Economics
Bertrand Competition
Bertrand competition is a market model where firms compete by setting prices for homogeneous goods. Named after economist Joseph Bertrand, this model assumes that firms choose prices rather than quantities, leading to a situation where prices are driven down to marginal cost. This can result in a "Bertrand paradox" where prices are driven to the lowest possible level.
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eBook - PDFAgents, Games, and Evolution
Strategies at Work and Play
- Steven Orla Kimbrough(Author)
- 2011(Publication Date)
- Chapman and Hall/CRC(Publisher)
Permission from Springer to republish this material is gratefully acknowledged. Chapter 11 Oligopoly: Bertrand Competition 11.1 Price Competition The Bertrand model models competition on the basis of price in an oligopoly. Each firm privately proposes a unit price for the goods on order and the lowest-price bid wins all of the business. What will the market price be? If there are very many firms in the market, it is easy to believe that the competitive price will prevail. The Bertrand model teaches us that this is also true in even the smallest oligopoly, consisting of just two firms. Here is a standard summary of the reasoning from a standard microeconomics text. If firm 1 really believes that firm 2 will charge a price ˆ p that is greater than the marginal cost, it will always pay firm 1 to cut its price to ˆ p − ε . But firm 2 can reason the same way! Thus any price higher than marginal cost cannot be an equilibrium; the only equilibrium is the competitive equilibrium. [322, page 488] In a different text (still standard) the same author makes the following remarks on the Bertrand result. It may seem somewhat paradoxical that we get price equal to marginal cost in a two-firm industry. Part of the problem is that the Bertrand game is a one-shot game: players choose their prices and then the game ends. This is typically not a standard practice in real-life markets. One way to think about the Bertrand model is that it is a model of competitive bidding. Each firm submits a sealed bid stating the price at which it will serve all customers; the bids are opened and the lowest bidder gets the customers. Viewed this way, the Bertrand result is not so paradoxical. [321, 293] Whether the one-shot result is paradoxical or not, we are interested in the iterated game, which is not addressed by the Bertrand model. The iterated game of price competition in an oligopoly is the subject of this chapter. 243
eBook - PDF- David Besanko, David Dranove, Mark Shanley, Scott Schaefer(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
If either firm lowers price, it will lose money on each unit sold. If either firm raises price, it would sell nothing. In Bertrand’s model with firms producing identical products, rivalry between two firms results in the perfectly competitive outcome. When firms’ products are differenti-ated, as in monopolistic competition, price competition is less intense. (Later in this chapter, we will examine Bertrand price competition when firms produce differentiated products.) Bertrand Competition can destabilize markets where firms must incur sunk costs to do business, because there is not enough variable profit to cover the sunk costs. If one firm should exit the market, the remaining firm could try to raise its price. But this might simply attract a new entrant that will wrest away some of the remaining firm’s business. Price competition may be limited if one or both firms runs up against a capacity constraint and cannot readily steal market share, or if the firms learn to stop competing on the basis of price. These ideas are covered in greater depth in Chapter 7. Why Are Cournot and Bertrand Different? The Cournot and Bertrand models make dramatically different predictions about the quantities, prices, and profits that will arise under oligopolistic competition. One way to reconcile the two models is to recognize that Cournot and Bertrand Competition may take place over different time frames. Cournot competitors can be thought of as choos-ing capacities and then competing as capacity-constrained price setters. The result of this “two-stage” competition (first choose capacities and then choose prices) is identical to the Cournot equilibrium in quantities. 18 More cutthroat Bertrand Competition results if the competitors are no longer constrained by their capacity choices, either because demand declines or a competitor miscalculates and adds too much capacity.
eBook - PDF- David Besanko, Ronald Braeutigam(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
The result of this “two-stage” competi- tion (first choose capacities and then choose prices) can be shown to be identical to the Cournot equilibrium in quantities. 15 In contrast, the Bertrand model can be thought of as short-run price competition when both firms have more than enough capacity to satisfy market demand at any price greater than or equal to marginal cost. Another difference between the Cournot and Bertrand models is that they make different assumptions about how a firm expects its rivals to react to its competitive moves. The Cournot firm takes its competitors’ outputs as given and assumes that its competitors will instantly match any price change the firm makes so that they can keep their sales volumes constant. This expectation might make sense in industries such as mining or chemical processing, in which firms typically can adjust their prices more quickly than their rates of production. Because a firm cannot expect to “steal” custom- ers from its rivals by lowering its price, Cournot competitors behave less aggressively than Bertrand competitors. Thus, the Cournot equilibrium outcome, while not the monopoly one, nevertheless results in positive profits and a price that exceeds mar- ginal cost. By contrast, a Bertrand competitor believes that it can lure customers from its rivals by small cuts in price, and it knows that it has sufficient production capacity to be able to satisfy this additional demand. These beliefs might make sense in a market such as the U.S. airline industry in the early 2000s, which had significant excess capac- ity. Many airlines at that time believed that they would fly their planes virtually empty unless they cut their prices below their competitors.
eBook - PDFContemporary Industrial Organization
A Quantitative Approach
- Lynne Pepall, Dan Richards, George Norman(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
It also makes clear that the deviation from such pricing depends on how much consumers value variety among products. The greater value that the typical consumer places on getting her most preferred version of the product, the higher prices will rise above marginal cost. The spatial model of price competition has provided a useful framework for empirical work. Many policy makers are interested in investigating how a change in market structure—through entry or mergers or regulatory policy–will affect price competition. Ultimately, the differences between Cournot and Bertrand Competition reflect underlying differ-ences between quantities and prices as strategic variables. The quantities chosen by Cournot firms are strategic substitutes—increases in one firm’s production lead to decreases in the rival’s output. In contrast, the prices chosen by Bertrand competitors are strategic complements. A rise in one firm’s price permits its rival to raise price, too. Our analysis of both quantity and price competition has been set in a static framework in which the market structure is taken as given. However, as we noted at the start of this book, the reality is that market structure is endogenous. Strategies that generate above normal profits for existing firms will induce new firms to enter over time. At the same time, incumbent firms may be able to take actions that deter such entry. In the following chapters, we extend our analysis to examine these issues. Problems 1. Harrison and Tyler are two students who met by chance the last day of exams before the end of the spring semester and the beginning of summer. Fortunately, they liked each other very much. Unfortunately, they forgot to exchange addresses. Fortunately, each remembers that they spoke of attending a campus party that night. Unfortunately, there are two such parties. One party is small. If each attends this party, they will certainly meet.
eBook - PDFIndustrial Organization
Contemporary Theory and Empirical Applications
- Lynne Pepall, Dan Richards, George Norman(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
It also makes clear that the devi- ation from such pricing depends on how much consumers value variety. The greater value that the typical consumer places on getting his or her most preferred brand or version of the product, the higher prices will rise above marginal cost. Ultimately, the differences between Cournot and Bertrand Competition reflect underlying differences between quantities and prices as strategic variables. The quantities chosen by Cournot firms are strategic substitutes— increases in one firm’s production lead to decreases in the rival’s output. In contrast, the prices chosen by Bertrand competitors are strate- gic complements. A rise in one firm’s price permits its rival to raise price, too. To be accurate, analysis of any industry requires familiarity with those industry features that determine whether the competitive rivalry is played out in a setting of strategic substitutes or strategic complements. Models of price competition based on con- sumer preferences and perceived quality have provided an extremely useful framework for aca- demicians and policy makers alike. It is important in this regard to identify the precise mechanism in which consumers’ preferences for specific brands and designs are modeled. For instance, depend- ing on the nature of consumer preferences, a merger between a high-quality and a low-quality firm that results in the transformation of the low- quality firm outlets to high-quality ones could either weaken competition because it removes a low-quality competitor or intensify competition because it adds to the high-quality supply. In the case of retail gasoline markets in Southern California, work by Hastings (2004) finds that a merger leading to removal of a low-quality firm raised prices, although subsequent work by Tay- lor, Kreisle, and Zimmerman (2010) offers some contrasting evidence. Problems 1. Suppose firm 1 and firm 2 each produce the same product and face a market demand curve described by Q = 5000 − 200P .
eBook - PDFMicroeconomic Foundations II
Imperfect Competition, Information, and Strategic Interaction
- David M. Kreps(Author)
- 2023(Publication Date)
- Princeton University Press(Publisher)
18.4. Differentiated Goods The discontinuity in demand that is present in Bertrand Competition is, of course, unrealistic. If one supplier of a good charges a few cents less than another supplier, do we really believe that all customers will abandon the second for the first? For a variety of reasons, while the good in question may have appearance of a commodity, there may be (even) slight differences in the good that lead some demand at supplier 2, even if her price is a bit greater than the price quoted by supplier 1. One simple way to investigate how this might work (and to compare Bertrand Competition with Cournot competition) is to write down “differentiated” demand functions. In a linear model, we have D n (p n , p ¬n ) = A n − a n p n + b n p ¬n ; n = 1, 2, (18.2) 26 Chapter Eighteen: Cournot and Bertrand where we assume that the A n and a n are positive. The sign of b n depends on the relationship between the two goods: If b 1 is positive, then a rise in the price of good 2 increases demand for good 1; roughly speaking, good 1 is a substitute for good 2. Negative b n , in contrast, would be the case where the goods are complements. Suppose the two duopolists have linear total-cost functions, with marginal costs k n . With this simple linear-demand-constant-marginal-cost parameterization, each duopolist’s problem is maximization of a concave objective function, so the first- order conditions for optimality (the optimal response of duopolist n to the price set by ¬n ) are sufficient for the unique optimal response: p ∗ n (p ¬n ) := A n + b n p −n + a n k n 2a n . And the unique Bertrand-Nash equilibrium is the profile ( ˆ p 1 , ˆ p 2 ) for which p ∗ n ( ˆ p ¬n ) = ˆ p n for n = 1, 2. To simplify the algebra, let C n = A n + a n k n ; then the solution of these two simultaneous linear equations is p n = 2a ¬n C n + b n C ¬n 4a n a ¬n − b n b ¬n .
- Roberto Serrano, Allan M. Feldman(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
Since we cannot use standard calculus techniques, we must reason along more abstract lines. Recall our definition of a Cournot equilibrium from Section 13.2 above. In a model where the two duopolists are reacting to each other by setting quantities, 13.6 Bertrand Competition 249 a Cournot equilibrium is a pair of output levels y ∗ 1 and y ∗ 2 that are consistent, in the sense that each firm i is maximizing its profit at y ∗ i , subject to what the other firm j has chosen, y ∗ j . Let us now define an equilibrium in a similar way, but for the current model where the two duopolists are reacting to each other by setting prices. A Bertrand equilibrium is a pair of prices p ∗ 1 and p ∗ 2 that are consistent, in the sense that each firm i is maximizing its profit with the choice of p ∗ i , subject to what the other firm j has chosen, p ∗ j . What can we say about a Bertrand equilibrium in the homogeneous goods case? Let ( p ∗ 1 , p ∗ 2 ) represent the equilibrium prices and ( y ∗ 1 , y ∗ 2 ) the corresponding equilibrium quantities. Here’s what we can conclude: (1) The firms must be charging the same price. That is, p ∗ 1 = p ∗ 2 = p ∗ . Suppose to the contrary that they are charging different prices, and without loss of generality, assume p ∗ 1 < p ∗ 2 . Then firm 1 is selling a positive quantity of the good, and firm 2 is selling nothing. (a) If p ∗ 1 < MC , then firm 1 has negative profits and would be better off shutting down. So this cannot be an equilibrium. (b) If p ∗ 1 = MC , firm 1 is making $0 on each unit it produces and sells. It could increase its price somewhat, while keeping it below p ∗ 2 , and make positive amounts on all the units it sells. (It would sell fewer units, but it would make money on each one.) So this cannot be an equilibrium. (c) If p ∗ 1 > MC , firm 1 is making positive profits on all the units it produces and sells.
eBook - PDFMicroeconomic Theory
Basic Principles and Extensions
- Walter Nicholson, Christopher Snyder(Authors)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
We will be somewhat loose with this definition, avoiding precise thresholds for how high the cross-price elasticity must be between goods within the group (and how low with outside goods). Arguments about which goods should be included in a product group often dominate antitrust proceedings, and we will try to avoid this contention here. 15.5.2 Bertrand Competition with differentiated products Return to the Bertrand model but now suppose there are n firms that simultaneously choose prices p i 1 i 5 1, . . . , n 2 for their differentiated products. Product i has its own spe-cific attributes a i , possibly reflecting special options, quality, brand advertising, or location. A product may be endowed with the attribute (orange juice is by definition made from oranges and cranberry juice from cranberries), or the attribute may be the result of the firm’s choice and spending level (the orange juice supplier can spend more and make its juice from fresh oranges rather than from frozen concentrate). The various attributes serve to differentiate the products. Firm i ’s demand is q i 1 p i , P 2 i , a i , A 2 i 2 , (15.24) where P 2 i is a list of all other firms’ prices besides i ’s, and A 2 i is a list of all other firms’ attri-butes besides i ’s. Firm i ’s total cost is C i 1 q i , a i 2 (15.25) and profit is thus π i 5 p i q i 2 C i 1 q i , a i 2 . (15.26) With differentiated products, the profit function (Equation 15.26) is differentiable, so we do not need to solve for the Nash equilibrium on a case-by-case basis as we did in the Bertrand model with identical products. We can solve for the Nash equilibrium as in the Cournot model, solving for best-response functions by taking each firm’s first-order con-dition (here with respect to price rather than quantity). The first-order condition from Equation 15.26 with respect to p i is ∂π i ∂ p i 5 q i 1 p i ∂ q i ∂ p i 2 ∂ C i ∂ q i # ∂ q i ∂ p i 5 0 .
- Walter Nicholson, Christopher Snyder(Authors)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
Bertrand’s scathing review of Cournot’s approach of applying mathematics to economics (J. Bertrand, “The’orie Mathematique de la Richess Sociale,” Journal de Savants [1883]: 499–508) was mistakenly credited with proposing the price-competition model by later authors, but the name stuck. Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 390 PART 6 ● Market Power would earn no profit, would make positive sales and profit by lowering its price to undercut the other. If the above-marginal-cost prices were equal, either firm would have an incentive to deviate. By under-cutting the price ever so slightly, price would hardly fall but sales would essentially double because the firm would no longer need to split sales with the other. A Nash equilibrium cannot involve a price less than marginal cost either because the low-price firm would earn negative profit and could gain by deviating to a higher price. For example, it could deviate by raising price to marginal cost, which, since it also equals average cost, would guarantee the firm zero, rather than negative, profit. 13-2f Bertrand Paradox The Nash equilibrium of the Bertrand model is the same as the perfectly competitive out-come. Price is set to marginal cost, and firms earn zero profit. The result that the Nash equilibrium in the Bertrand model is the same as in perfect competition even though there are only two firms in the market is called the Bertrand Paradox. It is paradoxical that competition would be so tough with as few as two firms in the market.
eBook - PDFPrinciples of Pricing
An Analytical Approach
- Rakesh V. Vohra, Lakshman Krishnamurthi(Authors)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
SEVEN Pricing and Competition The goal of this chapter is to convey the main principles of pricing in competitive environments. We approach them through a series of of thought experiments. The advantage of these experiments is that every variable within them can be controlled. This allows one to precisely isolate how each aspect of the competitive environment affects prices. The result will be a clearer and deeper understanding of pricing in competitive environments than any collection of anecdotes or string of ‘just so’ stories is able to deliver. To apply the lessons of this chapter, one must know some basic facts about the industry one is in – specifically, entry costs, exit costs, structure of demand, number, concentration and the distribution of rivals’ sizes. 7.1 The Pricing Dilemma Imagine two firms selling identical widgets to a market of 100 individuals. Each buyer is interested in purchasing at most one widget, and the RP of each buyer is $3. Each buyer will buy from the seller that offers them the largest surplus. Because the products are identical (in the eyes of each buyer), each buyer will purchase from the lowest-priced seller. In the event that both firms set equal prices (and so yield the same surplus to all buyers), the buyers divide equally between the two firms. 1 The production cost for each firm is $1 a widget. Production is instan- taneous and defect-free, so neither firm needs to worry about inventory, returns, and the other complications of real life. Production capacity is unlimited for both firms. 1 The situation just described is sometimes called the Bertrand model of competition. The name is in honor of the French mathematician, Joseph Bertrand (1822–1900). 159 160 Pricing and Competition Both firms and the 100 buyers exist for exactly one day. The firms must choose prices at which they will sell widgets simultaneously and indepen- dently of each other at the start of the day.
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