Oligopoly and monopolistic competition

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Oligopoly and monopolistic competition
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Cournot duopoly

• Assumptions
• Firms produce identical products
• Each firm maximizes profits by taking the current
  output of the other firm as given
• Market demand Pa b(Q1Q2)
• Demand curve for firm 1 P1(a-bQ2)-bQ1
• MR for firm 1 MR1(a-bQ2)-2bQ1
• Assume MC0 and set MRMC
• Reaction function of firm 1 Q1(a-bQ2)/2b

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• The Cournot equilibrium is where Q1Q2a/3b
  (derive)
• Combined output Q1Q22a/3b
• Market price Pa-b(2a/3b)a/3 (derive)
• Profit1TR1PxQ1(a/3)x(a/3b)a2/9b
• Example 13-1
• P56-2Q and MC20
• Find reaction functions and equil. P and Q
• P156-2Q2-2Q1 and MR56-2Q2-4Q1
• MRMC20, so 56-2Q2-4Q120 and
• Q19-Q2/2 set Q1Q2, then Q1Q26
• QQ1Q212 and P56-2x1232

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Bertrand duopoly

• Assumptions
• Identical products
• Each firm chooses price taking the other firms
  price as given
• Choices for firm 1
• Charge more than firm 2 will sell zero units
• Charge same as firm 2 will share market
• Charge less than firm 2 capture whole market
• Each firm will choose option 3 keep cutting
  price until PMC
• Example 13-2 Set PMC, or 56-2Q20, therefore
  Q18 and Q1Q29

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The Stackelberg model

• Assumptions
• The leader sets output first, assuming that the
  other firm will behave like a Cournot duopoly
• Demand curve for firm1 Pa-b(Q1R(Q1))
• (derive) P(a-bQ1)/2
• MR1a/2-bQ1 and Q1a/2b
• Derive Q2 by substituting Q1a/2b

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• Example 13-3
• Same demand and MC, find equil. P and Q
• Q29-Q1/2, substitute in demand function
• P56-2Q2-2Q138-Q1
• MR138-2Q1
• Set MRMC, 38-2Q120, then Q19
• Q29-9/24.5
• P56-2(94.5)
• QQ1Q294.5
• A comparison of the outcomes

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Game Theory

• Game theory is an important tool to study
  strategic behaviour and mutual interdependence of
  firms
• Four elements of game theory
• Players
• Possible strategies for each player
• Payoffs (resulting from the choice of a strategy
  be each player)
• Decision rule for each player

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• Types of games
• Cooperative or non-cooperative
• Two-person or many-player games
• Zero-sum or non-zero-sum
• Perfect information or asymmetric information
• Simultaneous of sequential
• Extent of communication permitted, cost of
  communication, side payments (bribes), coalition
  formation
• Assumptions
• Players are rational self-interest
• Payoffs are known to all players (becomes
  difficult and costly with many players and if
  preferences are not revealed)
• Are capable of choosing a strategy
• Not influenced by payoffs to others, but use them
  to analyze the possible choices of others (may
  not always hold altruism)

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• Choice of a decision rule
• Ron player rows
• Colleen plays columns
• One-time game
• Players dont know each other and there are no
  bribes
• Game a both players have a dominant strategy
• Games b, c, d Ron does not have a dominant
  strategy
• Choose always r1 (predispose Colleen for
  coalition)
• Choose always r2 (weaken Colleens)
• Choose r1 in b and c but r2 in d
• Flip a coin (costless decision-making)

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• From Colleens point of view (game d)
• If Ron chooses r1, she chooses c2
• If Ron chooses r2, she chooses c1
• If Ron flips a coin, she chooses c2 if she wants
  to max her payoff
• Expected payoffs if she chooses c1.5(1).5(-1)0
• Expected payoffs if she chooses
  c2.5(3).5(-2).5
• If she wants to minimize her loss (the coin shows
  r2 for Ron), she would choose c1
• Information about Rons personality type is of
  value to Colleen
• Even if she knew that what strategy he played in
  game c, she cannot determine with certainty what
  type of player he is and what strategy he will
  play in d

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• Using probabilities
• p1 is the probability that Ron will choose r1
• Colleens expected payoff from c1 is
• p1(1)(1-p1)(-1)2p1-1
• Her expected payoff from c2 is
• p1(3)(1-p1)(-2)5p1-2
• Solving for p1 shows that if p11/3 she should
  play c2 and if p1
• Using minimax minimize your max loss
  (regardless of what the other player chooses)
• Her max loss is -2 she will choose c1 where her
  loss is -1
• Conservative decision rule works well if Ron
  chooses r2 (misanthropist)

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• The prisoners dilemma
• One-time simultaneous-move game
• No communication
• Each player has a dominant strategy
• The result (based on each players self-interest)
  is not the best result for both players
• The Bertrand duopoly game
• Same idea as the prisoners dilemma
• Strategic interaction of firms in this oligopoly
  model
• The advertising game

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• Nash equilibrium
• Dominant strategy equilibrium
• No player has an incentive to change its strategy
  given the strategies chosen by the other players
• Nash equilibrium does not require a dominant
  strategy for each player

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• Repeated games
• Penalty if one player cheats cooperative outcome
  becomes more likely due to fear of retaliation
  and the chance that the game will be played over
  and over again
• Tit-for-tat strategy
• Do what the other player did in the previous
  round of the game
• Found to be a very successful strategy (earns
  higher payoffs than any other one)
• Final period should be unknown
• Difficult to penalize with many players and
  possible entry
• Cooperation is more successful if one firm in the
  cartel has a price-leadership or a
  quantity-leadership role (Saudi Arabia and OPEC)
• Ultimatum strategy if you defect once, Ill
  punish you forever

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• Sequential games
• A first mover advantage is possible
• In cases of price leadership and launching new
  products it is better to be second
• Strategic entry deterrence and costs of entry
• Entry with no fixed entry costs
• Potential entry with fixed costs of entry limit
  pricing strategy

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Monopolistic competition

• A spatial model
• In monopolistic competition products are not
  perfect substitutes like in perfect competition
• Products are imperfect substitutes due to
  distance
• Assumptions
• The product itself is standardized, but is
  offered at different locations
• Firms have increasing returns to scale
• People care about the cost of the product and
  transportation costs

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• The model
• Assume an island with a circumference of 1 km
• Four restaurants ¼ km apart
• Each consumer lives at most 1/8km from a
  restaurant
• Assume L consumers (scattered uniformly) and the
  cost of travel per km is t
• Each consumer eats 1 meal a day at the restaurant
  where the cost (for the meal and transportation)
  is lowest
• The restaurants cost is TCFMQ where F is fixed
  cost and M is a constant marginal cost

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• Suppose L100 and TC505Q
• Then each restaurant will serve 25 meals per day
  and its TC is 505(25)175 and ATC7
• If t24/km, the person who lives 1/8km from a
  restaurant has a cost of 2(1/8)(24)6
• The average cost is 3 (between 0 and 6)
• Therefore the average cost per meal is 7310
• What is optimal number of restaurants
• With one restaurant, the cost of the food is the
  lowest but transportation costs can be
  substantial
• If we open another restaurant we would like to
  see the average cost per meal to decline

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• Example
• If we now have 5 restaurants, each serves 20
  meals per day and ATC505(20)/207.50
• Transportation costs are 2(1/10)(24)4.8 with
  average transportation costs 2.4
• Total cost per meal is 7.502.49.9, i.e. less
  than with 4 restaurants
• The model is applicable in analyzing other
  product characteristics, not just location
• The spatial model and the hot dog vendors
• Advertising in monopolistic competition