Bertrand Competition

4 Key excerpts on "Bertrand Competition"

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  eBook - ePub

  Quantitative Techniques for Competition and Antitrust Analysis

  • Peter Davis, Eliana Garcés(Authors)
  • 2009(Publication Date)
  • Princeton University Press

    (Publisher)

  • To model competitive interaction, one must make a behavioral assumption about firms and an assumption about the nature of equilibrium. Generally, we assume firms wish to maximize their own profits, and we assume Nash equilibrium. The equilibrium assumption resolves the tensions otherwise inherent in a collection of firms each pursuing their own objectives. One must also choose the dimension(s) of competition by which we mean defining the variables that firms choose and respond to. Those variables are generally prices or quantity but can also include, for example, quality, advertising, or investment in research and development.

  • The two baseline models used in antitrust are quantity- and price-setting models otherwise known as Cournot and (differentiated product) Bertrand models respectively. Quantity-setting competition is normally used to describe industries where firms choose how much of a homogeneous product to produce. Competition where firms set prices in markets with differentiated or branded products is often modeled using the differentiated product Bertrand model. That said, these two models should not be considered as the only models available to fit the facts of an investigation; they are not.

  • An environment of perfect competition with price-taking firms produces the most efficient outcome both in terms of consumer welfare and production efficiency. However, such models are typically at best a theoretical abstraction and therefore they should be treated cautiously and certainly should not systematically be used as a benchmark for the level of competition that can realistically be implemented in practice.

  1 This will be familiar from introductory microeconomics texts as the “Marshallian” demand curve (Marshall 1890).

  2 This is called a quasi-linear demand function and gives the result because the first-order condition for good 1 collapses to

  which is the marginal utility of a monetary unit. That in turn is equal to one.

  3 This result is known as a “duality” result and is often taught in university courses as a purely theoretical equivalence result. For its very practical implications, see chapter 9

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  eBook - ePub

  Industrial Organization

  Theory and Practice

  • Don E. Waldman, Elizabeth J. Jensen(Authors)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  If Southwest charges a fare above MC = $70, American Airlines responds by charging a fare $1.00 less than Southwest’s fare, and the American Airlines reaction function lies at a distance $1.00 below the 45-degree line. By the same reasoning, Southwest’s reaction function lies at a distance $1.00 to the left of the 45-degree line. The Bertrand equilibrium is the Nash equilibrium at the intersection point ($70, $70).

  We can interpret the Bertrand model as a simultaneous move game. Both firms reason:

  If we set our fare at any p >MC, then our opponent will set its fare at p - ε, and we will sell nothing. But, if we set our fare at p = MC = $70, then we either capture the entire market or split the market 50–50. We should, therefore, set our fare equal to MC.

  Although the implications of the Cournot model seem plausible, the implications of the Bertrand model may at first seem a bit bizarre. In a Bertrand duopoly, price falls to MC, the perfectly competitive price, and there is allocative efficiency. We will not go through the formal analysis here, but this extreme result can be made much more reasonable by introducing some product differentiation into the Bertrand model, which we do in Chapter 10 .45 The introduction of product differentiation eliminates the highly implausible “all or nothing” nature of the model and results in an equilibrium price greater than marginal cost.

  The results of some experimental games support the Bertrand equilibrium. Fouraker and Siegel found that when student players selected prices rather than quantities and were given Bertrand-type profit payoffs, three-player games almost always resulted in the Bertrand outcome.46 The Bertrand result was also common with two players as long as the players did not have perfect price information about their competitor’s price.

  Some Empirical Examples of Bertrand Pricing

  Flath examined 70 four-digit Japanese industries using data from 1961 to 1990. He theorized three possible relationships between price-cost margins and the Herfindahl-Hirschman Index (HHI) each representing a different type of pricing model.47 If price-cost margins are proportional to the HHI this would indicate Cournot pricing. If price-cost margins remain constant in relation to variations in the HHI this would indicate Bertrand pricing. Finally, in Cournot industries where the firms supply both homogeneous and differentiated products, price cost-margins would vary linearly but not proportionally

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  eBook - ePub

  Managerial Economics

  A Strategic Approach

  • Robert Waschik, Tim Fisher, David Prentice(Authors)
  • 2010(Publication Date)
  • Routledge

    (Publisher)

  • When firms compete in prices, adding just one more firm to a market which was initially monopolized drives the market equilibrium to the perfectly competitive equilibrium, where both firms earn zero profits. This extreme result is known as the Bertrand paradox.

  • If the simple Bertrand model of price competition is extended to allow for product differentiation or capacity constraints, duopolists will generally earn positive profits in equilibrium when competing in prices.

  • The Stackelberg model describes a market where one firm can commit to the choice of a strategy before its competitor. When firms compete in quantities, the Stackelberg leader has a first-mover advantage and is able to increase profits and market share at the expense of its competitor.

  • Relative to the Cournot equilibrium when firms choose quantities simultaneously, the Stackelberg equilibrium is characterized by a lower equilibrium market price and a higher level of total market output.

  Notes

  1 This is often referred to as the Cournot model , after the pioneering work of the French economist Augustin Cournot from his 1838 text Researches into the Mathematical Principles of the Theory of Wealth .

  2 We want to restrict marginal cost c to lie between 0 and 120, else the equilibrium quantity could be negative.

  3 Notice that this graph shows the market equilibrium, so that the level of output q on the horizontal axis measures total output in the market, which is the sum of output of each firm. This is not the same as the information in Figures 6.2 to 6.4 , which showed each firm’s reaction function and allowed us to solve for each individual firm’s level of output.

  4 The label Bertrand equilibrium, and the concept of the Bertrand paradox, described later in this section, refer to the work of the French economist Joseph Bertrand (see Bertrand 1883).

  Exercises

  1 Consider a market where two firms are competing in quantities. Suppose that the market inverse demand function is given by:

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  eBook - ePub

  Strategic Investment

  Real Options and Games

  • Han Smit, Lenos Trigeorgis(Authors)
  • 2012(Publication Date)
  • Princeton University Press

    (Publisher)

  price competition, respectively. An interesting question is, When can one expect quantity or price competition? Cournot quantity competition more naturally arises in industries where firms set their investment and production decisions in advance and face higher cost for holding inventories. Firms first choose capacity (inflexible) and in a later stage choose production (quantity) to fill capacity. Here prices will adjust more quickly than quantities, with competitors expected to match any price change in order to meet their planned production, so price changes would not take business away from competitors. By contrast, Bertrand price competition pertains to markets where capacity is sufficiently flexible that firms can meet all demand at their chosen price. It is more applicable when firms’ products are homogeneous or undifferentiated, believing that they can take business away from competitors if they cut prices. In some cases, Cournot and Bertrand Competition may take place over different stages: competitors may choose capacities in the first stage, and then compete on price given the chosen capacities (resulting in a Cournot equilibrium in quantities). 6 A decision by a firm to set a high price has little risk or cost since if competition does not follow, it can revise its price back down. Moreover, the competitor can recognize that itself is better off in the long term to follow with the higher prices (even if the first period appears unprofitable). The above tit-for-tat strategy of matching the competitor’s price in the next period is robust, allowing the firm to do well in the long run; it is nice (never the first to defect), provocable (immediately punishing a defecting rival by matching its price next period), and forgiving (will go back to cooperative outcome if rival returns). In other cases firms may actually find it preferable to cooperate (e.g., by utilizing network investments) to increase the total value of growth opportunities in the industry

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