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Basic Oligopoly Models

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... choose quantities, market price depends on total quantity ... Buyers choose the firm with the lowest price. Firm with the lowest price captures the market. ... – PowerPoint PPT presentation

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Title: Basic Oligopoly Models


1
Chapter 9
  • Basic Oligopoly Models

2
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.

3
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.

4
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.

5
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
6
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.

7
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.

8
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.

9
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)

10
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.

11
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.

12
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.

13
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.

14
Solve for Q1
  • Similarly
  • Q1(Q2) 5 ? (1/2)Q2 5 ? (1/2)(10/3)
  • 5 ? 10/6 20/6 10/3.

15
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.

16
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.

17
Excel Worksheet (click)
18
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.

19
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.

20
Residual Demand
Sfollower
  • At P1, follower supply equals demand.
  • At P2, no follower supply.
  • At intermediate prices, leader faces residual D.

21
  • 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.

22
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

23
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.

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.

25
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.

26
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.

27
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.

28
Equilibrium
  • Equilibrium price equals marginal cost.

29
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

30
Competition vs. Monopoly
  • In general, QM (1/2) Qp
  • Total surplus is also half of competition

31
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)

32
  • Cournot produces more than Monopoly but less than
    Competition.
  • Surplus is also more than Monopoly but less than
    Competition.

33
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

34
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.
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