Managerial Economics & Business Strategy Chapter 9 Basic Oligopoly Models.

Managerial Economics & Business Strategy

Chapter 9Basic Oligopoly Models

Oligopoly

• Relatively few firms, usually less than 10. Duopoly - two firms Triopoly - three firms

• The products firms offer can be either differentiated or homogeneous.

• Firms behave strategically• Barriers to entry exist• “Let’s Play Oligopoly” WSJ, 1999

Role of Strategic Interaction

• What you do affects the profits of your rivals

• What your rival does affects your profits

• Strategic interdependence: You aren’t in complete control of your own destiny!

Cournot Model

• A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated)

• Firms set output, as opposed to price.• Each firm decides “how much” given its

beliefs about the output of the other firm.• Barriers to entry exist• Example: Oil production. Each firm produces

output independently and the market price is determined by the total amount produced.

Reaction Functions

• Suppose two firms produce homogeneous products.• Firm 1’s reaction (or best-response) function is a

schedule summarizing the amount of Q1 firm 1 should produce in order to maximize its profits given each quantity of Q2 produced by firm 2.

• Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.

Cournot Equilibrium

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

• No firm can gain by changing its own output

Cournot Equilibrium and Selecting Profit-Maximizing Q

• From inverse demand, find MR for each firm

• Set MR = MC• Solve for each firms reactions functions:

Q1(Q2) and Q2(Q1).

• Graph each firm’s reaction function (Q1 on x-axis and Q2 on y-axis, for example).

Cournot Equilibrium and Selecting Profit-Maximizing Q

Situation:

United Airlines and American Airlines fly passengers between Chicago and LA. Assume no other company can enter because they can’t get landing rights at both airports.

Facts:

Marginal Costs: MCAA = MCUA = $147/passenger.

Market Demand: Q = 339 – P or P = 339 – Q, where Q = QAA + QUA;

Thus, P = 339 – QAA – QUA

Cournot and Profit-Maximizing QTo maximize profits, each firm chooses Q at the level in which MR=MC. You can either find an expression for TR for firm i, then differentiate with respect to Qi. This will give each firm’s MR function. Alternatively, you can use the fact that MR has twice the slope of inverse demand function!

Marginal Costs: MCAA = MCUA = $147/passenger.

P = 339 – QAA – QUA, so

TRAA = 339QAA – QAA2 – QUAQAA

TRUA = 339QUA – QUA2 – QAAQUA

MRAA = 339 – 2QAA – QUA and MRUA = 339 – QAA – 2QUA

For AA: 339 – 2QAA – QUA = 147 and solve for QAA.

AA Rxn Func: QAA = 96 – 0.5QUA

UA Rxn Func: QUA = 96 – 0.5QAA

Cournot Equilibrium and Selecting Profit-Maximizing Q

To find Cournot Equilibrium (also a Nash equilibrium), plug one firm’s rxn function into the other firm’s.

QAA = 96 – 0.5(96 - 0.5QAA), and solving for QAA = 64.

Plug QAA = 64 into UA rxn function. QUA = 64. This outcome is due to the fact that MC are the same for both firms.

Cournot Equilibrium

64

64

QUA

QAA96

rAA

rUA

96Cournot Equilibrium

192

192

48

Collusion

If UA and AA collude, then see monopoly outcome.

MR = 339 – 2Q.Set MR=MC, 339 – 2Q = 147, Q = 96, where UA and AA split the passengers. P = 339 – Q, P = $243 versus $211 if competing duopoly

Cournot Equilibrium

64

64

QUA

QAA96

rAA

rUA

96Cournot Equilibrium

192

192

48

Collusion: each produce 48 & each would earn greater profits, but likely not sustainable.

Stackelberg Model• Few firms

Producing differentiated or homogeneous products

• Barriers to entry• Firm one is the leader

The leader commits to an output before all other firms

• Remaining firms are followers. They choose their outputs so as to maximize profits, given

the leader’s output.

• Example: Diamond production. DeBeers is the leader that sets diamond production, and smaller firms follow with their own levels of production.

Stackelberg Oligopoly• Assume AA has first-mover advantage;

thus, picks output before UA.• UA still has a rxn function, but AA doesn’t.• AA plugs UA rxn function into its TR

function.• Find AA MR function (differentiate TR)• Set MRAA = MCAA, solve for QAA.

• Plug QAA into UA’s rxn function and get QUA

Stackelberg Oligopoly• Recall, UA’s rxn function is

QUA = 96 – 0.5QAA

• TRAA = 339QAA – (96 – 0.5QAA)QAA – QAA2

• MRAA = 339 – 96 + QAA – 2QAA

• MRAA = 243 – QAA

• Set MRAA = MC,

243 – QAA = 147

QAA = 96

Therefore QUA = 48 and P = $195

Stackelberg Summary

• Leader produces more than the Cournot equilibrium output

Larger market share, higher profits First-mover advantage

• Follower produces less than the Cournot equilibrium output

Smaller market share, lower profits

Bertrand Model• Few firms

Firms produce identical products at constant marginal cost.

Each firm independently sets its price in order to maximize profits

• Barriers to entry• Consumers enjoy

Perfect information Zero transaction costs

• Example: Competitive bidding by identical contractors. In this case, the contractor bidding the lowest fee will win the contract.

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 continues...

• Equilibrium: Each firm charges P1 = P2 =MC

Comparing Oligopoly Models• Cournot:

P = $211 Profits for each firm = $4096 (= 211*64 – 147*64)

• Stackelberg: P = $195 (lower than Cournot because Q higher) Profits for AA = $4608 and $2304 for UA.

• Collusion P = $243 Profits for each firm = $4608

• Bertrand: P= $147 Profits for each firm = $0

Contestable Markets• Key Assumptions of Contestable Markets

Producers have access to same technology Consumers respond quickly to price changes Existing firms cannot respond quickly to entry by lowering

price Absence of sunk costs

• Key Implications of Contestable Markets Threat of entry disciplines firms already in the market Incumbents have no market power, even if there is only a

single incumbent (a monopolist)

• Note: if existing firms can respond quickly, then may keep new entrants out.

Contestable Markets• Video rentals: In 1998, who did you rent

movies from?

• Netflix enters 1999!

• http://digitalenterprise.org/cases/netflix.html

Summary• Different oligopoly scenarios give rise to

different optimal strategies and different outcomes

• Your optimal price and output depends on … Beliefs about the reactions of rivals Your choice variable (P or Q) and the nature of the product

market (differentiated or homogeneous products) Your ability to commit