Quantitative Techniques for Competition and Antitrust Analysis_2 pptx

4.1. Basic Concepts in Market Definition 163 heavily constrained—it cannot raise the price beyond the point where too many con- sumers would switch. Intuitively, we will argue that if this constraint is large enough to impose a significant restriction on the electricity producer’s ability to increase prices, then the market should be defined as the energy market (electricity plus gas or coal) and inthis wider market the electricitymonopolist will have little market power. In the paragraph above we have drawn a clear distinction between a world where very few consumers would switch following a price rise and a world where many consumers would switch following a price rise. In practice, of course, the world is often far less black and white and as a result we may ask how much price sensitivity is enough to define a narrow market? When does the ability to differentiate turn into market power? When is substitution “large enough”? How much substitution exactly does one need between two products to put them in the same market? Nat- urally, theory provides only very partial answers to such questions and as a result practitioners commonly use quantitative benchmarks that are generally accepted and which ensure some consistency in the decision-making process. For example, in much of the discussion that follows, we will consider whether price increases of 5% or 10% are profitable when defining markets. Even then it is important to note that market definition in practice often requires the exercise of evidence-based judgment, where the evidence can be of varying quality. 4.1.2 Supply and Demand Substitutability The key factors that limit market power—the ability to raise prices above the com- petitive level—are the extent of demand substitutability and the extent and nature of supply reaction, in particular, of supply substitutability. We describe each of these concepts below since any market definition exercise will examine each of them in detail. We also describe the fact that a market definition exercise usually proceeds along two dimensions: (1) a product market definition dimension and (2) a geo- graphical market definition dimension. Product and geographic market definition should, in principle, be considered together. However, it is common practice as a practical matter to examine first product market substitution on the demand and supply sides and then to go on to consider geographic market substitution, again on the demand and supply sides. In each case, the market definition process usually begins with a single candidate product, or occasionally with a collection of them. Demand substitutability describes the extent to which buyers respond to a price increase by substituting away to alternative products (product market definition) or alternative locations (geographic market definition). For example, if the price of gold goes up, then consumers may switch their consumption by buying less gold and perhaps more silver. If, when a firm attempts to increase its price, “enough” of her customers switch to substitute goods, then clearly her ability to raise prices is severely constrained. We want to include substitute products in our competition policy market whenever “enough” buyers, in a sense that will be made more precise 164 4. Market Definition below, would switch in response to a price increase. Of course, goods to which consumers do not switch in response to a price increase should be excluded from the market. Geographic market definition on the demand side considers the extent to which increasing a price in one area would induce consumers to purchase from alternative localities. There are numerous difficulties (and therefore fascinations) in such an apparently simple activity as evaluating demand substitutability. One common difficulty faced in practice is that sometimes there are simply no real potential close “substitute” products, or, alternatively, sometimes there are a very large number of them. 3 In the absence of identifiable discrete potential substitutes, a competition authority may capture demand substitution away to a diffuse set of alternatives by ignoring the substitution during the market definition phase of an investigation. In doing so, we must be sure to take proper account of it later during the competitive assessment phase of the investigation. This approach can lead to a relatively narrow market definition, but it does not mean the agency will find competition problems since even a monopolist can face a highly elastic demand curve and therefore have no ability to raise prices. Specifically, that will be the case when attempts to do so would be met by substitution of expenditure to other activities, even if they are only specified generically as an “outside” alternative. Supplier substitutability describes suppliers’ responses to an increase in a prod- uct’s price. When prices increase, consumers respond but so may rival suppliers since with higher prices available they have greater incentives to produce output. For example, in the market for liquid egg products 4 (such as those used for producing omelettes), the equipment used for processing and putting the product into cartons can also be used to produce cartons of fruit smoothies. That fact means that if the price of liquid egg went up sufficiently, suppliers of smoothies may potentially sub- stitute their production capacity to produce processed egg. Another example might involve red and yellow paint—if it is easy to switch machines from producing red paint to producing yellow paint, the returns to producing these two products can never be far apart. If yellow paint producers were more profitable than red paint producers, then we would soon enough induce some of the red paint producers to switch to producing yellow paint. As with all apparently simple concepts, there are numerous questions about ex- actly what is meant by supply substitutability. For example, the current Commission 3 An example of the latter includes the U.K. CC’s investigation into a “soft” gambling product known as the “Football Pools.” That inquiry received evidence from a survey of consumers who had recently stopped playing the Football Pools about their reasons for doing so. The survey found that 65% of lapsed customers had not switched expenditure to any kind of gambling product, while they had saved the money for a large variety of alternative uses, most of which were not obviously best considered as potential substitutes (see www.competition-commission.org.uk/inquiries/ref2007/sportech/index.htm). 4 See, for example, the discussion of the liquid egg market in Stonegate Farmers Ltd/Deans Foods Group Ltd (www.competition-commission.org.uk/inquiries/ref2006/stonegate/index.htm). 4.1. Basic Concepts in Market Definition 165 Notice on Market Definition 5 does not require a case officer to consider potential entrants as a source of supply substitutability for market definition purposes, though such entry might easily be considered in a more general sense a source of supply substitutability. Rather, the guidelines suggest that it is better to leave the analysis of the constraints imposed by potential competition to a later phase of the investigation. The rationale is that, among other things, the effects of entry are unlikely to be immediate. Still, economic theory says that, in some limited circumstances, even potential entrants may impose a price constraint on existing market players (see Baumol et al. 1982; Bailey 1981). This happens, for example, when incumbent’s prices are hard to adjust and potential entrants interpret current prices as being the prices for the post-entry situation. In this case, the incumbent needs to maintain a pre-entry price that is low enough to discourage entry. Thus, important judgements are often made around supply substitutability both in individual cases and in the guidance documents from various jurisdictions. To return to our earlier examples, one response to the red and yellow paint example might be to argue that supply substitution implies that the appropriate market definition involves one market for “paint.” Such an argument can be compelling, but there are significant limits to the appropriate scope of this type of argument for market definition. To see why, let us turn to the liquidegg and smoothie example. In thatcase, raw supply-side logicmight suggest a market definition would include both liquid egg and smoothies. However, such a conclusion appears to bean odd onesince these are patently different products. In fact, agencies would probably take the view that the appropriate responsewould be to view the potential movement of packaging and processing equipment as a supply response within the market for liquid egg. After all, the constraint arises on the liquid egg producers because machine capacity is moved across to produce liquid eggs and not because liquid eggs and smoothies are really competing, although the firms producing them may well be. The draft 2009 U.K. merger guidelines, for example, follow the U.S. guidelines in using this logic to suggest that demand substitution should play the primary role in defining the market while supply substitutability may tell us about the identity and scale of, in particular, potential competitors within that market. Thus the market would be for liquid egg, but the set of potential competitors may involve liquid egg and (formerly) smoothie producers. Finally, we note that the responses by rivals can be to enter or expand production following a price rise but theory suggests the response may also be to increase prices since prices are strategic complements. While quantity reactions by rivals may decrease the profitability of attempted price increases, price reactions by rivals to price increases may reinforce their profitability. It would appear to be an odd market definition practice that treated price and quantity responses asymmetrically irrespective of the context. Thus, practice has evolved to recognize the potential role of supply substitution but also to recognize that its role is limited for market 5 Commission Notice on Market Definition, OJ C 372 9/12/1997. 166 4. Market Definition definition. (See also the EU Notice on the Definition of the Relevant Market for the Purposes of Community Competition Law, which similarly significantly constrains the role of supply substitutability in market definition.) 4.1.3 Qualitative Assessment Before we progress to consider quantitative approaches to market definition, it is worth emphasizing that much of the time market definition relies at least in part on qualitative assessment. Indeed, qualitative evaluation is universally the starting point of any market definition exercise. Clearly,for example, it isprobably not necessary to do any formal market analysis to get to the conclusion that the price of ice cream will not be sensitive to the price for hammers. Indeed, if such qualitative assessments were not possible, it would be necessary to do a huge amount of work in every investigation to check out every possibility—an impossibility at current resource levels in most authorities. In practice, we can narrow down the set of possibilities to those which are plausible and also substantive. Very minor products, for example, may just not make a great difference to a competition evaluation. To do so, it is best to start with the product characteristics and the intended use(s) of the product. Doing so allows the investigator to define a broad and yet plausible set of possible demand substitutes. The products which are substitutes in use are sometimes known as the set of “functional” substitutes. For our purposes the concept of market definition is designed primarily to describe the set of products which constrain a firm’s pricing decisions. Thus, to be included in a market, it is not enough for products to be functional substitutes; they need to be good enough demand or (to the extent appropriate) supply substitutes to actu- ally constrain each other’s price. To illustrate the distinction, consider two differ- ent seafoods: smoked salmon and caviar. Both will be familiar items at least in terms of existence, even if the latter is not a regular feature of most of our dinner tables. Caviar is potentially a functional substitute for smoked salmon in that it could be served as part of a salad. Would that suffice to put smoked salmon into a broader market that includes caviar? To answer that question we must first con- sider the extent of demand substitutability at competitive prices, which for present purposes we can take as current prices. At the moment, the retail price of 100 g of smoked salmon in Europe can oscillate around €1.50–2.00. The price of 100 g of caviar can run into hundreds of euros. Intuitively, since the price of the smoked salmon is far below the price of caviar, those customers who consider the two to be close substitutes will be eating smoked salmon in their salads. Similarly, those who do not really like caviar will be eating smoked salmon while only those with a particularly intense taste for caviar will be prepared to pay such a large premium for it. 6 On the other hand, many of the consumers of smoked salmon 6 The reader will, of course, have picked up that we should probably worry about whether the fact that salmon and caviar need not be consumed in equal quantities is important. To aid discussion we will put 4.1. Basic Concepts in Market Definition 167 may like caviar and consider it to be a perfectly acceptable functional substitute at least in some uses (e.g., pre-dinner canapes), but would not actually substitute at current price levels. The lesson is that in a world with only those two products, salmon would be considered a market in itself at current price levels, despite the fact that caviar is indeed a functional substitute in many applications for current customers of salmon. Note that the force in this argument relies on the current price differential driving the set of current consumers of salmon to include those con- sumers for whom caviar may be a perfectly good functional substitute but caviar is so expensive that it is not a demand substitute. Since the extent of demand sub- stitutability between goods depends on their relative price levels, if prices were different, then the appropriate competition policy market definition could also be different. While such intuitive and unstructured arguments can be helpful, both formal and informal market definition exercises typically use the hypothetical monopolist test (HMT; see section 4.5 below for an extensive discussion) as a helpful framework for structuring decision making. The HMT test suggests that markets should be defined as the smallest set of products which can profitably be monopolized. The basic idea is that firms/products outside such a market cannot be significantly constrain- ing behavior of firms inside the market since they cannot constrain a hypothetical monopolist of all the products in the market. Usually, the HMT is described in terms of price, so we ask whether the hypothetical monopolist would be able to exploit a material degree of market power, that is, to raise the prices of goods inside the can- didate market by a small but significant amount. Of course, since firms can compete in quality, service, quantity, or even innovation, in principle the test can be framed using any of these competitive variables. Qualitative analysis can sometimes be enough to satisfactorily define the relevant market, indeed it is sometimes necessary to rely on purely qualitative analysis. That said, a more explicitly quantitative analysis of market data will often be very helpful for informing and supplementing our judgments in this area. 4.1.4 Supplementing Qualitative Evidence We will explore in detail a whole array of quantitative techniques for market defi- nition in the rest of this chapter. Before we do so, however, it is worth noting that an important element of the qualitative assessment typically involves an evaluation of the extent to which consumers view products as functional substitutes. While a qualitative assessment of (1) the various product characteristics of goods and (2) the uses to which consumers put the goods is usually helpful and sometimes all that is available, it is often possible to supplement such qualitative evidence with more quantitative evidence. this issue to one side. The key question will remain whether enough consumers will substitute enough volume from salmon to caviar to make increases in the price of salmon unprofitable. 168 4. Market Definition Table 4.1. Characteristics of London airports. Public Airport denomination Distance transport on Ryanair website; to center Private ‚ …„ ƒ bus service to of city car Bus Rail city promoted on Airports (km) (min) (min) (min) Ryanair website Stansted 59 85 75 45 London (Stansted); Ryanair bus service Heathrow 28 65 65 55 Not served by Ryanair Gatwick 46 85 90 60 London (Gatwick) Luton 54 44 60 25 London (Luton); Ryanair bus service London City 14 20 — 22 Not served by Ryanair Source: Ryanair and Aer Lingus proposed concentration, Case no. COMP/M.4439, p. 33. To illustrate, consider the evidence provided to the European Commission in its investigation of the proposed merger between Ryanair and Aer Lingus. 7 Ryanair argued that the London airports were not demand substitutes, at least for time- sensitive passengers. Consider table 4.1, which documents the time taken by various transport modes to each London airport from the center of the city, which brings some data to bear on the question of whether these airports are “too different” to be considered functional substitutes for customers who want to go from London to Dublin. Ryanair argued they were, while the Commission noted, among other things, that the U.K. Civil Aviation Authority considers that a “two-hour surface access time” is the relevant benchmark for airport catchment areas for leisure passengers. The Commission concluded that scheduled point-to-point passenger air transport services between Dublin and London Heathrow, Gatwick, Stansted, Luton, and City airports belong to the same market. Note that although the Commission has quantified an important set of characteristics of the potentially substitute products in a manner that helps it understand the extent of substitutability, it must ultimately make a judgment about whether these products are similar enough to be considered in the same market on the basis of this and other evidence. Analysis of consumers’ tastes can also help inform the question of substitutability. Continuing our discussion of the Ryanair andAer Linguscase, consider, forexample, the survey of passengers at Dublin airport that the Commission undertook. A sample of consumers at Dublin airport were asked: “Would you ever consider [a] flight to/from Belfast as an alternative to using Dublin airport?” The results are presented in table 4.2 and suggest that only 15–20% (the survey result is stated as 16.6% but taking the decimal places seriously would probably involve an optimistic view about 7 Case no. COMP/M.4439,which is availableat http://ec.europa.eu/comm/competition/mergers/cases/ decisions/m4439 20070627 20610 en.pdf. 4.2. Price Level Differences and Price Correlations 169 Table 4.2. Responses of passengers on airport use in Belfast. Valid Cumulative Valid Frequency Percent percent percent Yes 445 16.6 16.6 16.6 No 1,751 65.5 65.5 82.1 Do not know 388 14.5 14.5 96.6 No answer 90 3.4 3.4 100.0 Total: 2,674 100.0 100.0 — Source: Ryanair and Aer Lingus proposed concentration, Case no. COMP/M.4439, page 365. the right level of precision) of passengers view Belfast as a functional substitute for Dublin airport. A pure functional substitute question is quite hard to ask consumers since it may be outside their area of experience but the “ever consider” element of this question appears to make it quite powerful evidence, at least within a range of conditions not too dissimilarfrom those known to consumers (e.g., price differentials that are within most customers’ experience). 8 We will consider further the use of survey evidence later in the chapter. In the next section we examine the use of price information for market definition. Prices can be thought of as one way in which products will be “similar” or “different” in the eyes of consumers and the competition policy world has traditionally emphasized its importance. In doing so, it is important to note that firms do not always compete on price—they may compete in advertising, service, product quality, quantity, or indeed innovation. If so, then it may be important to analyze markets in those terms rather than price alone. A merger, for example, that leads to no increase in prices but a substantial lessening of service provision can potentially be even less desirable than a merger which leads to price increases. 9 4.2 Price Level Differences and Price Correlations Examining price differences and correlations is perhaps the most common empiri- cal method used to establish the set of products to be included in a product market. 8 It is important to note that such a general and inclusive survey question such as “ever consider” is very useful as evidence when the vast majority of replies are “no.” It is, however, distinctly less helpful for market definition when the vast majority of replies are “yes” since we simply would not know whether “ever consider” implied a significant constraint or it is just that, faced with an interviewer, customers could just about imagine situations where they could conceivably use Belfast instead of Dublin airport. 9 In terms of the welfare analysis of mergers, inward demand shifts caused by service or quality falls will sometimes result in far larger consumer (and/or total) welfare losses than the movement along a demand curve that occurs when prices rise. Deadweight loss triangles, in particular, are sometimes estimated to be small; see the chapter 2 discussion of the classic cross-industry study by Harberger (1954). 170 4. Market Definition Because correlations require only a small amount of data and are very simple to calculate, they are very commonly presented as empirical evidence in market def- inition exercises. Correlation analysis rests on the very intuitive assumption that the prices of goods that are substitutes should move together, an assumption we shall examine in this section. Despite the simplicity of this proposition, applying correlation analysis is not always straightforward and like any diagnostic tool can be extremely dangerous if applied with insufficient thought to the dangers of false con- clusions. In this section, we present the rationale for the use of correlation analysis in market definition and discuss the considerations vital to applying this methodology usefully. 4.2.1 The Law of One Price The “law of one price” states that active sellers of identical goods must sell them at identical prices. If one seller lowers price, it will get all the demand and the others will sell nothing. If a seller increases price above a rival, she will sell nothing. Since only the firm with the lowest price sells, the equilibrium result is that all active firms sell at the same price and share the customers. Formally, if goods 1 and 2 are perfect substitutes, the demand schedule of firm 1 is D 1 .p 1 ;p 2 / D 8 ˆ ˆ < ˆ ˆ : 0 if p 1 >p 2 ; D.p 1 / if p 1 <p 2 ; 1 2 D.p 1 / if p 1 D p 2 ; where the latter piece of the demand schedule defines the sharing rule; in this case it describes that if prices are equal then demand will be divided equally between the two players. Even in the case when goods are located in different places and consumers con- sider the price of “delivered” goods, the generalized law of one price suggests that prices of perfect substitutes will converge to differ only by the difference in transportation costs whenever arbitrage opportunities are exploited. Arbitrageurs are market participants that take advantage of price differentials that allow them to make money by buying wherever a good is relatively cheap and selling where it is relatively expensive. The existence of arbitrageurs both tends to force prices in two locations together and tends to induce a great deal of relative price sensitivity. One should always look for evidence of such arbitrage activities since they can be a strong indication of the bonds between apparently geographically disparate markets. For instance, prices of unregulated commodities or currencies on the world market are kept relatively homogeneous (absent the transport costs) by the presence of active arbitrageurs. The law of one price applies only to goods which are perfect substitutes, at least once transported to the same location. Of course, most goods are not perfect sub- stitutes but may nonetheless be close enough substitutes to ensure that demand 4.2. Price Level Differences and Price Correlations 171 schedules and hence prices are closely interrelated. The intuition from the law of one price is that similarities in the levels of prices can indicate that goods are close substitutes. Taking this idea one step further, price correlation analysis is based on the idea that prices of close substitutes will move together. We will develop this idea using a formal economic model below, but intuitively it means that we expect prices of substitute goods to move together across time or across regions. Thus, both similarity in the level of prices and also co-movement of prices may be helpful when attempting to understand the extent of substitutability between goods. 4.2.2 Examples of Price Correlation Price correlation analysis involves comparing two price series. The comparison could be across time, in which case we compare the time series of the products’ prices. But it could also be a comparison across space, in which case we compare a cross-sectional sample of both products’ prices. 4.2.2.1 Nestl´e–Perrier In the Nestl´e–Perrier merger, a key question became whether the relevant market was the market for still water, the market for water, or the market for nonalcoholic drinks. Price correlations were calculated between brands in the different categories and produced the results shown in table 4.3. The brands are labeled from A to I. The table reports correlations between prices of goods of individual brands of still water (A–C), sparkling water (D–F), and soft drinks (G–I). From the results, it appears fairly clear that this evidence suggests that the relevant market is the market for water, including bothstill and sparkling waters but excluding soft drinks. The price correlation between brands of still water and sparkling water is of similar magnitude as the correlation of brands within the group of still waters, at around 0.9. This is clearly a rather high number and is sufficiently close to 1 so as to appear not to leave a great deal of doubt as to its interpretation. In contrast, the positive correlations between the prices of water and soft drinks is low, between 0 and 0.3. That said, the table produces negative price correlations between soft drinks and water, which might suggest that if the price of water rises, the prices for soft drinks decrease and vice versa. This is a rather odd result and it would be interesting to dig a little deeper to understand the causes of such correlation. Although there are a variety of possible causes, one potential explanation is that soft drinks and water are complementary products. The very low correlation within the group of soft drinks is also worth noting. It might be arguable from these data that branded soft drinks present a market of their own. Even with a very high price correlation, other evidence could potentially outweigh the correlation analysis. For example, we might also find survey evidence from consumers suggesting that they are clearly segmented by either having a strong preference for eitherstill or sparkling water. Intuitively,supply substitutability seems 172 4. Market Definition Table 4.3. Correlations between prices of brands of still water (A–C), sparkling water (D–F), and soft drinks (G–I). ABCDEFGHI A1 B 0.93 1 C 0.91 0.94 1 D 0.91 0.85 0.86 1 E 0.94 0.97 0.95 0.92 1 F 0.93 0.99 0.96 0.88 0.99 1 G 0.11 0.05 0.01 0.33 0.02 0.01 1 H 0.57 0.55 0.25 0.16 0.24 0.27 0.17 1 I 0.77 0.75 0.81 0.86 0.86 0.79 0.33 0.11 1 Source: Charles River International (previously Lexecon), “Beyond argument: defining relevant mar- kets,” which reports on analysis performed in the EU competition inquiry into the French mineral water market, OL L 356. See www.crai.com/ecp/assets/beyond_argument.pdf, where the table reports fifteen brands rather than the nine selected here. OJ L 356. Case under EEC regulation 4064/89. Case no. IV/M 190 Nestl´e/Perrier (1992). While the decision document omits all of the correlation table for confidentiality reasons, paragraph (16) of the decision provides some information regarding the brand identities in the table. In particular, it tells us that: “The coefficient of correlation of real prices among the different brands of waters ranges between a minimum of 0.85 (Badoit and Vittelloise) and 1 (H´epar and Vittel).” likely in this case but supposing there was evidence from company documents or testimony that the machines for each type of water were impossible to move across to produce the other and we also found evidence that company pricing policies were such that they induced a high correlation in prices for some other reason, perhaps simply that the same person currently prices the two goods. The fact that prices are currently correlated may not reassure us that if it were in fact profitable to raise prices for say sparkling water, then prices would indeed be increased. This concern, for example, was raised in the U.K. Competition Commission’s 2007 investigation into the groceries market because most supermarket chains operated a “national” pricing strategy so that prices were perfectly correlated across the country. 10 Nonetheless, the CC decided that it was appropriate to define local markets because there was no evidence of demand substitutability and little evidence of supply substitutability while the CC took the view that firms could potentially abandon such pricing policies if it were profitable to do so. 4.2.2.2 The Salmon Debate In the United Kingdom, it became relevant for a merger case to establish whether Scottish farmed salmon was a distinct market or whether the market included, in 10 See the U.K. Competition Commission market inquiry into the groceries market, which is available at www.competition-commission.org.uk/inquiries/ref2006/grocery/index.htm. [...]... characteristics, and market shares to estimate aggregate market demand equations, and hence market elasticities of demand and substitution patterns Or else we can use individual level data to estimate individual level demand equations and their associated substitution patterns Given the latter we can then add up across an appropriately weighted collection of individuals to derive market demand curves and hence... before, this carries absolutely no information for predicting the value of the variable today And, in particular, if a shock occurs, it is not at all persistent: in the next period there is absolutely no trace of it This archetype stationary series is called a form of “white noise.” As a UniformŒ 1; 1 to be a variable that in each period concrete example, define " t takes a value randomly between 1 and. .. when, for example, prices respond to changes in market conditions only with a time lag Even if two products are in fact good long- or mediumterm demand substitutes, we may see little contemporaneous correlation in prices and wrongly conclude that the products are not related 4.2.4 Rival Cost and Demand Data for Price Correlation Analysis As in all quantitative analysis, one cannot draw more information... variation is useful for estimating demand as well The price and also sales data from this experiment were collected and used in Davis (2002) 4.3 Natural Experiments 187 I91 North Haven 2 New Haven 3 I95 4 Orange I95 Branford 1 Milford 5a,b Figure 4.8 Map of locations of cinemas involved in the experiment The theater labeled “4” was the Branford 12 screen cinema whose price was cut for three weeks Table... the pricing experiment performed by the Branford 12 cinemas Theater 1 2 3 4 5a 5b Showcase Orange Showcase North Haven 8 York Square (art house) Branford 12 Showcase Milford 5 Milford Quad Chain National Amusements National Amusements Independent HOYTS National Amusements National Amusements Pricing strategy/ response $4.50 for three weeks $4.50 for three weeks No change $5 for three weeks No change... correlated and so this potential false positive explanation is not supported by the facts A related cause of false positives in a price correlation exercise is the occurrence of common demand shocks, when cov.a1 ; a2 / ¤ 0 To see why, consider any two normal goods, say cars and holidays When the economy is good we will tend to see high demand, and hence high prices, for both cars and holidays and yet,... for over ten years and 70% for over twenty years The Swift 2 survey found that over 50% of customers had played for more than twenty years with the brand they play with now In short, there appeared to be a clear tension between the GfK survey results using the methodology where a brand went away for an entire customer base, which suggested significant switching, and the other survey and qualitative 27... b12 p2 and q2 D a2 b22 p2 C b21 p1 : Assuming each product is produced by a different firm which respectively maximize 12 For a critique of the use of price correlation analysis, see, for example, Werden and Froeb (1993a) A response is provided by Sherwin (1993) 4.2 Price Level Differences and Price Correlations 175 profits and compete in prices, we can calculate each firm’s reaction function and then... terms of demand substitutability The formulas for the Nash equilibrium prices reduce to c1 c2 a1 a2 NE NE p1 D and p2 D : C C 2 2b11 2 2b22 Note that from these expressions we can see that there are several ways in which we can find positive price correlations even though the products are not related on the demand side and are not substitutes 4.2.3.1 False Positives: Correlated Inputs or Demand Shocks... observe a time series of any length T and the date at which we start observing it will not affect the joint distribution of the data This property is sometimes known as “strict” stationarity and other forms of stationarity are also possible For example, we may only require that the first and second moments of the series do not vary over time and this would be a weaker form of stationarity 178 4 Market . as p NE 1 p NE 2 D  4b 11 b 22 4b 11 b 22  b 12 b 21 àc 1 2 C a 1 2b 11 C b 12 4b 11  c 2 C a 2 b 22 ÃÃ Ä 4b 11 b 22 4b 11 b 22  b 12 b 21 àc 2 2 C a 2 2b 22 C b 21 4b 22  c 1 C a 1 b 11 ÃÃ D  c 1 2 C a 1 2b 11 C b 12 4b 11  c 2 C a 2 b 22 ÃÃ  c 2 2 C a 2 2b 22 C b 21 4b 22  c 1 C a 1 b 11 Ãà ‹ D. b 12 b 21 àc 1 2 C a 1 2b 11 C b 12 4b 11  c 2 C a 2 b 22 Ãà ; p NE 2 D  4b 11 b 22 4b 11 b 22  b 12 b 21 àc 2 2 C a 2 2b 22 C b 21 4b 22  c 1 C a 1 b 11 Ãà : First note that the prices depend on the intercepts of the demand equations. b 12 b 21 àc 2 2 C a 2 2b 22 C b 21 4b 22  c 1 C a 1 b 11 ÃÃ D  c 1 2 C a 1 2b 11 C b 12 4b 11  c 2 C a 2 b 22 ÃÃ  c 2 2 C a 2 2b 22 C b 21 4b 22  c 1 C a 1 b 11 Ãà ‹ D v t ; where the question mark