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## Product Line Rivalry: How Box Office Revenue Cycles Influence Movie Exhibition Variety**

### BibTeX

@MISC{Chisholm_productline,

author = {Darlene C Chisholm and George Norman},

title = {Product Line Rivalry: How Box Office Revenue Cycles Influence Movie Exhibition Variety**},

year = {}

}

### OpenURL

### Abstract

Abstract: This paper analyzes how product line rivalry by multi-product oligopolists is affected by market size and product substitutability. We show that the choice of product line and of the degree of overlap in competing product lines is determined by the tension between two effects: the drive to "be where the demand is" and the desire to weaken competition and intra-firm product cannibalization. Product lines are shown to be wider and more overlapped in large markets and when product substitutability is weak. We provide econometric support for our main hypotheses using data on weekly film-programming choices by the first-run movie theatres in a large US metropolitan market. ** We are grateful to the DeSantis Center for Motion Picture Industry Studies of Florida Atlantic University College of Business and Economics for providing a grant to fund this research and to Synergy Retail for compiling the data set used in this paper. For valuable comments and suggestions, we thank seminar participants at the DeSantis Center Summit Workshop at Florida Atlantic University. We are grateful to Vicky Huang, Anna Kumysh, and Vidisha Vachharajani for their careful research assistance and to Sorin Codreanu for his data-management programming assistance. Page 2 of 22 Introduction We analyze the impact of consumer attitudes, market size and strategic interaction on firms' choices of product lines. The seminal analysis by 1 When we extend the analysis to multi-product firms additional forces affect the product line/output choices. On the one hand, an extensive product line potentially constrains product line choices by the firm's rivals. On the other hand, extending the firm's product line potentially cannibalizes sales from the firm's own products 2 and, if rivals are not constrained in their product line choices, leads to a tougher competitive environment. Our analysis addresses two further issues that are largely ignored in the literature. We should expect the choice of product line and the degree of product line overlap to be affected by whether the products on offer are viewed as being close substitutes or not. 3 We should also expect to find that these choices are affected by the size of the market, with firms choosing broader product lines and more product line overlap, in larger as opposed to smaller markets because there is greater benefit from "being where the demand is" in larger markets. 1 A classic example is the Anderson/Neven (1991) result that single-product Cournot competitors supplying a line market will perfectly agglomerate. 2 This underpins the argument by 3 Page 3 of 22 Casual empiricism supports our suggestion that the choice between broad and narrow product lines is affected by market size and consumer attitudes. In large markets with diverse consumer tastes we find broad product lines, with firms offering multiple products that are largely indistinguishable from each other: mass automobile production (Ford, GM, Toyota); lowend cameras (Nikon, Minolta, Pentax); low-end computers (Dell, HP, Compaq) are obvious examples. 4 In smaller markets and/or markets in which consumer tastes are rather less diverse, by contrast, we find narrower product lines with firms seeking to supply particular niches: in automobile production BMW and Jaguar or Mercedes-Benz and Lexus are obvious examples. We test these hypotheses directly using data from the motion-pictures exhibition market in a major metropolitan area. A first-run movie theatre can be thought of as a multi-product firm, with the individual products being the films showing at the theatre on a particular week. Comparing the weekly film programming choices of competing first run theatres over a period of a year allows us to investigate the impact on programming similarity (product line overlap) of market size and of the degree of substitutability between theatres (proxied as the distance between the competing theatres) The literature on product line rivalry is not extensive: for a recent review, see 3) their formal analysis considers the case in which two firms each produce two products, with two of the four products being closer substitutes than the other two. In their concluding remarks they briefly consider the possibility that there might be equilibria in which both firms produce all four products but this possibility is not explored. Moreover, while the role of market size in determining the width of the product line is hinted at, it is not formally analyzed. In summary, our theoretical analysis extends the existing literature in a number of important directions. First, we endogenize the product line decision. Second, we investigate the impact of market size and the degree of product substitutability on the product line choice. Third, we show that all but one of the equilibria exhibit prisoner's dilemma characteristics, with firms choosing product lines that are "too broad". simple enough to articulate. Each firm adopts a restricted product line with the trigger strategy that if either firm switches to a more extended product line the non-deviating firm will revert to the Nash equilibrium product line, leading to more product line rivalry and tougher competition. Mutual forbearance offers several advantages compared to tacit coordination based on multimarket contact. First, on a purely technical note, this strategy has bite even when the markets are symmetric. 6 Second, mutual forbearance is much easier to monitor than are agreements on prices or outputs: I might not know precisely how much my rival is producing of a particular product but I certainly know whether she is producing that product. Third, mutual forbearance is difficult to detect by the antitrust authorities: the fact that firms are not competing head-to-head may be obvious but the firms can argue that this is a simple commercial decision. The remainder of the paper is organized as follows. We outline the basic model in section 2. Sections 3 and 4 present and discuss the nature and welfare properties of the subgame perfect equilibrium. In section 5 we investigate the conditions under which firms might wish to adopt mutual forbearance in their choice of product lines. Section 6 tests our main hypotheses using data on the weekly programming choices of first-run movie theatres in the Greater Boston metropolitan area. Brief concluding remarks are given in section 7. The Model We use a variant of a consumer demand model first formulated by ). Denote by N ⊆ M the set of differentiated goods for which there is strictly positive 6 In the Bernheim and Whinston analysis, slack enforcement power in one market is used to sustain cooperation in another market where cooperation would not otherwise be sustainable. This is effective only if the two markets are asymmetric. Page 6 of 22 aggregate supply: N = {i ∈ M: q Ai + q Bi > 0}. Suppose that N contains n of the M differentiated goods. Then consumer utility is assumed to be In (1) y is an outside good produced competitively, Q i > 0 is the aggregate quantity of the ith differentiated good in N supplied to the market, V is a positive parameter, s is a measure of market size and γ ∈ [0, ∞] is a direct measure of the degree of substitutability between the differentiated goods. Note that since the utility function is quasi-linear, consumers' decisions with respect to consumption of the differentiated goods are independent of their consumption decisions with respect to the outside good. Maximizing (1) subject to the standard budget constraint gives the inverse demand function for the ith good: Inverting this system gives the direct demand functions (Motta This demand system has two particularly attractive features for our purposes. First, aggregate demand "does not depend upon the degree of substitution" between products. Second, "in the case of symmetry … aggregate demand does not change with the number of products n" (Motta op. cit., p. 253). In other words, the utility function (1) does not exhibit a "love of variety", by contrast, for example, with the Dixit/Stiglitz (1977) utility function. This feature is particularly important for our analysis. It implies that a decision by a firm to extend its product line does not change aggregate demand but rather results in a finer segmentation of the existing We follow Suppose that firm k chooses to produce a subset N k of the differentiated goods, with N k containing n k goods. Then firm k's total costs are In (4) F is a set-up cost, v is constant marginal cost, and c is a switching cost; the cost of retooling as firm k switches production from one product to another. As can be seen, production is assumed to exhibit both economies of scale and economies of scope. Since we do not model the entry decision we can normalize F and v to zero without loss of generality. It follows that the profit of firm k, given that it chooses product line N k is: where p i is given by (2), N = N A ∪N B and n is the number of distinct products in N. 8 The firms compete in a two-stage game. In the first stage they choose their product lines N k and in the second stage they compete in quantities. The solution concept is, as usual, subgame perfection. Analysis In the interests of tractability, we follow Brander and Eaton and assume in the remainder of the analysis that M = 4; that is, each firm can produce up to four products. 9 This implies that there are 225 potential strategy combinations in the second-stage quantity game. However, 7 These properties also characterize the Hotelling model that has become the standard workhorse in the analysis of product differentiation. Note also that while aggregate demand may be unaffected by the width of the product line, the individual firm's market share will be affected by its choice of product line. 8 Recall from our discussion of equation Page 8 of 22 many of these are strategically equivalent: for example, ({1, 2, 3}, {3, 4}) is strategically equivalent to any strategy combination in which firm A (B) produces three (two) of the four products, with the firms having one product in common, such as ({1, 2, 4}, {1, 3}). We adopt the numbering convention that when the product lines are not perfectly overlapped firm A produces the lower indexed products and firm B the higher indexed products. 10 Solution of the two-stage game is considerably eased by the following important result that characterizes the pay-off matrix for the first-stage product line game: 11 Lemma 1: Suppose that inverse demand is given by (1) and that n k < 4 (k = A, B). Then a strategy for firm k (k = A, B) that exhibits less product line overlap strictly dominates a strategy with more product line overlap. For example, suppose that firm A chooses {1, 2, 3}. Then for firm B {1, 2, 3} is strictly dominated by any three-product strategy that includes product 4, {1, 2} is strictly dominated by any two-product strategy that includes product 4 and {1}, {2} and {3} are strictly dominated by {4}. The intuition underlying Lemma 1 is simple enough. When given the choice, firms prefer indirect competition -introducing a product that the rival is not offering -to direct competitionintroducing a product that goes head-to-head with a rival's product. Our numbering convention and Lemma 1 imply that we can restrict the product line strategy space to {{1, 2, 3, 4}, {1, 2, 3}, {1, 2}, {1}} for firm A and {{1, 2, 3, 4}, {2, 3, 4}, {3, 4}, {4}} for firm B. The equilibrium quantities and prices for the second-stage quantity subgame are presented in ( The exception arises with any product line choices in which one firm produces all four products 10 This is analogous to the assumption in the spatial model that one firm always locates "to the left" of the other. 11 Proof is long and tedious and in the interests of brevity is omitted. Details can be obtained from the authors on request. Page 9 of 22 and the other firm produces only one. Output by the four-product firm of the one product in which there is head-to-head competition is positive only if the degree of substitutability γ < 8. For any higher degree of substitutability, the four-product firm prefers not to offer the overlapped product. 12 This is an extreme version of a pattern that characterizes all of the equilibria in Equilibrium prices behave as we might have expected. Prices are lower when product lines are more extensive and are lowest, at V/3, when products are in head-to-head competition. 13 Now consider the first-stage product line game. 14 Our model is characterized by four parameters, s, V, c and γ. However, given the results of the second-stage quantity subgame in Then profit to firm k in any strategy combination is of the form s. . In other words, equilibrium for the first-stage product line game is fully determined by the two parameters α and γ. We then have the following: 12 We take this into account in solving the product line first-stage game: it has no practical effect on the equilibria. 13 Given Lemma 1, this arises only in strategy combinations such that all four products are offered. 14 We do not explicitly report the pay-off matrix. This can be obtained from the authors on request. Page 10 of 22 Proposition 1: Equilibrium to the product line first-stage game is: ({1, 2, 3, 4}, {1, 2, 3, 4}) for α > α 44 (γ) ({1, 2, 3}, {2, 3, 4}) for α ∈ (α 33l (γ),α 33u (γ)) ({1, 2}, {3, 4}) for α ∈ (α 22l (γ),α 22u (γ)) ({1, 2}, {4}) for α ∈ (α 11 (γ),α 22l (γ)) ({1}, {4}) for α < α 11 (γ). Where: It is easy to confirm that each of these functions is increasing in γ. Proposition 1 is illustrated in Product lines are broader and product line overlap more extensive when α is high or γ is low. The product line choice balances two forces: competition with the rival and cannibalization of the firm's own products. A low value of γ is equivalent to the degree of substitutability between products being low, implying that cannibalization and competition effects are both weak, encouraging broader products lines and more product line overlap. We know from equation Welfare Comparisons In this type of differentiated product model total surplus is aggregate utility minus total cost. A complicating factor in evaluating total surplus in the different strategy combinations, however, is that these comparisons are not functions solely of α and γ. Define: 15 They are, of course, still in competition with each other since the products are substitutes. Page 12 of 22 Lemma 2: (a) Total surplus is less with strategy combination (c) Total surplus is always less with strategy combination ({1, 2},{3, 4}) than ({1}, {4}). Comparison with the critical values of α in equation Lemma 3: Consumers gain and producers lose from broader product lines. Broader product lines with more product overlap lead to more intense inter-and intrafirm competition, lowering prices and benefiting consumers. Since we assume that there is no "love of variety" in our setting, there is no countervailing increase in aggregate demand. Rather, more extensive product lines lead to a finer segmentation of the overall market. The result is that profits fall and consumer surplus rises as product lines broaden. 5. Mutual Forbearance 16 There is one partial exception. In comparing ({1, 2}, {4}) with ({1}, {4}) when the former is an equilibrium, firm A gains from the more extensive product line and firm B loses. However, aggregate profit in the configuration ({1, 2}, {4}) is less than aggregate profit with ({1}, {4}). Page 13 of 22 An immediate implication of Lemma 3 is that every symmetric subgame perfect product line configuration other than ({1}, {4}) (and its equivalents) has prisoner's dilemma characteristics. Both firms would prefer narrower product lines and less product line overlap but in a one-shot-game are unable to sustain a narrowing of their product lines. Suppose, however, that the game is repeated indefinitely. This raises the possibility that the firms can tacitly agree to adopt narrower product lines, with the agreement supported by a trigger strategy, even if they continue to act non-cooperatively in the second-stage quantity subgame. There is the further possibility, of course, that the firms might coordinate both stages of the game -product lines and outputs. An obvious reason for concentrating solely on cooperation in the first-stage product line game is that cooperation in the quantity-setting subgame will typically be more difficult to monitor in any "real life" setting. By contrast, an agreement to restrict product lines is relatively easy to police: I might not know precisely how much of a product a rival is producing, but I certainly know whether she is producing that product. In considering the sustainability of a tacit agreement to restrict product lines, but not outputs, we confine our attention to the case in which the subgame perfect equilibrium strategy combination is ({1, 2, 3, 4}, {1, 2, 3, 4}). Now consider the familiar trigger strategy for firm k: "I shall continue to restrict my product line in the current period so long as we have both restricted our product lines in every previous period. Otherwise I shall extend my product line to four products." Standard analysis indicates that the agreement to restrict product lines to r products is sustainable for any discount factor greater than d r , where An Application to the Movie Exhibition Market The weekly movie programming choices by first-run movie theatres in a well-defined metropolitan area provides an interesting test of our theoretical analysis for several reasons. First, if we take the screening of an individual movie as a single product, the individual movie theatre is an obvious example of a multi-product firm. Second, given that competing first-run movie theatres can, and do, show many of the same films, this is an obvious case of the type of head-to-head competition that our theoretical analysis envisages. Third, given that we can identify the movie theatre programming choices of competing first-run movie theatres, we can generate a simple measure of similarity in programming choices. 18 Fourth, there is considerable seasonality in movie theatre attendance, with movie audiences building up as we approach major 17 These are equivalent respectively to per period discount rates less than 25 per cent and 15.4 per cent. 18 We exclude from our study art house and second-run theatres on the assumption that such theatres serve markets with consumer preferences for different attributes (film offerings and currency) from the first-run theatre market. Page 15 of 22 holidays and declining thereafter. 19 This provides us with a direct test of our first hypothesis, that product line overlap, movie programming similarity, is greater when the market is larger. Finally, the first-run movie theatres in our sample are located at different distances from each other. It seems reasonable to suggest that we can treat distance between theatre pairs as a measure of substitutability -the more distant are two theatres from each other, the lower the degree of substitutability they exhibit. Then we have a test of our second hypothesis, that the degree of product line overlap (programming similarity) is inversely related to substitutability. Our econometric analysis is based upon data drawn from the first-run motion-pictures exhibition market in the Boston greater metropolitan area, which contains 13 first-run theatres. For each theatre, for each week from June 30, 2000 through the week of June 22, 2001, we have information from Nielsen EDI on which films were playing, and on the revenues generated at each theatre by each film for that week. We supplemented these data by recording screening times on the Friday of each week, for each film, for each theatre in our data set. Screening-time information was determined by reviewing Boston Globe movie advertisements on microfilm. Our measure of programming similarity uses an approach suggested by Jaffe (1986). For each theatre pair ij we construct a weekly angular similarity index a ijt distributed on the interval [0, 90], where 0 indicates perfectly overlap in programming choices and 90 indicates that there is no overlap. Details of how a ijt is constructed are provided in the Appendix. We also divided the total set of ij pairs into three subsets -theatre pairs that are within five miles of each other, theatre pairs that are between five and ten miles apart and theatre pairs that are more than 25 miles apart -and calculated the weekly mean of a ijt for each subset, 19 See Einav (2006) for a careful analysis of seasonality in movie theatre-going. Page 16 of 22 denoted A 5t, A 10t and A 25t respectively. These are illustrated in (Figure 3 near here) Summary statistics for the similarity measures are given in