Industrial Organization MarieLaure Allain and Jrme Pouyet

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Industrial Organization Marie-Laure Allain and
Jérôme Pouyet

• 21/01/2009

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Oligopolistic competition

• Imperfect competition between firms that have
  some degree of market power
• Happens whenever there is a limited number of
  firms in a market (i.e. always)
• Barriers to entry (fixed costs, institutional
  barriers)
• Product differentiation (transport costs,
  different production process, quality
  differenciation)
• Strategic interactions of various decision makers
• Oligopolistic market structure reactive
  environment
• Non-cooperative game theory
• Distortions price, quantities, quality,
  incentives (investment, innovation), services
• Some instruments can be changed more quickly than
  others difference between long run /short run.

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Imperfect competition and welfare

• Welfare effect of imperfect competition depends
  from numerous factors
• Market structure (number of firms, threat of
  entry, degree of differentiation)
• Firms behavior (collusion, equilibrium selection,
  contracts, exclusion)
• Caveat competition restrictions may sometimes be
  welfare-enhancing

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Competition policy

• Competition policy is the set of policies and
  laws which ensure that competition in the
  marketplace is not restricted in such a way as to
  reduce economic welfare (Motta).
• US Sherman Act (1890, agreements and contracts,
  monopolization practices), Clayton Act (1914,
  mergers), Robinson Patman Act (1936, price
  discrimination)
• EU Treaty of Rome (1957, Articles 81and 82 after
  renumbering by the Treaty of Amsterdam)
• Control of market structures avoid
  monopolization
• by merger control
• US Brown Shoe (1962)
• EU MCI World Com/Sprint, 1999 (rejected by both
  EC and US DoJ), General Electric / Honeywell
  (approved by US DoJ, rejected by EC)
• by divestiture or dismantlement (Standard Oil
  Company, 1911 ATT, 1982 Consent Decree)
• Control of competitive behavior prevent
  welfare-restricting agreements and contracts

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1) Cournot competition model (1838)

• First paradigm of imperfect competition
• Quantities are the strategic variable
• e.g. small-scale daily markets where prices
  adjust to clear the market
• Tour operators book the quantity of flights and
  hotel rooms approximately 18 months in advance.
  Once catalogues are published, prices adjust in
  the short-run.
• See later the Kreps-Sheinkman model
• One-stage game
• n firms choose their quantities simultaneously
• The price is then fixed by equalizing demand and
  supply
• Firm is objective is to maximize its profit

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Cournot competition

• Assuming that each profit function is
  strictly concave in qi and twice differentiable,
  the FOCs implicitely define firm is reaction
  function
• The second term (ii) is negative because market
  price responds to the quantity (the firm is not
  atomistic) negative externality towards the
  competitors, so that Cournot total quantity is
  higher and market price lower than monopoly
  quantity.
• The reaction function is downward sloping iff

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Cournot competition

• Comparison with the monopoly (Lerner index) in
  equilibrium,

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Cournot competition

• With linear demand and constant marginal costs (
  assuming there is not too much cost
  heterogeneity)
• Remark each profit increases in the average
  marginal cost, and decreases in the number of
  firms.

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Technical discussionin the two-firms case (see
Tirole, 5.7)

• Existence of a pure strategy equilibrium
• Sufficient conditions
• sufficient for this convex cost function and
  concave demand
• FOC then define continuous reactions function
• ( uniquely defined if )
• For the reaction functions to intersect
• each firm would produce a positive quantity if
  it were a monopoly
• even if i produces its monopoly quantity, j
  still produces a strictly positive quantity

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Existence of a pure strategy Cournot equilibrium
Cournot equilibrium
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Existence of a pure strategy Cournot equilibrium

• Problems of non existence
• When the profit function is not concave, reaction
  functions may not be continuous for instance if
  the demand is convex enough
• Jumps in the reaction functions may hinder the
  existence of pure strategy equilibria
• Uniqueness
• Even when it exists the equilibrium may not be
  unique
• Sufficient condition whenever they intersect,
  is steeper than
• Sufficient for this

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Stackelberg competition

• Sequential choice of quantities
• Simple example
• 2 firms
• linear demand
• Constant marginal cost c
• Determine the Cournot equilibrium
• Determine the Stackelberg equilibrium when 1 is
  the leader
• First-mover advantage
• Remark in some games, first mover drawback

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2) The Bertrand paradox (1883)

• Framework
• 2 identical firms produce the same good
  (perfectly homogenous) with constant marginal
  cost c
• Price is the strategic variable
• For a given price p, demand is D(p)
• More precisely, all the demand goes to the less
  expensive firm

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The Bertrand equilibrium

• The only Nash equilibrium is such that both price
  pc and get zero profit
• All consumers buy at the lowest price
• Zero demand for 1 if 2 undercuts
• Boils down to perfect competition, with only two
  firms on the market.

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3) Resolutions of the Bertrand paradox critical
assumptions

• Search and switching costs
• Symmetry of costs and constant return to scale
• Capacity constraints may limit the ability of a
  firm to undercut its rival and clear the market
• Edgeworth criticism (Kreps and Sheinkman)
• Horizontal differentiation Hotelling, Salop
• Vertical differentiation
• Repeated Bertrand game collusion (folk theorems)

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Bertrand competition and asymmetric firms

• Example in the Bertrand framework, suppose that
  firm 1 has a lower marginal cost than firm 2
• Determine the equilibrium of the price
  competition game.

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Search costs

• Suppose buyers are not informed initially about
  the firms prices. They choose one firm randomly
  and discover the price. If they want to choose
  another firm, they have to pay a search cost to
  discover the other firms price.
• There exists an equilibrium (BPE) in which both
  firms set the monopoly price
• Given these prices and the search cost, a buyer
  has no incentive to visit another firm once he
  has randomly chosen (note buyers beliefs)
• Given this behavior from the buyers, a firm has
  no incentive to decrease its price.
• Example restaurants for tourists vs. for locals
  (differentiation between firms wrt search costs).

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Switching costs insights

• Framework
• Two symmetric firms
• Two periods (t1,2), no discounting (d1)
  Marginal cost at each period t
• One buyer with utility at date t
• Switching cost s for the buyer to change his
  supplier between dates 1 and 2.
• Firms cannot commit to a sequence of prices.

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Switching costs insights

• At date 2, the firm who sold in period 1
  exercises her market power by pricing
• Foreseeing this, firms are willing to price at
  (at a loss) at date 1 to capture the
  buyer who will become a valuable follow-on
  purchaser at date 2
• Bargain then ripoff strategy discounts first
  to attract consumers, then increased prices on
  the captive demand
• Conclusion in this basic setting, switching
  costs do not affect the life-cycle price
• Competition over time

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3.1) The Edgeworth criticism (1925)

• Edgeworth As firms have limited capacities,
  they are not able to produce an infinite quantity
  and may not be able to produce enough to satisfy
  all the demand there may be some residual demand
  for a firm setting a price higher than the
  Bertrand equilibrium price (marginal cost pc)
• Kreps and Scheinkman (1983, Bell Journal of
  Economics) Quantity precommitment and Bertrand
  competition yield Cournot outcome

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KS-The model

• 2 firms produce a homogeneous good at the same
  marginal cost c
• Demand D(p)d-p
• Benchmark Cournot equilibrium

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KS-The model

• The game
• 1) firms 1 and 2 simultaneously choose their
  capacities X1 and X2, with the unit cost c
• 2) firms 1 and 2 simultaneously set their final
  prices p1 and p2
• Efficient rationing rule

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KS - equilibrium

• Proposition there exists an equilibrium where
  the firms choose binding capacities equal to the
  Cournot outcome
• In this equilibrium the firms make strictly
  positive profits
• Note the result depend strongly on the choice of
  the efficient rationing rule (Cf. Davidson and
  Deneckere, 1986)

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KS - proof

• First step consider stage 2
• Assume
• Define
• Both firms price above
• Assume

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KS - proof

• Both firms set the same price
• Assume
• Either 2 satisfies all its demand D10
• Or
• Locally,

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KS - proof

• Both firms thus set the same price above
• Assume
• Consider i such that
• It is profitable for i to undercut

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KS - proof

• The only possible equilibrium is thus
• It is an equilibrium (straightforward)
• Each firm sells its capacity
• Looking for SPE, stage 1 is equivalent to the
  Cournot game each firm chooses its Cournot
  quantity as a capacity.
• Conclusion the choice of a capacity is a
  pre-commitment that enables the firms to relax
  further competition and gain strictly positive
  Cournot profits instead of zero Bertrand profits.
• Role of capacity investment as a precommitment
  see Gelman and Salop, Judo economics (part II)

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3.2) Product differentiation

• Another crucial assumption of the Bertrand model
  is the homogeneity of the product
• Yet in practice, some consumers may continue to
  buy from the most expensive firms because they
  have an intrinsic preference for the product sold
  by that firm notion of differentiation
• Two types of product differentiation
• Horizontal differentiation for identical prices,
  consumers choose different products
• Vertical differentiation for identical prices,
  consumers choose the same product

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Horizontal differentiation

• Even at a given quality, consumers have
  different tastes
• Consumers preference for product specificities
  create horizontal differentiation
• Spatial localisation matters ( temporal
  availability, one-stop-shopping and product
  complementarities,)
• Information on product availability is also
  relevant
• The cross elasticity of demand is not infinite
  residual demand for the high-price product

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The Hotelling model (1929)

• Stability in competition, Economic Journal
• Continuous and uniform location of consumers
  along a segment (linear city, or tastes)
• Two firms are located on the segment and compete
  in prices to sell the same good produced at zero
  marginal cost
• Price decisions are taken once location is fixed
  (price is more flexible than location)
• Consumers pay a transportation cost to go to the
  shop to purchase the good (or utility loss when
  not consuming their preferred variety)
  cdistance to the shop
• Each consumer purchases one unit of the good
  irrespective of the price (covered market
  assumption) at the lower delivered cost
  (including transportation cost)

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Hotellings result

• Given the locations a and b,
• For equal prices, a buyer prefers the firm which
  is closer to his location
• As long as the two prices are close enough
• the indifferent consumer is such that
• Profits
• Hotelling derives the FOC to determine the final
  equilibrium prices given a and b. Given a, firm
  2s profit is increasing in b Hotelling
  concludes with a principle of minimum
  differentiation aggregation of the firms who
  chose to locate as close as possible to each
  other.

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The criticism of dAspremont, Gabszewicz and
Thisse

• In On Hotellings Stability in competition,
  Econometrica 1979 , they prove that the price
  solution is not a Nash equilibrium when both
  sellers are close to the center of the segment,
  but not at the same location.
• If abl (both firms at the same localisation)
  there exists a unique price equilibrium Bertrand
• If abltl, but both firms are close to the center,
  there exists a profitable deviation in the
  pricing game, as the profit function is not
  concave

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• As Hotelling concludes that both firms have a
  tendency towards the center, this deviation
  occursNo equilibrium in the two-stage game.
• Introducing quadratic transportation costs solves
  this problem price eq. solution everywhere.
  However, the result is reversed maximum
  differentiation.
• The game
• (1) firms choose locations simultaneously
• (2) firms choose prices simultaneously

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Hotelling quadratic transport costs

• Demand is derived from the indifferent consumer
• The equilibrium prices are thus
• It is straightforward that
• ? Maximum differentiation

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Hotelling - Final remarks

• Two opposite effects
• Market share effect given the price structure,
  each firm wants to move toward the center to
  increase its market share
• Strategic effect if i comes closer to j, then j
  reduces its price and increases price competition
• The strategic effect dominates the market share
  effect
• Horizontal differentiation is a very realistic
  answer to the Bertrand paradox
• Limit demand is inelastic as each consumer
  consumes exactly a single unit of this commodity
  irrespective of its price (market is covered by
  assumption v must be sufficiently large)
• Equilibrium location is not socially optimal
  should minimize transport costs (1/4,3/4).
• Empirically, some industries choose maximal
  differentiation (specialist food retails), others
  seem to converge (clothing,)

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Vertical differentiation

• Competition with different qualities
• Two firms, 1 and 2
• qualities resp.
• Aggregate mass of buyers
• Heterogeneity indexed uniformly by
• Unit demand, valuation for quality given by
• Assume the market is covered in equilibrium (to
  be checked ex post)

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Vertical differentiation

• The marginal buyer is indifferent between the two
  goods
• Demand faced by the two producers

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Vertical differentiation

• Firms set their prices simultaneously in
• equilibrium,
• Profits are

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Vertical differentiation and entry

• When the heterogeneity between buyers is low, the
  low quality producer makes zero profit while the
  high quality producer makes a strictly positive
  profit
• Intuition on the consequences for entry
• a firm entering the market with a low quality
  cannot compete with the high quality producer.
• A firm entering with a high quality triggers a
  tough price competition
• See Shaked and Sutton, 1983