ECONOMICS 3200M Lecture 7 January 27, 2006

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ECONOMICS 3200MLecture 7January 27, 2006
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Cartels

• Factors facilitating formation of cartels
• Ability to raise price without attracting entry
  closeness of substitutes, ease of entry
• Expected benefits form forming cartel exceed
  expected costs (negotiating agreement, monitoring
  members, enforcing agreements, penalties for
  violating competition laws)
• Symmetric cost structures and degree of vertical
  integration/internalization
• Multi-market contact possibility of local
  warfare spreading to other markets
• Low costs for detecting cheating
• Few firms monitor market shares
• Prices widely known
• Homogeneous product
• Prices relatively insensitive to external factors
  demand shocks, changes in input costs

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Cartels

• Incentives for cheating free rider
• Methods to prevent cheating
• Market-sharing arrangement
• Most favoured nation clauses seller guarantees
  buyer that seller will not offer lower price to
  nay other buyer
• Meet the competition clause seller guarantees
  buyer that it will match lowest price offered by
  competitors
• Trigger prices if market price reaches trigger
  price (agreed upon floor price), each firm will
  be free to expand output to pre-cartel levels
• MAD strategy mutually assured destruction

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Cartels

• Tacit collusion in highly concentrated market
• Recognized industry leader sets prices, others
  follow
• Regular price announcements
• Mark-up pricing

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Oligopoly

• Small number of competitors small undefined
• Strategic interactions among firms small number
  implies that each firm knows that strategies it
  selects will have significant impact on profits
  of rival(s)
• Necessary to consider each rivals behaviour in
  order to select optimal strategy for each
  instrument for competing in market
• Instruments for competing include price,
  marketing strategies, cost structures, product
  characteristics, distribution channels
• Each firm maximizes its profit given its beliefs
  how each rival will behave
• 2 firm, 2 strategy example (dominant strategy)
• Firm 2
• Advertise Dont advertise
• Advertise 10, 5 15, 0
• Firm 1
• Dont advertise 6, 8 10, 2

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Oligopoly

• Non-cooperative game one-time (single period)
  game
• Reputation and history unimportant no
  possibility for learning
• Concept of Nash equilibrium
• Profits of firm 1 depend upon strategies selected
  by each of its M-1 competitors from strategy sets
  available
• ?i ?i (A1, A2, , AM)
• Strategy set for firm i (Ai) consists of Ti
  strategies
• Ai ?1i, .., ?Tii, where each strategy in the
  set (?) consists of values for each of the K
  instruments (a) in strategy j (?ji) for firm i
• ?ji aji1, .., ajiK
• Firm 1, given strategies selected by M-1 rivals,
  cannot do better by choosing a strategy set other
  than the equilibrium set
• ?i (A1, A2, , Ai, , AM) ? ?i (A1, A2, ,
  Ai, , AM)

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Oligopoly

• Dominant strategy
• Credible strategy
• Potential entrant
• Enter Stay out
• High price 50, 10 100, 0
• (Accommodate entry)
• Incumbent
• Low price 30, -10 40, 0
• (Warfare)
• High price dominant strategy for incumbent so
  threat of warfare not credible may lead to
  future entry
• Price warfare to deter first entrant and signal
  to future entrants (establish credibility)

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Oligopoly

• Simple case 2 firms, single instrument and
  single strategy in strategy set (K1 T1, M2)
• Ai ai
• ?1 ?1 (a1, a2)
• First-order condition for profit-maximization ?
  ?1/ ? a1 , yields reaction function
• a1 R1 (a2)
• Nash equilibrium pair of strategies (values for
  instruments) so that
• a1 R1 (a2) and a2 R2 (a1)
• Solution is intersection of reaction functions
• In Nash game, each firm ignores the effect of its
  decision on behaviour of its rivals

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Oligopoly

• Simple case 2 firms, single instrument and
  single strategy in strategy set (K1 T1, M2)
• Stackelberg leader select optimal value for a1,
  given firm 2s reaction function
• Max ?1 ?1 a1, R2 (a1)
• First-order condition for profit-maximization d
  ?1/ d a1 , yields
• ? ?1/ ? a1 ? ?1/ ? a2 d a2/ d a1 0
• Strategic substitutes dR1/ da2 lt 0 (reaction
  function downward sloping)
• Strategic complements dR1/ da2 gt 0 (reaction
  function upward sloping)

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Oligopoly

• Bertrand competition
• Duopoly case can be extended to M-firm
  oligopoly
• Homogeneous products, single instrument P
• Identical costs structures unit costs C
• Strategic complements since reaction functions
  upward sloping if firm 1 decreases price, firm
  2 must imitate otherwise suffers significant loss
  of demand
• Nash equilibrium
• P1 P2 C
• ?1 ?2 0
• Different cost structures C1 gt C2
• Firm 2 drives firm 1 out be setting P C1 - ?
• Monopoly price if PM (C2) lt P
• Constrained monopoly pricing (limit pricing) if
  PM (C2) gt P

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P2 (P1, C2)
P1
P1 (P2, C1)
1
P2
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Oligopoly

• Cournot competition
• Duopoly case
• Homogeneous products, single instrument Qi
  (quantity produced by each firm)
• Demand function P(Q) 1 Q 1- Q1 Q2
• Ci (Qi) Ci Qi (constant returns), where C1 ? C2
• Firm 1
• Max ?1 (Q1, Q2) Q1 (1- Q1 Q2) C1 Q1
• d ?1 /d Q1 1- 2 Q1 - Q2 - C1 0
• Reaction function for firm 1 Q1 1- Q2 - C1/2
  R1 (Q2)
• Strategic substitutes since d Q1/d Q2 lt 0
• Reaction function for firm 2 Q2 1- Q1 C2/2
  R2 (Q1)

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Oligopoly

• Cournot competition
• Nash equilibrium solve by equating reaction
  functions
• R1 (Q2) R2 (Q1)
• Q1 1 C2 2C1 /3
• Q2 1 C1 2C2 /3
• P 1 C1 C2 /3
• ?1 1 C2 2C1 2/9
• ?2 1 C1 2C2 2/9
• If C1 lt C2 ? ?1 gt ?2
• With symmetric costs and N firms Ci C
• Qi 1 - C/(N1)
• P 1 NC/(N1)
• As N increases, Qi decreases, P decreases
  towards C and the profit for each firm decreases
  towards 0

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Q1
Q2 R2 (Q1, C2)
1
Q1 R1 (Q2, C1)
Q2
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Oligopoly

• In monopoly (if no X-inefficiency), Bertrand
  competition and perfect competition models,
  production occurs at lowest cost
• Higher cost producer cannot survive
• With Cournot competition, higher cost producer
  can survive

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Oligopoly

• Stackelberg competition
• Firm 1 is the leader and firm 2 is the follower
  why?
• Firm 1 knows firm 2s reaction function assume
  same demand and cost conditions as in Cournot
  example
• Firm 1
• Max ?1 (Q1, Q2) Q1 (1- Q1 Q2) C1 Q1
• Q2 1- Q1 C2/2 R2 (Q1)
• ?Max ?1 (Q1) Q1 (1- Q1 C2)/2 C1 Q1
• d ?1 /d Q1 0.5- Q1 0.5C2 - C1 0
• Q1 1 C2 2C1 /2 gt Q1 (Cournot) 1 C2
  2C1 /3
• Q1 (follower) lt Q2 (Cournot)
• Leader has higher profits than in Cournot game
  Firm 1 a leader most likely because it ahs lower
  costs

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Q1
Q2 R2 (Q1, C2)
S
N
Q1 R1 (Q2, C1)
Q2