University of Hong KongECON6021 Microeconomic Analysis

Oligopoly

IntroductionThree models of oligopoly. Cournot competition Bertrand competition Stackelberg competition

CournotCompetition

An industry is characterized as Cournotoligopoly if1. There are few firms in the marketserving many consumers.

2. The firms produce either differentiatedor homogeneous products.

3. Each firm believes rivals will hold theiroutput constant if it changes its output.

4. Barriers to entry exist.

Reaction Functions andEquilibrium. further simplification: duopoly – 2 firmsonly

reaction function defines theprofit-maximizing level of output for afirm for given output levels of the otherfirm.

Q1 r1Q2.and

Q2 r2Q1.

Point E thus corresponds to the Cournotequilibrium– where neither firm has aunilateral incentive to change its output

If the (inverse) demand in ahomogeneous-product Cournot duopoly is

P a bQ1 Q2,where a and b are positive constants, thenthe marginal revenues of firms 1 and 2 are

MR1Q1,Q2 a bQ2 2bQ1MR2Q1,Q2 a bQ1 2bQ2

Assume that total cost functionsC1Q1 c1Q1 and C2Q2 c2Q2.

Equating MRMC, we havea bQ2 2bQ1 c1

for firm 1, anda bQ1 2bQ2 c2

for firm 2. Their reaction functions are

Q1 r1Q2 a c12b 12 Q2

for firm 1, andQ2 r2Q1 a c2

2b 12 Q1

Isoprofit Curves. How to graphically determine the firm’sprofits.

Four aspects of the figure are important tounderstand.1. Every point on a given isoprofit curvefor firm 1 yields firm 1 the same levelof profits.

2. Isoprofit curves that lie closer to firm l’s

monopoly output (Q1M) are associatedwith higher profits for that firm.

3. The isoprofit curves for firm 1 reachtheir peak where they intersect firm l’sreaction function.

4. The isoprofit curves do not intersectone another.

Changes in MarginalCosts. What happens if there is a decline in firm2’s marginal cost?

Collusion Whenever a market is dominated by only afew firms, firms can benefit at the expenseof consumers by ”agreeing” to restrictoutput or, equivalently, charge higher

prices. Such an act by firms is known ascollusion.

StackelbergOligopoly

An industry is characterized as aStackelberg oligopoly if:1. There are few firms in the marketserving many consumers.

2. The firms produce either differentiatedor homogeneous products.

3. A single firm (the leader) selects anoutput before all other firms choosetheir outputs.

4. All other firms (the followers) take asgiven the output of the leader andchoose outputs that maximize profitsgiven the leader’s output.

5. Barriers to entry exist.

Model Two firms–Firm 1 is the leader with a“first-mover” advantage, and Firm 2 is thefollower, who maximizes profit given theoutput produced by the leader.

same cost functions, and demand functionas in Cournot model

Follower’s reaction function:

Q2 r2Q1 a c22b 12 Q1,

which is simply the follower’s Cournotreaction function. After taking into account the follower’sresponse, the leader’s profits are

1Q1 a b Q1 a c22b 12 Q1 Q1 c

The leader chooses Q1 to maximize1Q1.

It is straightforward to show that theleader’s output is

Q1 a c2 2c12b .

Bertrand OligopolyAn industry is characterized as a Bertrandoligopoly if:1. There are few firms in the marketserving many consumers.

2. The firms produce identical productsas a constant marginal cost.

3. Firms engage in price competition andreact optimally to prices charged bycompetitors.

4. Consumers have perfect informationand there are no transaction costs.

5. Barriers to entry exist.

Model Consider a Bertrand duopoly, and bothfirms have the same marginal cost.

Price war – Both firms charge a priceequal to marginal cost: P1 P2 MC!

Conclusions Three models of oligopoly have beenintroduced.

Interdependence of choices areemphasized.

Collusion improves firms’ collectiveprofits (at the expense of consumers)