Abstract
We have seen in previous chapters how equilibrium price is substantially higher in monopoly than in perfectly competitive markets. In this chapter, we begin to investigate how price and output are determined in oligopoly markets that lie between these polar extremes. There are two types of oligopoly models, those that assume cooperative behavior and those that assume noncooperative behavior. In this chapter, we focus on cooperative settings or cooperative games. In the next two chapters we discuss noncooperative models.
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- 1.
It is sometimes called conscious parallelism, as firms make strategic moves in concert without being formal members of a cartel. Concert actions do not necessarily imply collusion, however, as competitive firms may behave in unison as well. For further discussion, see Scherer and Ross (1990, Chap. 9).
- 2.
- 3.
This problem is identical to that of a multiplant monopolist, except that 1 and 2 refer to production plants, not firms, in the multiplant monopoly problem.
- 4.
We can see this by considering a more general model, where the objective is to maximize Π = p(Q) · Q − TC1 − TC2 with respect to q 1 and q 2, where TC i is firm i’s total cost. The first-order conditions are
$$ \frac{{\partial \Pi }}{{\partial {q_1}}} = p + \frac{{\partial p}}{{\partial {q_1}}}Q - {\hbox{M}}{{\hbox{C}}_1} = 0, $$$$ \frac{{\partial \Pi }}{{\partial {q_2}}} = p + \frac{{\partial p}}{{\partial {q_2}}}Q - {\hbox{M}}{{\hbox{C}}_2} = 0, $$where MC i is firm i’s marginal cost. These conditions imply that the marginal revenue for the industry must equal marginal cost of production, whether produced by firm 1 or firm 2. Notice how the first-order condition for an individual firm that maximizes its own profit is different from the first equation above. For firm 1, the difference is that the second term within the equal signs in the first equation above would be multiplied by q 1 instead of Q. This means that when firm 1 considers increasing q 1, it pays attention to the effect that this has on the total revenue of the entire industry, rather than just its own total revenue, when it is a member of the cartel. Because ∂p/∂q 1 and Q > q 1, the firm’s marginal benefit of producing an additional unit of output is less under a cartel. Thus, each firm will produce less output in a cartel setting.
- 5.
This equation maps out a curve that is much like an indifference curve in consumer theory and an isoquant in production theory. For an isoprofit function, profit is held constant rather than utility (in an indifference curve) or firm production (in an isoquant). For a review of indifference curves and isoquants, see Bernheim and Whinston (2008), Pindyck and Rubenfield (2009), or Varian (2010).
- 6.
In a price war, each firm has an incentive to undercut the price of its competitor, which can lead to competitive pricing. We discuss the details of price undercutting in the next chapter.
- 7.
That is, when q 1 = 4 and q 2 = 3, firm 1’s profit equals (12 − q 1 − q 2)q 1 = 20 and firm 2’s profit equals (12 − q 1 − q 2)q 2 = 15.
- 8.
In the next chapter, we will see that this is a special type of Nash equilibrium, first investigated by Cournot (1838).
- 9.
In this case, firms play a game with antitrust authorities, which may cause them to limit price below the joint profit-maximizing level to avoid antitrust scrutiny.
- 10.
This is sometimes called a most-favored-nation clause (Salop 1986).
- 11.
Chen and Liu (2011) point out that there may be other reasons for implementing a most-favored-customer clause. In their study of electronics retailers, they found that Best Buy introduced such a clause in order to gain market share from its chief competitors.
- 12.
See Salop (1986) for more detailed discussion.
- 13.
Normally, firm i is assumed to revert to a Nash equilibrium price or output strategy once firm j cheats.
- 14.
The reason is that with homogeneous goods, all consumers will buy from the low-priced producer. Thus, that firm will sell approximately the monopoly output and its competitors will sell nothing. This is consistent with a Bertrand outcome, which we will discuss in Chap. 10.
- 15.
Note that when D is less than 1, the left-hand side of the inequality does not sum to infinity.
- 16.
- 17.
The notable exception is the study by Asch and Seneca (1975), which found that colluding firms earned lower profits than noncolluding firms. Their empirical model does not control for industry differences or other important determinants of profitability, however. Another potential concern is that cartels may form in less profitable industries.
- 18.
For a review of auction theory and a discussion of eBay auctions, see Hasker and Sickles (2010).
- 19.
Eckbo (1976) also finds that cartel success is more likely when demand is sufficiently inelastic. This implies few close substitutes for the cartelized product and a greater gain in profits when moving from a competitive to a cartel outcome.
- 20.
Alternatively, Rotemberg and Saloner (1986) argue that price cuts are more likely during boom periods, because the benefit from price cutting is greater during a boom.
- 21.
This discussion borrows from Adams and Mueller (1990) and Scherer (1996).
- 22.
These include Carnegie Steel, Federal Steel, American Steel and Wire, American Plate, American Steel Hoop, American Bridge Company, and Lake Superior Consolidated Iron Mines.
- 23.
United States v. United States Steel Corporation et al., 251 US 417 (1920). Although this behavior would be considered illegal today, the Supreme Court acquitted US Steel because the government challenged the monopoly status of the company (under Section 2 of the Sherman Act) rather than its collusive behavior (under Section 1). The government could not make a strong enough case that US Steel had monopolized the market because its market share had fallen from 65% to 52% from 1907 to 1915.
- 24.
- 25.
Ecuador, Gabon, and Indonesia also joined OPEC but later left.
- 26.
OPEC’s stated objective “is to co-ordinate and unify petroleum policies among Member Countries, in order to secure fair and stable prices for petroleum producers; an efficient, economic and regular supply of petroleum to consuming nations; and a fair return on capital to those investing in the industry.” Available at http://www.opec.org, accessed May 15, 2010.
- 27.
- 28.
To illustrate, consider a cartel that increases profits by $10 billion and has a probability of being successfully caught and convicted of 50%. In this case, the expected gain from forming a cartel is $10 billion minus 0.5 · f, where f is the amount of the fine. For the fine to successfully deter a cartel, the expected gain must be negative. For this to be true, f must exceed $20 billion.
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Tremblay, V.J., Tremblay, C.H. (2012). Cartels. In: New Perspectives on Industrial Organization. Springer Texts in Business and Economics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3241-8_9
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