqqP

)(

)()(

Symmetric Cournot competition with N firms; linear case

• Demand is given by ; marginal cost equals c.• Optimal rule under symmetry gives or or

market output

• Increasing or decreasing in N? Can we recognize monopoly and perfect competition (P=c) as extremes?

• Competitive model is really the limit of oligopoly model.

15

Bertrand Model• 2 (or more) firms

– Firms produce identical products at constant marginal cost.– Each firm independently sets its price in order to maximize

profits

• Consumers enjoy– Perfect information – Zero transaction costs

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Bertrand Equilibrium• Firms set P1 = P2 = MC! Why?

• Suppose MC < P1 < P2

• Firm 1 earns (P1 - MC) on each unit sold, while firm 2 earns nothing

• Firm 2 has an incentive to slightly undercut firm 1’s price to capture the entire market

• Firm 1 then has an incentive to undercut firm 2’s price. This undercutting reasoning continues...

• Equilibrium: Each firm charges P1 = P2 = MC

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Bertrand Paradox• Two firms are enough to eliminate market power

– If firms are symmetric, market power is eliminated entirely– If firms are asymmetric (MC1 < MC2), market power is

substantially reduced

• Solutions (in course on Industrial Organization):– Capacity constraints– Repeated interaction– Product differentiation– Imperfect information