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PPT – Basic Oligopoly Models PowerPoint presentation | free to view - id: b8a2a-ZDc1Z

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Chapter 9

- Basic Oligopoly Models

Several Interacting Firms

- Oligopoly refers to markets in which firms

interact strategically. - Each firms decision depends upon what it

believes other firms will do. - More than one firm, but not many.
- Interdependence of decisions makes managers

problem complex. - Number of possible beliefs about other firms

behavior leads to many models of oligopoly.

Assumptions

- All models assume
- 1. Few firms who try to predict reactions of

other firms. - 2. Barriers to entry even in the long run.
- except for contestable markets, which assumes

free entry and exit.

Sweezy Model (Kinked Demand)

- Firms choose prices.
- Each firm believes a price reduction will be

matched but a price increase will not be matched. - Demand is more elastic to price increase than to

price decrease.

Kink in Demand

- At current price P, demand is more elastic for a

price increase than for a price decrease.

P

price is matched

price not matched

P

D

Q

Equilibrium P and Q

- At current Q, there is a gap in MR.
- At lower Q, MR gt MC. At higher Q, MR lt MC.
- Therefore, Q is optimal.

Predictions

- MC may shift and leave the optimal Q and P

unchanged. - Model explains reluctance of firms to change

prices, even as MC changes. - Therefore, price can be sticky.

Cournot (Quantity Competition)

- Firms choose quantities, market price depends on

total quantity supplied. - Firms assume other firms quantities remain the

same. - Each firm has a reaction function that determines

the best quantity for any given level of other

firms quantities.

A Duopoly Example

- The equilibrium choices are given by the

quantities that satisfy both reaction functions. - Firm 1s problem choose Q1 to
- max ?(Q1,Q2) P(Q1,Q2)?Q1 ? TC1(Q1)
- where
- P(Q1,Q2) 10 ? (Q1Q2)
- Set MR1(Q1,Q2) MC1(Q1)

Deriving MR

- Firm 1s demand can be written

P (10 ? Q2) ? Q1 - Firm 2's quantity is assumed constant and so is

part of the intercept. The slope of demand is

?1. - MR1 (10 ? Q2) ? 2Q1
- Same intercept, twice the slope.

Firm 1s Reaction Function

- If MC1 0, then set
- MR1 (10 ? Q2) ? 2Q1 0 MC
- and solve for Q1 as a function of Q2
- Q1(Q2) 5 ? (1/2)Q2
- This is firm 1s reaction function.
- It specifies what Q1 should be for any Q2.

Firm 2s Reaction Function

- Firm 2s problem is similar and reaction function

is - Q2(Q1) 5 ? (1/2)Q1
- This is due to symmetry of the example.
- Solve these two equations for the two unknowns,

Q1 and Q2.

Solve for Q2

- Q2(Q1) 5 ? (1/2)Q1
- 5 ? (1/2) 5 ? (1/2)Q2
- 2.5 (1/4)Q2
- Q2 (4/3)(2.5) 10/3.

Solve for Q1

- Similarly
- Q1(Q2) 5 ? (1/2)Q2 5 ? (1/2)(10/3)
- 5 ? 10/6 20/6 10/3.

Price and Profits

- P(Q1,Q2) 10 ? Q 10 ? 20/3 10/3.
- Profits for firm 1 are
- ?1(Q1,Q2) P?Q1 ? TC1
- (10/3)(10/3) ? 0 100/9 11.11
- Total profits of both firms are
- ?1 ?2 200/9 22.22.

Collusion

- MRM 10 ? 2QM 0 MC gt QM 5
- If the firms had colluded on quantity, they would

choose to each produce half of the monopoly

quantity QM Q1 Q2. - or QM 5 and P 10 ? 5 5.
- Total profits are
- ?M PM?QM ? 0 5?5 25
- Each firm gets ?i (1/2) 25 12.5 gt 11.11.

Excel Worksheet (click)

Better Off Colluding

- Each firm makes a higher profit if the two firms

collude and act like a monopolist. - This is one explanation for the desire of firms

to horizontally merge. - Anti-trust regulation prohibits collusion because

it produces less surplus.. - We will return to this later.

Stackelberg (Price Leader)

- One firm (follower) chooses a quantity taking the

other firms quantity as given. - Price leader chooses a quantity that considers

the supply of follower. - The follower behaves like a Cournot firm.
- The leader is more sophisticated.

Residual Demand

Sfollower

- At P1, follower supply equals demand.
- At P2, no follower supply.
- At intermediate prices, leader faces residual D.

- Leaders reaction function takes into account the

followers reaction function. - Using the residual demand, the leader determines

its MR and sets it equal to MC.

Algebraic Example

- Market demand P 50 ? (QLQF)
- Costs TCL 5 2QL
- TCF 5 2QF
- Followers reaction function set
- MRF MCF
- MRF (50 ? QL) ? 2QF 2 MCF
- Solve for QF 24 ? (1/2)QL

The Leaders QL

- Substitute the follower's reaction function into

market demand function to get the residual

demand - P 50 ? 24 ? (1/2)QL ? QL
- 26 ? (1/2) QL
- Set MRL 26 ? QL 2 MCL
- to get QL 24.

The Followers QF

- Substitute QL into followers reaction function
- QF 24 ? (1/2)24 12.
- Substitute Q QL QF 36 into market demand
- P 50 ? 36 14.

Profits

- ?L(QL) P?QL ? 5 ? 2QL
- 14?24 ? 5 ? 2?24 283.
- ?F(QF) P?QF ? 5 ? 2QF
- 14?12 ? 5 ? 2?12 139.

Bertrand (Price Competition)

- Firms choose their own prices, taking the other

prices as given. - Firms sell perfect substitutes.
- Buyers choose the firm with the lowest price.
- Firm with the lowest price captures the market.

Firm 1s Demand

- QD if P1 lt P2
- Q1 (1/2)QD if P1 P2
- 0 if P1 gt P2
- Given P2, firm 1 chooses P1 lt P2.
- Given P1, firm 2 chooses P2 lt P1.
- Outcome is P MC.

Equilibrium

- Equilibrium price equals marginal cost.

Comparing the Models An Example

- demand P 1,000 ? Q1 ? Q2
- costs TCi 4Qi i 1,2
- Competitive market Q Q1 Q2
- Ppc MC 4, Qpc 996, ?i 0
- Monopoly MRM 1,000 ? 2Q 4 MC
- QM 498, PM 502
- ?M (PM ? 4)QM (502 ? 4)498 248,004

Competition vs. Monopoly

- In general, QM (1/2) Qp
- Total surplus is also half of competition

Cournot Reaction Functions

- Q1 498 ? (1/2)Q2
- Q2 498 ? (1/2)Q1
- Q1 Q2 332 (1/3)Qpc
- Pc 1,000 ? 664 336, ?i 110,224.
- In general, if there are N Cournot firms
- Qi Qpc/(N1)

- Cournot produces more than Monopoly but less than

Competition. - Surplus is also more than Monopoly but less than

Competition.

Collusion and Bertrand

- Cournot collusion is the same as monopoly
- Qi (1/2)QM 249.
- Pc PM 502, ?i (1/2)?M 124,002.
- Bertrand is the same as perfect competition PB

PPC MC, QB Qpc, ?i 0

Entry in Oligopoly

- Contestable Markets Free entry and exit
- If ? gt 0, entry occurs, P falls until P AC.
- If ? lt 0, exit occurs, P increases until P AC.
- LR equilibrium implies ? 0.
- Same as long-run perfect competition, even if

there are few firms.