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Intermediate Microtheory and Strategy |
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28 October 2003Market Structure II: Monopolistic Competition, Oligopoly, and Product DifferentiationIn this unit we shall evaluate some of the more common market structures in US and other contemporary economies, especially at the retail level. These models are more realistic, and thus somewhat more complex, than the polar-case models of competition and monopoly. The monopolistic competition model features free entry, many sellers, and product differentiation, while the oligopoly model features limited entry, few sellers, and may feature product differentiation. Thus if one were to focus on the subject of product differentiation, there are monopolistically competitive and oligopolistic models of product differentiation. Lecture Outline
Lecture NotesIntroduction to Monopolistic Competition, Oligopoly, and Product DifferentiationMonopolistic competition is a market structure that combines the features of a competitive market structure (many small buyers and sellers, similar costs, no significant entry/exit costs, no information costs) with product differentiation. Thus the monopolistic competition model is the model for situations in which there is competitive interaction and product differentiation. Monopolistic competition is usually conceptualized using the Representative consumer model: In this model, all firms compete equally for all consumers. This model is appropriate for particular segments of the restaurant industry, (for example, the Mexican food restaurant market or the pizzaria market) in which firms produce differentiated products but all compete for the same consumers (people wanting Mexican food or pizza). This may also be a useful model for understanding urban gasoline station markets, where different brand-name gasolines compete against one another for same the pool of consumers, or the urban grocery store market. Another good representative consumer model application would be the airline travel market. The representative consumer model is the standard version of the monopolistic competition model. As we shall see, in the representative consumer model the firms dissipate all rents in equilibrium, either through entry or through non-price competition. Oligopoly is a very broad class of models that feature:
Oligopolies are very common in many consumer products markets, such as automobiles, breakfast cereal, soft drinks, motion picture and filmed production and distribution, long-distance telecommunications, cigarettes, etc. High entry/exit costs can be generated in the form of rent-dissipating image advertising. Unlike any other class of market structure model, firms in a noncooperative oligopoly engage in strategic rivalry with one another. Strategic interaction is a key defining characteristic of noncooperative oligopoly models. Cooperative oligopoly models are models of collusion, which may be overt or tacit. Oligopolies may or may not feature product differentiation. The common homogeneous-product, noncooperative oligopoly models are Cournot, Bertrand, and von Stackelberg (leader-follower). Oligopoly models that feature product differentiation are usually referred to as product differentiation models, and are described below. Product differentiation can occur in a monopolistically competitive environment, or in more oligopolistic environments. Product differentiation is generally viewed in the context of noncooperative rivalry, though it is possible to have a cooperative, differentiated-product market structure. When we refer to product differentiation models, however, these refer to differentiated-product oligopoly models, which are perhaps the single most common market structure scenario in US retail markets. These models describe differentiaion spatially. Spatial or location model: In this model, each consumer prefers products that have certain characteristics. These may be geographical (i.e., one store is a lot closer than another), where firms' products are differentiated in geographical space, or these may be product-oriented (i.e., some people like blue corn tortilla chips while others like white or yellow), where firms' products are differentiated in product type space. The above example illustrates horizontal differentiation, meaning that people differ in their preference ranking for the goods in question. Alternatively (or simultaneously, if you are in to complexity), we can have vertical differentiation, in which people can generally agree on a preference ranking (i.e., a BMW is better than a Yugo). This work was first developed by Hotelling (1929) for geographical differentiation, but since then has been generalized by Lancaster (1966), Salop (1979), and others to include product-type differentiation as well. This is the standard product differentiation model. The Model of Monopolistic Competition and The Representative ConsumerIn this model we have the following set of assumptions:
Deriving the Monopolistically Competitive Equilibrium 1. A good starting point for the monopolistically competitive market is the situation in which there are a number of firms that are monopolizing their own individual market shares. DRAW STANDARD MONOPOLY MARKET 2. New entrants are drawn into the market over time. As entry occurs, the given market demand is divided amongst more and more firms, meaning that entry causes an incumbent firm's demand to shift inward, reducing profits. 3. Recall that we assume that firms here have essentially identical costs. Thus the process of entry ends when economic profit is zero, which, interestingly, occurs at the point where a firm's demand is tangent to its average total cost curve. DRAW NEW DIAGRAM Properties of the monopolistically competitive equilibrium:
Oligopoly ModelsLet's first focus on noncooperative models of oligopoly. In this class of model we have the following set of assumptions:
Cournot model: This is a very commonly used model of noncooperative oligopoly. While it features firms engaging in quantity rivalry, which seems less reasonable than direct price competition, the Cournot model yields outcomes in which there is an inverse relationship between market concentration and the extent to which market outcomes yield marginal cost pricing. Cournot oligopoly models can feature identical or differentiated products, identical or heterogeous costs, and a wide variety of numbers of firms. The most simple formulation is a duopoly with identical costs and products. Thus there will be two firms, firm 1 and firm 2. Lets derive the Cournot duopoly equilibrium: First lets assume a very simple linear inverse demand function P(Q) = a - bQ, where Q = q1 + q2. 1. profit functions:
2. best response functions (reaction functions):
Note that these best response functions tell us that the output of firm 1 is a function of the output that firm 1 thinks firm 2 is setting, thus q1(q2). Note that as q2 rises, firm 1's best response is to reduce its output at the rate of 1/2. Note with these best response functions that if the other firm sets its output equal to zero, the remaining firm will set its output equal to: [a-c]/2b which you should be able to demonstrate is equal to the profit maximizing output of a monopolist with profit function aQ - bQ² - cQ. 3. Cournot equilibrium: While Cournot understood the equilibrium consequences of his model, it was not until around 1950 that a man named Nash developed a game-theoretic solution concept now referred to as the Nash equilibrium. Thus the Cournot equilibrium is often times called the Cournot-Nash equilibrium. The key to the Nash equilibrium concept is the idea of a mutual best response equilibrium.. In other words, in a noncooperative market, equilibrium only can be said to occur if (1)firm 1 takes a best response to firm 2's act that (2) firm 2 correctly anticipated when it acted in the first place, and vice versa. Thus there is no motive for either firm to change its act, and the system is in equilibrium. Specifically, in the Cournot-Nash equilibrium each firm correctly anticipates the action taken by its rival when it reacts, because otherwise its wrong and must re-adapt, which thus does not satisfy the concept of an equilibrium. Thus to solve for the equilibrium we substitute firm 2's best response function for q2 in firm 1's best response function, and vise versa. If we do that, we get q1 = [a - c]/3b = q2 Thus market output in the Cournot equilibrium is 2[a - c]/3b, which falls right in between the monopoly equilibrium output level [a-c]/2b and the marginal-cost-pricing (competitive) output level [a-c]/b. DRAW THIS DIAGRAM FOR THE LINEAR DEMAND, CONSTANT MARGINAL COST CASE You can also demonstrate that as the number of Cournot rivals increases, the total market output moves closer and closer to the competitive. Thus price approaches marginal cost as the number Cournot rivals rises, implying a direct relationship between market structure and market performance. To see this, first we re-define market output to be a function of N identical Cournot rivals; P(Q) = P(Nqi), where i refers to a representative firm. Then we re-do the step-2 best response functions for the more general case: 2. best response functions (reaction functions), N-firm case:
So what does the final derivation tell us? First, the left-hand-side of the last equation above is referred to as the Lerner index, and it tells us the extent to which price exceeds marginal cost. Recall that in perfectly competitive market structures P = MC. Thus the Lerner index tells us the extent to which market performance deviates from the perfectly competitive benchmark. The smaller the Lerner index, the more competitive is the market structure. Now on the right hand side we have 1/nEd. As 'n', the number of Cournot rivals, rises, the Lerner index falls, indicating a linkage between market structure (number of rival Cournot oligopolists) and market performance. We can also evaluate a Cournot oligopoly market in which firms are heterogeneous in costs. While we won't derive that here (though you can experiment with it), the result is that 'low cost' Cournot firms have larger market shares than 'high cost' Cournot firms. You can see this in one of my own papers (Hackett, "Pollution-Controlling Innovation in Oligopolistic Industries: Some Comparisions Between Patent Races and Research Joint Ventures," Journal of Environmental Economics and Management,, November 1995). The Bertrand model of noncooperative oligopoly was developed because Bertrand (who was the first in a generation to pick up the Cournot work and actually understand its implications) criticized the Cournot idea of quantity rivalry, and instead argued that firms actually engage in price rivalry. If firms are identical, and if there are no binding capacity constraints, then the Bertrand noncooperative oligopoly model has the unsatisfactory result that even with only two firms, the equilibrium is P = MC. Price rivalry drives price downward as firms vie for market share. Minutely undercutting your rival's cost results in you getting the entire market for yourself, and this dynamic results in the 'competitive' outcome regardless of market structure. Obviously if products are differentiated, or if firms collude (cooperate), or if buyers are poorly informed of price, then the extreme Bertrand equilibrium result will not occur. Another common noncooperative oligopoly model was developed by von Stackelberg, and involves a dominant firm (the leader) and a competitive fringe (the followers). Basically the dominant firm knows how the fringe will react to its actions, and so can take action that tailors the anticipated fringe response to best suit the dominant firm's profitability. Cooperative OligopolyBasically here we have the theory and practice of cartels and tacit collusion. Cartels are most likely to form when there is a relatively small number of firms (making coordination and monitoring easier), difficult entry conditions (allowing price increases to be more durable), a trade association that can coordinate output market shares, monitor prices, and even allocate orders, and some credible form of punishment for cheaters. Thus to be successful, cartels must be able to raise price without inducing substantial increased competition from nonmembers. Moreover, expected punishment for forming a cartel must be low relative to the advantages. Finally, the cost of establishing and enforcing an agreement must be low relative to the expected gains. There have been many cartels throughout the history of the US. One prominent cartel involved the heavy electronics industry in the 1950s. The members were GE (42% mkt share), Westinghouse (38%), Allis-Chalmers (11%), and I-T-E (9%). Their arrangement was to rotate who the winning bidder would be for big Federal hydroelectric projects such as the Tennessee Valley Authority based on the above-mentioned, pre-determined market shares. They were caught by reporter Julian Granger of the Knoxville New-Sentinel on May 9, 1959. Granger discovered that on a recent government project up for bid, the winning bidder, Westinghouse, had bid $96,760, while Allis-Chalmers, GE, and I-T-E all bid exactly $112,712. Digging deeper, Granger found that on a conductor cable job, all the losing (high) bids came in at exactly $198,438.24. Obviously there was collusion among the heavy electronics manufacturers in which they were deciding who would be the winning bidder, and pre-determining exactly the amount by which all the high bids would come it at. In retrospect, given that bids on government contracts are public, this latter plan was a dumb idea. Eckbo (1976) studied 51 formal international cartels (where US antitrust law doesn't operate) in 18 industries over the period 1918 - 1964. Cartel success was defined by whether it was able to raise price to three times the level of the marginal cost of the high cost cartel member (a tough standard). Eckbo found that 19 of the 51 satisfied this requirement for success. Of these 19, one of them (the Iodine cartel) lasted 61 years; it required all sales to go through a central office in London (thus monitoring cheating). The other 18 lasted between 2 and 18 years, with the average being 6.6 years. Of the successful cartels, 3 broke down for nonmarket reasons such as government intervention or war. 7 had internal conflicts among cartel members, whereas 9 ended because of external forces, in particular competition from nonmembers or highly elastic demand. Factors that led to success were (i) the ability of the cartel to detect and prevent cheating by members, and (ii) the cartel faces a relatively inelastic demand. While economists have thought that collusion only really works among small numbers of individuals, Owen (1977) found that 75 percent of all realtors in California charged exactly a 6 percent commission on sales. In the 1940s and 50s the Natioanl Association of Realtors and local associations enforced an agreement requiring all members to sell at a fixed commission rate, and established entry barriers by only allowing members to access the Multiple Listing Service. From the 1920s to the 1960s commission rates rose from 2 percent up to 6 percent, indicating growing cartel power. From the 1960s to 1980 a series of private suits and Supreme Court decisions brought an end to the formal cartel agreements, leaving these associations open to treble damage claims for collusion. By the late 1970s the number of brokers and realtors rose from 150,000 to 400,000 in California alone (1 in 50 people in CA were in real estate!). When firms in an oligopoly coordinate their actions despite the lack of an explicit cartel agreement, we say that the resulting coordination is tacit collusion. Empirical evidence by Hay and Kelley (1974) indicates that collusion of all kinds is more likely in highly concentrated industries. 42% of the Department of Justice price-fixing cases Hay and Kelley studied involved industries in which the largest 4 firms (the 4-firm concentration ratio) had over a 75% combined market share. In another 34 percent of the cases, the 4-firm concentration ratio was between 51 and 75%. In contrast, only 6% of the cases involved industries with 4-firm CRs of 25 percent or less. Models of Product DifferentiationThe first, and perhaps most influential model, is that of Hotelling's Linear City model. This is a noncooperative oligopoly model of horizontal product differentiation. In its most simple form, here are the model assumptions:
The consumer at location 'x' (x is a location value between 0 and 1) is indifferent between these two firms is on the balance point -- all consumers to the left of her buy from firm A, and all consumers to the right of her buy from firm B:
Thus firm A gets x share of the N consumers, while firm B gets (1-x) share of the N consumers. We can thus derive firm A and B's demand curves:
Intuition: If Pb is higher than Pa, then firm A's market share exceeds a 50%; while if Pa exceeds Pb, then firm A's market share falls below 50%. At what rate does A's market share fall as Pa rises above Pb? At a rate of 1/2t, where (recall) t is the consumer's transportation cost. Thus the higher is the consumer's transportation cost, the smaller is the effect of price differentials in determining market shares. In other words, high transportation costs create "firm loyalty" that weakens the role of price differentials in determining market shares, and thus steepening the demand curves for individual firms and raising equilibrum prices. 1. To show this, first derive the two firm's profit functions:
2. Take the derivatives of these profit functions with respect to price:
3. Note that since 'c' (constant marginal cost) is identical for the two firms, we can solve these two equations simultaneously:
4. Finally, plugging in Pa = Pb into the step-2 equations, and then dividing across by the relevant 'P' yields:
Interpretation: Again, we show that the Lerner index of competition is directly related to 't', the travel cost for consumers that fully determines the extent of product differentiation in this very simple model. The higher is 't', the higher is price above marginal cost, and thus the higher is the value of the Lerner index, indicating that as 't' rises, the extent to which market performance matches the perfectly competitive benchmark declines. The Salop model of product differentiation is similar to the Hotelling model, except that it occurs in 'product type space' rather than 'geographical space', and has the innovation of occurring on the surface of a circle rather than along a fixed line segment (thus there are no 'ends' to product type space). The Salop model equilibrium is very similar to that of the Hotelling model: the stronger are individual preferences for a particular type of good (i.e., a blue rather than a red car, a sport/utility vehicle rather than a sedan), the greater is the value of the Lerner index (assuming that firms can monopolize a spot on product type space). Nonprice CompetitionThere are a number of reasons why we might see nonprice rather than direct price competition. One obvious reason would be when prices are exogenously fixed (fixed outside the control of the firms themselves) by way of price regulation. This was the case prior to the deregulation of the airline industry in the very early 1980s. With rates fixed by the CAB, airlines competed for customers by way of non-price factors such as:
We may also see nonprice competition in highly concentrated oligopolies in which a form of tacit collusion prevents direct price competition. Thus firms compete by way of image advertising and quality. The advantage of nonprice competition is that, while rivals will likely react to nonprice competition, their reaction is often times slower and less direct than would be the case for a price cut. Image advertising is a good example of nonprice competition. The optimal level of image advertising is simply that level that causes incremental profit to increase the most. Think of image advertising as increasing demand over what it would otherwise be. This increase may simply prevent loss of demand (market share) due to the advertising of others, or it may represent capture of new market share over and above existing levels. The marginal revenue (or marginal benefit) derived from advertising is the firm's marginal revenue from additional sales net of the marginal cost of producing those additional sales, meaning that the marginal benefit of advertising is the net marginal revenue (similar to profit contribution) from increased sales. The marginal cost of advertising is the amount of advertising expenditure required for a one-unit increase in demand (Q). Firms should increase advertising expenditures up to the point at which the marginal benefit = marginal cost. For example, suppose that the demand for a firm's differentiated product is given by: Q = 40,000 - 10P or, P = 4000 - .1Q The firm's total cost function is given by: TC = $500,000 + $60Q The firm's optimal (yearly) output occurs where MR = MC: 4000 - .2Q = 60, Q = 19,800 Profit = 4000(19,800) - .1(19,800)² - 500,000 - 60(19,800) = 116,900,000 The firm is considering the incremental plan of an advertising campaign that would cost $1,000,000 and is anticipated to increase sales by 50% over existing levels. To evaluate this, first determine what the projected post-advertising demand will be: Q(new) = 1.5(40,000 - 10P) = 60,000 - 15P or, P = 4000 - .06667Q The new optimal output occurs where 4000 - .1333Q = 60, Q = 29,700.75 Profit = 4000(29,700.75) - .1(29,700.75)² - 1,500,000 - 60(29,700.75) = 204,328,425.06. In this example it abundantly pays for the firm to price advertise. Empirically Defining Product Markets and Measuring Market StructureFirst consider how the Bureau of the Census defines product markets. An economic census is taken every 5 years, and the resulting data set is extensively used by economists in their empirical research. The census has created a classification system called the Standard Industrial Classifications of Economic Activity, more commonly referred to as SIC codes. SIC codes work as follows: We begin with the broadest definitions of industries, such as agriculture, mining, construction, manufacturig, transportation, wholesale and retail trade, finance, services, public administration, and other. These are are given 2-digit codes to distinguish them from one another. SEE TABLE 11.1 in the Hirschey/Pappas text Within a given 2-digit industry there are SIC codes distinguish different constituent industries up to a 7-digit level. SEE TABLE 11.2 in the Hirschey/Pappas text Perhaps the most important level of industrial classification is the 4-digit industry. SEE TABLE 11.3 in the Hirschey/Pappas text A common market share measure is the concentration ratio. Concentration ratios measure the market share held by the largest N firms, where N can be 2, 4, 8, etc. The most commonly used concentration ratio is C-4, meaning the market share held by the largest 4 firms in a SIC industry (again, often times a 4-digit SIC industry). Another way of measuring market structure that is used in antitrust cases by the Department of Justice and the Federal Trade Commission is the Herfindahl-Hirschman Index or HHI: HHI = s1² + s2² + s3² + ... + sn², where si is firm i's market share (in percentage terms), and 'n' denoting the set of n firms in the industry. Note that the HHI can range from 10,000 to approximately 0. Question: under what circumstances do we get a large HHI, and under what circumstances do we get a small HHI? The Department of Justice is responsible for evaluating whether or not to allow mergers between firms engaged in interstate commerce. The key issue is whether a merger of firms within a given industry will significantly impair competition. The Justice Dept has developed a set of merger guidelines that utilize the HHI:
Competitive Strategy in Monopolistic Competition and OligopolyA key element of competitive stategy is to create a competitive advantage, meaning a unique ability to create, distribute, or service products valued by customers. Except in rare circumstances, it usually pays to try to differentiate your products from those of your rivals. Doing so steepens the demand curve for the firm's product, thus reducing consumers' price sensitivity. This is called the principle of maximum differentiation. One of the few situations in which this principle does not hold is when a firm has pioneered a new market, in which case other firms may have an incentive to imitate the pioneer firm, at least initially.
All pages copyright Steve Hackett unless otherwise noted. |
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