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Chapter 5 Imperfect competition


Title: Markets and market failures: theory and public policies Author: Sylvie Lambert Last modified by: E.Caroli Created Date: 8/27/2008 5:06:51 PM – PowerPoint PPT presentation

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Title: Chapter 5 Imperfect competition

Chapter 5Imperfect competition
  • An introduction to the theory of games
  • Some oligopoly models
  • Monopolistic competition

Collusion between firms
  • Collusion is difficult to achieve on a
    competitive market. Might seem less difficult to
    achieve among oligopolists, that is in industries
    served by only a small number of firms.
  • However, collusion usually appears extremely
    difficult to sustain.
  • Because it is the interest of each firm
    individually is usually not in the interest of
    all firms taken as a whole.
  • Similar to the prisoners dilemma

Prisoners dilemma
  • 2 prisoners
  • If one of the 2 confesses, the confessor will be
    freed while the other one will spend 20 years in
  • If both confess, they both get an intermediate
    sentence (say 5 years).
  • Payoff matrix
  • Dominant strategy confess

The sustainability of collusion
  • Consider 2 firms that are the sole providers of
    mineral water on a given market.
  • Market demand curve is given by P 20 Q
  • MC 0
  • Collusion each firm will offer half of the
    monopoly output and sell it at the monopoly
  • Monopoly quantity 20 2Q 0 ? Q 10 and P
  • If both firms abide by this agreement
  • Each will sell 5 units of output
  • Profit P 50 0 50.

The sustainability of collusion (ctd 1)
  • Each firm actually has two options it can abide
    by the agreement or defect. Assume that defection
    means cutting the price from 10 to 9.
  • If one firm abides by the agreement and the other
    one defects. What happens?
  • The defector will capture the entire market
    because of its lower price. He will sell Q 20
    9 11 and make a profit of 99.
  • The other firm sells nothing and makes zero
  • If both firms defect, they will end up splitting
    the 11 units of output sold at a price of 9 and
    will make an economic profit of 49.5

The sustainability of collusion (ctd 2)
  • Payoff matrix
  • Dominant strategy defect
  • As this example is set up firms do not do much
    worse when they defect that when they cooperate.
  • However, if firms find it in their interest to
    defect once, they are likely to defect again.

  • Oligopolists compete on prices but also by
    advertising. When a firm advertises its product,
    its demand increases for 2 reasons.
  • First people who never used that type of product
    before learn about it, which leads some of them
    to buy it.
  • Second other people who already consumed a
    different brand of the product will switch brand
    because of advertising.
  • US cigarette industry brand-switching effect of
    advertisement is very strong.

Advertising (ctd)
  • Payoff matrix
  • Dominant strategy advertise

Nash equilibrium
  • In many games, not every player has a dominant
  • The dominant strategy for Firm 1 is to advertise.
  • But Firm 2 has no dominant strategy
  • is the Nash equilibrium of the game

Nash equilibrium definition
  • A Nash equilibrium is a combination of strategies
    such that each player's strategy is the best he
    can choose given the strategy chosen by the other
  • At a Nash equilibrium, neither player has any
    incentive to deviate from his current strategy.
  • In a prisoner's dilemma, the equilibrium is a
    Nash equilibrium.
  • But a Nash equilibrium does not require both
    players to have a dominant strategy.

The maximin strategy
  • In the previous example, we have assumed that
    Firm 2 believes that Firm 1 will act rationally.
  • However, Firm 2 may not be sure that Firm 1 will
    act rationally.
  • When Firm 2 has no dominant strategy and is not
    sure of what Firm 1 will do, what should it do?
  • If firm 2 is extremely cautious, it may choose
    the maximin strategy it will choose the strategy
    that maximises the lowest possible value of its
    own payoff.
  • In this situation, the maximin strategy is not to

Repeated play in prisoner's dilemma
  • Strategy to prevent defection tit-for-tat
  • How it works the first time you interact with
    somebody, you cooperate. In each subsequent
    interaction you do what the person did in the
    previous interaction.
  • Robert Axelrod (The Evolution of Cooperation,
    1984) tit-for-tat performs very well against a
    large number of alternative strategies
  • Conditions for tit-for-tat to be successful
  • There must be a rather stable set of players each
    of whom can remember what the others have done in
    previous interactions.
  • Players must allocate a sufficiently high value
    to the future.

  • These conditions are often met in human
    populations. Many people interact repeatedly and
    keep track of what others did in the past.
  • Examples
  • World War I
  • Business world
  • Additional condition there is not a known fixed
    number of future interactions.
  • Does tit-for-tat generate widespread collusion?
    By no means cartels tend to be highly unstable.
  • Problem of selective punishment
  • Risk of entry

Sequential games
  • In many games, one player moves first and the
    other one can choose his strategy with full
    knowledge of the first player's choice
  • Example USA versus Soviet Union during much of
    the Cold War
  • Given the assumed payoff, USA may threaten to
    retaliate, but if the payoffs are as displayed
    above, this is not credible.
  • In order to be sure that there won't be any risk
    of nuclear war, the USA should install a
    "doomsday" machine

USA versus Soviet Union
Useless investments Sears Tower
  • Consider the example of the Sears Tower in
    Chicago (the highest building).
  • A company X considers whether to build a higher
    building. Its concern is that Sears may react by
    building an even higher building.

Sears Tower strategic entry deterrence
  • Before Sears had originally built its tower
    option of building a platform at the top on which
    it could subsequently build an addition that
    would make the building taller.
  • Building the platform costs 10 units but reduces
    the cost of making the building taller by 20
  • This platform is an example of strategic entry

Sears Tower (ctd)
  • Some oligopoly models
  • Monopolistic competition

The Cournot model
  • The central assumption of the model is that each
    firm treats the amount produced by the other firm
    as a fixed quantity that does not depend on its
    own production decisions.
  • Suppose the market demand curve for mineral water
    is given by
  • and suppose MC 0
  • The demand curve for firm 1's water is

The Cournot duopoly (ctd 1)
The Cournot model (ctd2)
  • Firm 1's demand curve is the portion of the
    original demand curve that lies to the right of
    this vertical axis.
  • ? So, it is sometimes called the residual demand
  • The rule for firm 1's profit maximisation is MR
    MC 0.
  • Marginal revenue has twice the slope as demand so

The reaction functions
  • The optimal output level is given by
  • This is firm 1s reaction function
  • Firm 2s reaction function is given by

The reaction functions (ctd)
The Nash equilibrium of the Cournot model
  • The intersect of both reaction functions is the
    Nash equilibrium of the Cournot model

How profitable are Cournot duopolists?
  • Since their combined output is 2a/3b, the market
    price will be
  • At this price, each will have a total revenue
    equal to the economic profit given by

The Bertrand model
  • Each firm chooses its price on the assumption
    that its rival's price remains fixed.
  • Suppose that the market demand and cost
    conditions are the same as in the Cournot
    example. Suppose firm 1 charges an initial price
  • Then firm 2 faces essentially 3 choices
  • It can charge more than firm 1 and sell nothing.
  • It can charge the same as firm 1 in which case
    both firms will split the market demand at that
  • It can sell at a marginally lower price than firm
    1 and capture the entire market.
  • This last option is always the most profitable.

The Bertrand model (ctd)
  • As in the Cournot model the situations of the
    duopolists are completely symmetric in the
    Bertrand model.
  • So, the strategy of selling at a marginally lower
    price will be chosen by both firms.
  • In this case, there is no stable equilibrium the
    price-cutting process will go on until the price
    reaches the marginal cost 0.
  • In this case, both duopolists will share the
    market equally.

The Stackelberg model
  • What would a firm do if knowing that its rival is
    a naïve Cournot duopolist?
  • This firm would choose its own output level by
    taking into account the effect of that choice
    upon the output level of its rival.
  • Returning to the Cournot model, assume that firm
    1 knows that firm 2 will treat firm 1's output as
  • Firm 2's reaction function is
  • Knowing this, firm 1 can substitute R2(Q1) for Q2
    in the equation for the market demand curve.

The Stackelberg model (ctd 1)
  • The demand curve addressed to firm 1

The Stackelberg model (ctd 2)
  • Firm 1 Stackelberg leader
  • Firm 2 Stackelberg follower

Comparison of outcomes
  • A monopoly with the same demand and cost curves
    as the Cournot duopolist would have produced
  • The Cournot duopolists
  • P a/3
  • Q 2a/3b.
  • The Bertrand duopolists
  • P MC 0
  • Q a/b, so that each of them produce a/2b.
  • This is similar to the perfect competition

Comparison of outcomes (ctd 1)
  • The Stackelberg model
  • P a/4
  • Q 3a/4b
  • P1 a2/8b and P2 a2/16b
  • ? In the Stackelberg model, the leader fares
    better than the follower.

Comparison of outcomes (ctd 2)

Contestable markets
  • William Baumol, John Panzer and Robert Willig,
    Contestable Markets and the Theory of Industry
    Structure, 1982.
  • The idea is that monopolies sometimes behave just
    like perfectly competitive firms.
  • This will happen when entry and exit are
    perfectly free.
  • Costless entry there are no sunk costs
    associated with entry and exit
  • When sunk costs are high, new firms will not
    enter the market even if the incumbent is making
    high profits
  • When sunk costs are almost zero, new competitors
    will enter the market with the idea that they
    will pull out if post-entry business proves non

Contestable markets (ctd)
  • The contestable market theory
  • Cost conditions will determine how many firms
    will end up serving the market.
  • But there is no clear relationship between the
    actual number of competitors in a market and the
    extent to which prices and quantities are similar
    to what we would see under perfect competition.
  • Critics there are substantial sunk costs
    involved in all activities

Competition under increasing returns to scale
  • Suppose that there exists a duopoly in an
    industry where there are increasing returns to
  • 2 firms started at an early stage of development
  • Should we expect that one firm will drive the
    other one out of the market?
  • 2 solutions
  • Merge problem of antitrust laws.
  • Price war none of the 2 firms has any interest
    in doing that.
  • without a threat of entry, a live-and-let-live
    strategy is very likely to be adopted

Competition under increasing returns to scale
  • Suppose now that a firm has a monopoly position
    and that potential entrants face substantial sunk
  • Potential entrants may be reluctant to enter the
    industry and face a potentially ruinous price war
    with the incumbent
  • Last solution
  • Buyers may be willing to approach a potential
  • Local authorities usually do that

  • Monopolistic competition

Monopolistic competition
  • Monopolistic competition occurs when
  • Many firms serve a market with free entry and
  • But in which the product of each firm is not a
    perfect substitute to the product of the other
    firms on the market.
  • The degree of substitutability between products
    determines how closely the industry resembles
    perfect competition

The Chamberlin model
  • Developed in the 1930s by Edward Chamberlin and
    Joan Robinson.
  • Assumption there exists a clearly defined market
    composed of many firms producing products that
    are close but imperfect substitutes for one
  • So, each firm faces a downward-sloping demand
    curve but behaves as if its price and quantity
    decisions should not affect the behaviour of the
    other firms in the industry
  • Firms are perfectly symmetric so if it makes
    sense for a firm to alter its price in one
    direction, it will make sense for the other firms
    to do the same

The individual firms demand curves
  • Each firm faces 2 demand curves


Chamberlinian equilibrium in the short run

Chamberlinian equilibrium in the long run

Perfect competition versus Chamberlinian
monopolistic competition
  • Perfect competition generates allocative
    efficiency whereas monopolistic competition does
  • The Chamberlin model is more realistic than the
    perfect competition model on, at least, one
  • Perfect competition the price is equal to the
    marginal cost ? firms are indifferent to the
    opportunity of filling a new order.
  • Monopolistic competition the price is higher
    than the marginal cost ? firms will be very keen
    on filling an additional order.
  • In both market structures, long-run profits are 0.


Criticisms of the Chamberlin model
  • The model considers a group of products which are
    different in some unspecified way but that are
    likely to appeal to any given buyer.
  • George Stigler it is impossible to draw
    operational boundaries between groups of products
    in this way.
  • The Chamberlinian industry group quickly expands
    to contain all possible consumption goods in the
  • Complicates the perfect competition model without
    altering its most important predictions.
  • Does not depart sufficiently from the perfect
    competition model
  • Assumption that each firm has an equal chance to
    attract any of the buyers in an industry not
    always true


The spatial interpretation of monopo-listic
  • One concrete way of thinking about the lack of
    substitutability is distance.
  • ? The seminal paper in this literature has been
    published by Harold Hotelling in the Economic
    Journal in 1929
  • Consider a small island with a big lake in the
    middle. Business activities are necessarily
    located at the periphery of the island.
    Restaurants meals are produced under increasing
    returns to scale.
  • Circumference of the island is 1 mile. Initially
    4 restaurants, evenly spaced.
  • Min. distance 0 and Max distance 1/8 miles.
  • L customers scattered uniformly around the circle
    and the cost of travel is t per mile.


The initial location of restaurants
  • Total cost curve of the restaurant is
  • TC F MQ
  • ? ATC TC/Q F/Q M


The average cost of a meal with 4 restaurants
  • If TC 50 5Q where Q is the number of meals
    served each day.
  • If L 100 and there are 4 restaurants, each
    restaurant will serve 100/4 25 persons a day.
  • So, the total cost is TC 50 (5x25) 175 per
    day. Average total cost is TC/25 7 per meal.
  • Clearly this is higher than if there are only 2
    restaurants each serve 50 meals per day with AC
    50(5x50)/50 6.
  • What is the average cost of transportation if
    there are 4 restaurants?
  • In this case the farthest someone can live from a
    restaurant is 1/8 miles so that he round trip is
    1/4 miles.
  • If the travel cost is 24 per mile the total
    travel cost will be 6.


The average cost of a meal with 4 restaurants(ctd)
  • Since people are uniformly scattered around the
    loop, straightforward calculation (!) show that
    the average round trip is 1/8 miles
  • Trick this is the average between maximum
    distance (1/4) and minimum distance which is 0
  • So, the average transportation cost is 3.
  • The overall average cost per meal is 7 3 10


The optimal number of locations
  • Results from a trade-off between the fixed cost
    of opening new locations and the savings from
    lower transportation costs
  • What is the best number of outlets to have?
  • If we increase the number of restaurants from 4
    to 5, what happens to the average cost?
  • Each restaurant serves 20 meals per day, with an
    ATC 50(5x20)/20 7.5
  • The distance between 2 restaurants is now 1/5
  • So the maximum round-trip distance is 1/5 miles.
  • The minimum being 0, the average round-trip
    distance is 1/10 miles.
  • So, the average transportation cost is 24 x 1/10


The optimal number of locations (ctd 1)
  • The overall average cost is therefore 7.5 2.4
    9.9. So, adding a fifth restaurant reduces the
    average cost of the meal by 0.1.
  • Adding a 6th restaurant, the overall AC goes up
  • ? The optimal number of restaurants is 5.
  • What is the best number of outlets to have?
  • If we increase the number of restaurants from 4
    to 5, what happens to the average cost?
  • Each restaurant serves 20 meals per day, with an
    ATC 50(5x20)/20 7.5


The optimal number of locations (ctd 2)
  • The distance between 2 restaurants is now 1/5
    miles. So the maximum round-trip distance is 1/5
  • The minimum being 0, the average round-trip
    distance is 1/10 miles.
  • So, the average transportation cost is 24 x 1/10
  • The overall average cost is therefore
  • AC 7.5 2.4 9.9.
  • So, adding a fifth restaurant reduces the average
    cost of the meal by 0.1

  • In order to generalise this result, let us assume
    that there are N outlets around the loop.
  • The distance between adjacent outlets is 1/N and
    the maximum one-way trip length is half of that
  • If people are uniformly distributed around the
    loop, the average one-way trip length is 1/4N and
    the average round-trip distance is 1/2N.
  • The average transportation cost is
  • The total cost of meals is

Generalisation (ctd 1)
Generalisation (ctd 2)
  • The first order condition is
  • Applying this to our example yields

An example
  • Why are there many so many fewer small food
    stores than 30 years ago (and so much larger
  • Food stores face strongly increasing returns to
  • Transportation costs have decreased

The analogy to product characteristics
  • Consider the various airline flights between two
    cities on a given day. People have different
    preferences for travelling at different times of
    the day.

The analogy to product characteristics (ctd)
  • Virtually, any consumer product can be
    interpreted in the context of the spatial model.
  • On the automobile market, there exists a very
    large variety of options.
  • Of course, it would be much cheaper if there were
    only a couple of models.
  • But people are willing to pay a little extra for
    variety as they are willing to pay some more for
    a more conveniently located shop.
  • Car manufacturers are said to "locate" on the
    "product-space". Their aim is to make sure that
    few buyers are left without a choice that lies
    "close" to the car that best suits them.
  • Similar interpretations apply to cameras,
    vacations, bicycles, etc

Paying for variety
  • Wastefully high levels of product variety?
  • In our model we have assumed that all customers
    face the same transportation costs.
  • This is clearly not the case in reality.
  • Demand for variety increases sharply with income
    it is a luxury.
  • So, firms usually set prices in a different way
    for their different products.
  • Typically, they will price their basic products
    very close to the marginal cost
  • And the more fancy products several times the
    marginal cost.

The Hotelling model
  • 2 hot-dog vendors who can choose where to settle
    along a beach.
  • Suppose the beach is 1 mile long and is bounded
    by natural obstacles.
  • Suppose the vendors charge the same price and
    customers are evenly distributed along the beach.
    They buy one hot-dog from the nearest vendor.
  • Where should vendors position themselves?

The Hotelling model (ctd)
  • A and B are the locations that minimise average
    travel distance for all customers.
  • Yet, they are not optimal from the perspective of
    the vendors.
  • The only stable outcome is for each to locate at
    C. Each gets half of the market as before, but
    now the average one-way distance is ¼ of miles,
    i.e. twice as much as before.
  • Having both vendors at the centre of the beach is
    optimal for vendors but not for customers.
  • In this case, the "invisible hand" does not guide
    resource allocation so as to produce the greatest
    good for all.

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