Lecture 1 Roadmap, Contents, Basic Concepts

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Lecture 1Roadmap, Contents, Basic Concepts

• Kerschbamer Imperfectly Competitive Markets

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Scenarios that Yield Imperfectly Competitive
Outcomes

• There are at least three scenarios in which
  markets yield non-competitive outcomes
• there is a single dominant firm in the market
  (the monopoly case)
• there is more than one firm in the market, but
  market conditions (number of firms,
• degree of product differentiation, type of
  competition . . . ) are such that imperfectly
• competitive outcomes result from normal
  competition, even when no individual
• firm is dominant (the standard oligopoly case)
• there is more than one firm in the market, market
  conditions are such that (either
• perfectly or imperfectly) competitive outcomes
  result from normal competition,
• but firms take actions that undermine normal
  competition and help them to get
• outcomes that (in the limit) resemble those
  reached by a single dominant firm
• (impeded competition cartel formation,
  explicit or tacit collusion, horizontal
• or vertical mergers, entry deterrence, etc.)
• In this lecture series we look at each of those
  three cases in turn.

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I The Monopoly Case

• This case is interesting and relevant in its own
  (for instance, Alitalia has a monopoly
• on flights from Turin to Milan, while Air France
  has a monopoly on flights from
• Toulouse to Paris) and it is an important
  building block for the other two parts
• For instance, acting like a multi-product
  monopolist is the best that can be reached by
• collusion. Thus, comparing the multi-product
  monopoly outcome with the outcome
• of normal competition yields important
  insights in
• incentives for firms in the market to collude
• consequences of collusion for consumers
• Also, acting like a multi-stage monopolist is an
  outcome that can be reached by a
• vertical merger between two adjacent monopolies.
  Thus, comparing the multi-stage
• monopoly outcome with the outcome of normal
  competition yields important
• insights in

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I The Monopoly Case (Cont.)

• An important real-world relevant topic in the
  monopoly part is price-discrimination.
• Although price-discrimination is not necessarily
  welfare decreasing, it has repeatedly
• been in the focus of competition policy (probably
  because it is a sign of market power).
• We will first look at the classical forms of
  price discrimination, covering
• first-degree price discrimination
• second-degree price discrimination
• third-degree price discrimination
• bundling and tying
• Then we will look at intertemporal
  price-discrimination covering both

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II Oligopoly

• In the oligopoly part we start with a
  particularly implausible framework
• two firms (duopoly)
• one homogeneous good
• many price-taking consumers
• no fixed costs
• no capacity constraints
• same constant marginal cost for both firms
  (symmetry)
• In this simple framework, we analyze the four
  basic forms of oligopolistic competition
• Cournot competition
• Bertrand competition

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II Oligopoly (Cont.)

• Next we lift the unrealistic assumptions one
  after the other in order to see how market
• outcomes change
• in the type of competition (price or quantity)
• in the number of firms (form the small to the
  large number case)
• in the degree of differentiation (from almost
  perfect substitutes to almost perfect
• complements)
• in the tightness of capacity constraints
• in the degree of asymmetry between firms
• . . .
• Some of the questions we plan to address are
• Is competition always better for consumers than
  monopoly?

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III Impeded Competition

• Here (again) we start with a(n) (unrealistic)
  framework by assuming that firms are able to
• write enforceable cartel agreements.
• First we ask the question, if firms could write
  enforceable cartel agreements, and if all firms
• join a cartel, what would their market strategy
  be?
• Then we turn to the question whether firms would
  be willing to join an all-inclusive cartel
• (if they could write enforceable cartel
  agreements), and if not, what would the condition
  for
• cartel stability be?
• Then we turn to a more realistic scenario, where
  cartel agreements are not enforceable
• (because they violate competition laws and are
  therefore not enforced in courts of law)
• The first question of interest is, if no external
  enforcement is available, how can firms be
• prevented from deviating from a
  (competition-hampering) agreement?
• A possible answer is If the same firms compete
  repeatedly on the same market, they might
• be able to reach a collusive outcome by making
  their behavior today dependent on the
• performance of the competitors yesterday.

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III Impeded Competition (Cont. 1)

• Then we look deeper in the economics of (explicit
  or tacit) collusion.
• A main question in this part of the lecture is,
  which characteristic of an industry affect
• the sustainability of collusion?
• We look at supply side factors as
• type of competition (Bertrand vs. Cournot)
• number of competitors in the market
• barriers to entry
• frequency of interaction
• degree of asymmetry between competitors
• prospect of innovation

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III Impeded Competition (Cont. 2)

• Then we look at mergers, asking questions as
• when are mergers profitable for those firms who
  merge?
• when are mergers profitable for the competitors
  of the merging firms?
• what is the effect of mergers on consumers and
  welfare?
• We will start with horizontal mergers where two
  or more firms on the same production
• or distribution stage integrate into a single
  unit.
• There we will see that in absence of direct
  efficiency gains, the short-run impact of
• horizontal mergers in markets where goods are
  substitutes is to
• increase or decrease profits for those who merge
• increase profits for non-merging competitors
• increase industry profits

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III Impeded Competition (Cont. 3)

• But, many real worlds mergers involve some form
  of efficiency gain and efficiency gains
• tend to
• increase profits for those who merge
• decrease the profits for non-merging competitors
• increase industry profits
• increase consumer surplus
• increase welfare
• Thus, the desirability of horizontal mergers in
  markets where goods are substitutes depends
• on the magnitude of efficiency gains.
• Then we turn to vertical mergers where two or
  more firms or complementary production
• or sales stages integrate into a single unit.

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III Impeded Competition (Cont. 4)

• Various effects of vertical mergers will be
  discussed
• Possible positive effects of vertical mergers
  include
• avoiding multiple marginalization problems
• avoiding or reducing other vertical externalities
• avoiding hold ups and promoting idiosyncratic
  investments
• avoiding mis-syncronizations
• Possible negative effects of vertical mergers
  include
• increasing market power
• enabling exclusionary behavior
• distorting input choices

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Contents

• Part 0 Basic Concepts (Lecture 1)
• Basics Quasilinear Preferences and Product
  Differentiation
• 1.1 Quasilinear Preferences
• 1.2 Heterogeneous Goods
• Representative Consumer Models
• Model of Dixit (1979)
• Vertical Product Differentiation
• Model of Shaked and Suttons (1982) v(q, ?)
  q?

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Contents (Cont. 1)

• Part I Monopoly
• 2. Dominant but Non-Discriminating Firms (Lecture
  2)
• Textbook Monopoly
• Social Loss of Monopoly
• Multiproduct Monopoly
• Multistage Monopoly (Double Marginalization)
• 3. The Price Discriminating Monopoly (3 Lectures
  Lectures 3-5)
• First Degree Price Discrimination
• Second Degree Price Discrimination
• with a Single Two-Part Tariff
• with a Menu of Two-Part Tariffs
• Optimal Second-Degree Price Discrimination
• Third Degree Price Discrimination
• Bundling
• Intertemporal Price Discrimination

Lecture 1 Roadmap, Contents, Basic Concepts
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Contents (Cont. 2)

• Part II Oligopolistic Competition
• 4. Oligopolistic Competition (4 Lectures
  Lectures 6-9)
• Homogeneous Goods and the Four Market Games
• Cournot Competition
• Bertrand Competition
• Stackelberg-Cournot Competition
• Stackelberg-Bertrand Competition
• Increasing the Number of Competitors
• The Effects of Barriers to Entry
• The Effects of Capacity Constraints
• The Role of Product Differentiation
• Type of Competition and Market Outcomes
• (Product Differentiation) x (Type of Competition)
• Market Demand/Inverse Demand
• Cournot Competition
• Bertrand Competition
• Stackelberg-Cournot Competition
• Stackelberg-Bertrand Competition

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Contents (Cont. 3)

• Part III Impeded Competition
• 5. Cartel Formation (Lecture 10)
• What does a Cartel Maximize?
• The Cartel Instability Problem
• Seltens Four are Few and Six are Many
• Market Game
• Cartel Bargaining
• Cartel Participation
• The All-Inclusive Cartel

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Contents (Cont. 3)

• 6. Collusion (2 Lectures 11-12)
• Collusive Agreements and Retaliations
• Discount Factor/Present Value
• Nash Reversion
• A Simple Framework
• The Economics of Collusion
• Relevant Factors for Sustainability of Collusion
• Type of Competition
• Number of Competitors
• Barriers to Entry
• Frequency of Interaction / Market Transparency
• Degree of Asymmetry Between Competitors
• Prospect of Innovation
• Demand Dynamics
• Demand Fluctuations
• Observability of Demand
• Discussion

Lecture 1 Roadmap, Contents, Basic Concepts
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Contents (Cont. 4)

• 7. Mergers (2 Lectures 13-14)
• Horizontal Mergers
• Horizontal Mergers and Market Power
• Horizontal Mergers and Efficiency Gains
• Horizontal Mergers and Structural Effects
• Vertical Mergers
• Vertical Mergers and Pro-competitive Effects
• Vertical Mergers and Anti-competitive Effects

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Technical Issues Partial Equilibrium Analysis

• Standard Microeconomics main focus is on
  general equilibrium.
• In a general equilibrium model everything
  depends on everything a change in the price of
• potatoes might result in changes everywhere in
  the economy inclusive the demand for red
• pens.
• This is too complicated for our purposes we will
  therefore take a partial equilibrium
• perspective.
• The partial equilibrium approach envisions the
  market for a single good (or a group of goods)
• for which each consumers expenditure constitutes
  only a small portion of his overall budget.
• When this is the case, it is reasonable to assume
  that
• only a small fraction of any increase in wealth
  will be spent on the market for this good
• (those goods) ? wealth effects should be small
  (really?)
• changes in the market for this good (those goods)
  will lead to small changes (in prices) in
• the rest of the economy ? cross-price effects
  between this market and the rest of the

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Partial Equilibrium Analysis (Cont.)

• Throughout this lecture series we take those two
  conditions not only as given, we rather
• assume (these are the partial equilibrium
  assumptions)
• that wealth effects are not only small, but
  absent and
• that cross-price effects between the market(s)
  under consideration and the rest of the
• economy are not only small but absent.
• The fixity of prices of all other goods justifies
  treating the expenditure on those other goods
• as a single composite commodity, called the
  numeraire.
• The absence of wealth effects justifies looking
  at consumer preferences that are quasilinear
• with respect to the numeraire commodity.
• Suppose there are two commodities, good X and the
  numeraire, good Y. Let xi ? R and
• yi ? (-8, 8) denote consumer is consumption of
  goods X and Y respectively.
• Definition. Consumer is preference relation on
  bundles of good X and good Y in
• R x (-8, 8) is quasilinear with respect to good
  Y if

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Quasilinearity

• Definition. Consumer is preference relation on
  bundles of good X and good Y in
• R x (-8, 8) is quasilinear with respect to good
  Y if
• all the indifference sets are parallel
  displacements of each other along the axis of
  good Y
• good Y is desirable.
• Note that the definition assumes that there is no
  lower bound on the possible consumption of
• the numeraire commodity. Why is this convenient?
• Also note that quasilinear preferences have the
  property that the consumers entire preference
• relation can be deducted from a single
  indifference set.

FIGURE HERE 1
Quasilinear Preferences (w.r.t. good Y)
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Quasilinearity (Cont. 1)

• Result. A continuous preference relation ? on R
  x (-8, 8) is quasilinear w.r.t. the
• second commodity if and only if it admits a
  utility function of the form vi(xi,yi) ui(xi)
  yi.
• Proof. Omitted see any advanced micro textbook.
  
• In terms of our partial equilibrium
  interpretation, we think of good X as the good
  whose
• market is under study and of the numeraire as
  representing the composite of all other goods
• In this interpretation, yi stands for the total
  money expenditure on these other goods.
• Throughout, we normalize the price of the
  numeraire to 1 and we let p denote the price of
• good X. The following assumptions on ui(xi) turn
  out to be useful
• ui(.) is bounded above and twice differentiable
• 0 lt ui(0) lt 8

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Quasilinearity (Cont. 2) An Example

• Note that with those assumption ui(xi) can be
  interpreted as consumer is willingness
• to pay for xi units!

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Quasilinearity (Cont. 3)

• Omitting the subscript i, the consumers problem
  of choosing her most preferred consumption
• bundle given price p for good X, price 1 for
  good Y and wealth w (in units of the numeraire)
• can be represented as
• maxx0,y v(x, y) u(x) y s.t. px y w
• In any solution to this problem, the budget
  constraint holds with equality.
• Substituting for y from this constraint, we can
  rewrite the consumers problem solely in terms
• of choosing his optimal consumption x of good X
  
• maxx0 u(x) px w
• which has the necessary and sufficient FOC
• u(x) p, with equality if x gt 0
• At any interior solution, this condition says
  that the consumers marginal benefit from
• consuming an additional unit of good X exactly
  equals its price.

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Quasilinearity (Cont. 4) Deriving Demand
FIGURE HERE 5
FIGURE HERE 4
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Quasilinearity (Cont. 5)

• In what follows, the rule that assigns the
  optimal consumption level x to each price-wealth
  
• situation (p,w), is denoted by d(p,w) if we look
  at individual demand and by D(p,w) if we
• look at aggregate demand.
• Under the assumption (of previous slides) that
  there is no lower bound on the possible
• consumption of the numeraire commodity, demand
  will not depend on w, so we will
• simplify the notation to d(p) and D(p),
  respectively,
• What if the lower bound on y is respected?
• Now you see what the partial equilibrium analysis
  is good for
• demand does not depend on income
• demand does not depend on prices outside the
  sector under consideration
• the area under the demand function has a
  straightforward interpretation
• optimal quantity of the good under consideration
  does not depend on the distribution of

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Quasilinearity and Heterogeneity of Goods

• Much of this lecture series will focus on
  industries where goods are heterogeneous.
• The quasilinear framework can easily be extended
  to allow for more that one non-
• numeraire good.
• In what follows we consider a single
  representative consumer (we can therefore drop
  the i
• subscript) who decides about the quantities x1, .
  . . , xm of the goods X1, . . . , Xm (note the
• misuse of notation the subscript denotes the
  good now).
• The preferences of the consumer are represented
  by the quasilinear utility function
• v(x1, . . . , xm, y) u(x1, . . . , xm) y
  with
• u(x1, . . . , xm) 0 for x1 x2 . . . xm
  0
• Note that u(x1, . . . , xm) can be interpreted as
  the representative consumers willingness to
• pay for a bundle containing x1 units of good X1,
  x2 units of X2, . . .
• Similarly ?u(x1, . . . , xm)/?xj is the marginal
  . . .

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Quasilinearity and Heterogeneity (Cont. 1)

• What is the interpretation and sign of
• ?²u/(?xj?xk) for j ? k ?
• We will sometimes look at the following simple
  linear form (by Dixit 1979)

where a gt 0, b gt 0 and g ? (-b, b). Denote the
price of good X1 by p1 and the price of good X2
by p2 (the price of the numeraire is still
normalized to unity) and derive demand for both
goods D1(p1, p2) . . . D2(p1, p2) . . .
inverse demand for both goods P1(x1, x2) . .
. P2(x1, x2) . . .
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Other Models of Heterogeneous Goods

• Representing heterogeneous goods via parameters
  in the utility function of a
• representative consumer (as done on previous
  slides) is often not the most natural way
• of modelling heterogeneous goods.
• For many research questions (for example, in
  scenarios where firms choose product
• characteristics or products variety) it is more
  natural to model heterogeneity directly
• over product characteristics.
• In the rest of this lecture, we discuss the most
  prominent models of this variety.

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Other Models of Heterogeneous Goods (Cont.)

• Assumptions
• (non-numeraire) goods are distinguished in a
  single, one-dimensional characteristic
• denoted q, where q ? qmin, qmax
• consumers are heterogeneous and are distinguished
  in a single one-dimensional
• characteristic denoted ?, where ? ? ?min, ?max
  
• characteristic ? is distributed over consumers
  according to c.d.f. F(?)
• consumers are interested in a single unit of one
  of the varieties of the good at most
• the willingness to pay of a consumer with
  characteristic ? for a good with
• characteristic q is given by v(q, ?)
• In this framework we discuss two classes of
  models with heterogeneous goods
• models of vertically differentiated goods

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Vertical Product Differentiation 1

• Defining Features
• all consumers have the same attitude toward the
  characteristic q
• if one consumer has a higher willingness to pay
  for qi than for qj, then all others too
• Examples durability, freshness, energy
  consumption, capacity . . .
• A Simple Model (Shaked and Suttons 1982)
• goods are described by their quality q
• consumers are characterized by their quality
  consciousness ?
• ? is uniformly distributed on 0, 1
• the willingness to pay of a consumer with quality
  consciousness ? for a good with
• quality q is given by v(q,?) q?

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Vertical Product Differentiation 2

• Suppose first that only one quality, denoted by
  q1, is available at price p1.
• Which consumers will buy the good?

FIGURE HERE 6
Denoting the mass of consumers who buy quality q1
at price p1 by D1(p1) and the mass of consumers
who do not buy by D0(p1) we get D0(p1) . . .
D1(p1) . . .
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Vertical Product Differentiation 3

• Suppose now that the two qualities q1 and q2 are
  available at prices p1 and p2, respectively.
• Which consumers will buy which quality?
• A consumer with quality consciousness ? will buy
• quality 1 if . . .
• quality 2 if . . .
• no quality if . . .
• To get some structure in the problem define
• ?10 as the consumer who is exactly indifferent
  between buying quality 1 and not buying at all
• (if quality 2 is not available) then ?10 is
  given by the equation
• ?10 . . .

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Vertical Product Differentiation 4

• Assume 0 lt p2 p1 lt q2 q1 ? ?21 ? (0, 1)
• Two cases need to be distinguished, depending on
  whether ?21 is willing to buy or not (how
• do you check for that?)
• Case 1 ?10 lt ?20 ? p1/q2 lt p2/q2

FIGURE HERE 7
In this case we get D0(p1, p2) . . . D1(p1,
p2) . . . D2(p1, p2) . . .
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Vertical Product Differentiation 5

• Again we assume 0 lt p2 p1 lt q2 q1 ? ?21 ?
  (0, 1)
• Case 2 ?10 gt ?20 ? p1/q2 gt p2/q2

FIGURE HERE 8
In this case we get D0(p1, p2) . . .
D1(p1, p2) . . . D2(p1, p2) . . .
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Horizontal Product Differentiation 1

• Defining Features
• consumers have different attitudes toward the
  characteristic q
• one consumer has a higher willingness to pay for
  qi than for qj, another a consumer
• might still have a higher willingness to pay
  more for qj than for qi
• Examples taste of the ice-cream color, design,
  or size of the T-shirt location of the good
• An important subclass of this class of models is
  the class of models of spatial
• differentiation.
• In models of spatial differentiation
• q is the place of availability of the product
  (which is otherwise homogeneous)
• ? is consumer ?s location

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Horizontal Product Differentiation 2

• A Simple Model of Spatial Differentiation
  (Hotelling 1929)
• goods are characterized by their location q in a
  city represented as lying on a line
• segment of length 1 q ? 0, 1
• consumers are characterized by their address ? on
  the same line segment
• consumers addresses are uniformly distributed on
  0, 1
• gross willingness to pay is r for each consumer
• consumption entails travel cost t/2 per unit of
  distance, where distance is 2? q
• the net willingness to pay of a consumer with
  address ? for a good located at q is
• v(q,?) r - t? q
• the mass of consumers is normalized to 1
• Note that there is also a non-spatial
  interpretation of this model, where

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Horizontal Product Differentiation 3

• Suppose first that only one product variant, q1
  1, is available at price p1
• Which consumers will buy the good?

FIGURE HERE 9
Denoting the mass of consumers who buy product
variety q1 at price p1 again by D1(p1) and the
mass of consumers who do not buy by D0(p1) we
get D0(p1) . . . D1(p1) . . .
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Horizontal Product Differentiation 4

• Suppose now that only product variant q2 0 is
  available at price p2
• Which consumers will buy the good?

D0(p2) . . . D2(p2) . . .
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Horizontal Product Differentiation 5

• Suppose now that the goods are available on both
  locations, at q1 0 at price p1 and at q2 1
• at price p2
• Which consumer will buy at which location?
• A consumer with address ? will buy
• at location q1 0 if . . .
• at location q2 1 if . . .
• at no location if . . .
• To get some structure in the problem define
• ?10 as the consumer who is exactly indifferent
  between buying at location 1 and not buying at
• all (if location 2 is not available) then ?10
  is given by the equation

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Horizontal Product Differentiation 6

• Assume p1 p2 lt t ? ?21 ? 0, 1
• Two cases need to be distinguished, depending on
  whether ?21 is willing to buy or not
• (how do you check for that?)
• Case 1 ?10 lt ?20

FIGURE HERE 11
In this case we get D0(p1, p2) . . . D1(p1,
p2) . . . D2(p1, p2) . . .
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Horizontal Product Differentiation 7

• Again we assume p1 p2 lt t ? ?21 ? 0, 1
• Case 2 ?10 gt ?20

FIGURE HERE 11
In this case we get D0(p1, p2) . . . D1(p1,
p2) . . . D2(p1, p2) . . .
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Horizontal Product Differentiation 8

• Up to now we have assumed
• prices are exogenously given
• product variety is exogenously given
• product characteristics are exogenously given
• Later we want to endogenize each of these
  variables
• endogenizing prices is no problem in Hotelling
• endogenizing product variety might lead to
  problems because of asymmetries ? Salop
• endogenizing p. characteristics might lead to
  problems as profits discontinuous in own price

FIGURE HERE 12
FIGURE HERE 13
Effect of a small decrease in price (from p1 to
p1) in Hotelling
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Horizontal Product Differentiation 9

• Solution to the Discontinuity Problem
• DAspremont et al. (1979) linear city with
  v(q,?) r t(q ?)2

Solution to the Asymmetry Problem Salop (1979)
circular city with v(q,?) r t q ?