A Measure For Market Delineation

Jacques C. Bourgeois, Carleton University
ABSTRACT - The present paper briefly reviews those measures used in the market delineation task. However, its main purpose lies in presenting an objective means to accomplish this task. The proposed methodology derives a statistic based on consumer derived judgmental data.
[ to cite ]:
Jacques C. Bourgeois (1979) ,"A Measure For Market Delineation", in NA - Advances in Consumer Research Volume 06, eds. William L. Wilkie, Ann Abor, MI : Association for Consumer Research, Pages: 514-518.

Advances in Consumer Research Volume 6, 1979      Pages 514-518


Jacques C. Bourgeois, Carleton University


The present paper briefly reviews those measures used in the market delineation task. However, its main purpose lies in presenting an objective means to accomplish this task. The proposed methodology derives a statistic based on consumer derived judgmental data.


The concept of a market has been described in many ways, but it still remains elusive. Often specific applications have appeared in the literature, such as the beer market, the retail market, the computer market, the job market, the youth market. All of these views of a market have two things in common: 1) they include a group of consumers seeking to fulfill a need, and 2) a group of producers seeking to deliver need-satisfying products. Thus, a market may be defined as the arena of potential exchanges between consumer and producer. The word "potential" is used to imply the possibility of future markets based, for example, on unsatisfied needs or the development of new technology. A market is a set of consumers and producers with something in common. That is, they both want to trade to fulfill a need. The consumer seeks to "procure" need fulfilling products, while the producer seeks to "deliver" need fulfilling products. Thus, it could be viewed as the intersection of (or exchange arena between) a group of producers (supply) and a group of consumers (demand). Perhaps the following simple graphic model best illustrates this concept.



Others have similarly expressed this perspective of a market. For instance, Steiner (1968) defined a market as "the entire web of interrelationships between buyers, sellers, and products that is involved in exchange". Nickels (1978) defines a market as "a particular group of people and/or organizations that have wants and needs that may be partially satisfied through a marketing exchange".


Several definitions have been used in identifying a market and generally these are presented as a function of the author's field of study (e.g., economics, marketing, law). It is not the purpose of this review to recapitulate these definitions. A detailed review of these definitions is contained elsewhere (Day and Shocker, 1976). The literature reviewed in this paper will be concerned with those "measures" used to operationalize these definitions. The review and format which follows, draws from that suggested in an earlier paper (Day and Shocker, 1976). The literature has been dichotomized following two general perspectives: 1) behavioral measures and 2) perceptual measures. This division has previously been suggested by Krech and Crutchfield (1948). They suggested the use of these two perspectives as a proper means for recognizing a "group". In our context, a group is interpreted as that set of buyers and sellers in the process of exchange - a market. It is also interesting to note that a similar categorization of measures has been applied by Day and Shocker (1976) when they used a behavioral and judgmental dichotomy.

Behavioral Measures

Bass, Pessemier and Tigert(1969) identified, through factor analysis, groups of products in terms of their similarity in usage rates. The resultant factors were groups of products considered to be substitutes or complements. This procedure has been questioned (Day and Shocker, 1976) in terms of the relevance of the criterion. That is, it would seem to be a big assumption to use synonymously similarity in purchase rates and the concept of substitutability.

The concept of cross-elasticity of demand is another behavioral measure. It is one that has had some acceptance in the courts (Dean, 1962 and Werth, 1965). The idea of product substitution has gained attention not only for consumer products but, more recently, for industrial products, due to the increasing costs of raw materials. For instance, Business Week (Sept. 14, 1974) reported the efforts of three major soft drink makers (including Coca-Cola) who made a switch from sugar to high fructose corn syrup. Business Week also examined other examples, but all served to illustrate that when a product can act as a substitute (high cross-elasticity of demand), then these products can be considered in the same market. On the other hand, Day and Shocker (1976) suggest that despite the impressive credentials of this measure, it is widely criticized and infrequently used. This would be due largely to the fact that it is based on an assumption seldomly satisfied - that is, it assumes that there is no response by one firm to a change in marketing variable(s) of another.

Brand switching measures are also behavioral measures based on conditional probabilities of purchasing a particular brand or product. Depending upon the transition patterns between products, markets can thus be defined. Two products with high transition probabilities would be considered in the same market. This approach also suffers from certain shortcomings, namely that it relies on the stability of the customer choice process and on the feasibility and reliability of using panel data.

Perceptual or Judgmental Measures

Decision sequence analysis (Bettman, 1971, 1974; Haines, 1972, 1974) and similarly the application of utility trees in economics (Strotz, 1957, 1959) are judgmental measures used for the market delineation task. Basically, these examine the consumer's process in evaluating alternatives. The set of choices are set along a decision hierarchy - a sort of lexicographic model. This decision hierarchy is then used to partition the market. However, there exist problems with this technique as well. Much of the analysis of protocol data used in decision analysis deals at the individual level and aggregation over a segment still poses a problem in this area of research. On the other hand, the operationalization of a utility tree has more recently met with some success (Bourgeois, Haines, Sommers, 1975).

Customer judgements in terms of their perceptions of product usage have been used to develop market boundaries (Stefflre, 1971). In this instance, an "items by uses" matrix is collected such as to yield a similarity matrix. Then, all similar products within this matrix are placed near each other, such as to have product clusters stand out. The problems here lie in determining how similar the products must be before they are clumped. In addition, the technique employed to create the respondent-generated product set remains, at this point, subjective, although Srivastava, Shocker and Day (1977) seem to have recently offered a solution to this problem. A somewhat similar approach to that of Stefflre has been suggested by Bourgeois, Haines and Sommers (1975). In this instance, respondents are asked to group brands; respondents arbitrarily determine the number of groups used, as well as the criteria for forming these groups. Based on the homogeneity of respondents' perceptual judgements, market boundaries are defined. The shortcoming here is that the respondent's "choice sets" are made independent of "intended usage" (or usage situation). Thus, it may be possible for two products to be substitutes in a particular situation, while in a situation with completely different "intended usage", we might find these same two products not so closely related.


Given the above brief review, what is needed is a measure which relies on the basic definition presented at the start of this paper, while overcoming the shortcomings presented in the literature review. The following statistic is derived as such a measure. While using the above dichotomy, one may class this approach as a consumer based judgmental measure.

The problem in delineating a market lies in finding the intersection of demand and supply for need fulfilling products. That is, we must identify a group of products supplied or available to the consumer which are also perceived by these consumers as substitutes. It has been stated Moran, 1973), at the highest level of generalization, that, "to some degree, in some circumstances, almost anything can be a partial substitute for almost anything else". At the lowest level we may find, at most, two similar products, and indeed, two similar products may not even exist. Thus in fact, there is a similarity continuum, that is, a degree of similarity between any two and all products. The problem lies in identifying and measuring a product's position along this continuum.

Given that a market is that arena of exchanges where supply and demand meet, an operationalization of such a definition should include the producers' outputs, as represented by a total set of offerings - a product set. On the other hand, the demand side is represented by consumers' wants for need satisfying products. Ideally, each consumer should find a product to satisfy his exact needs. This would actually involve producing one product for each individual. Obviously, this is not a practical solution, given our present technology. Thus, producers offer what they believe to be the correct set or products while consumers satisfice by choosing among the available alternatives.

In choosing among the available product set, consumers must trade-off between the various alternatives. This trading-off is affected by external (e.g., marketing variables) and internal (e.g., perceptual distortion, perceived risk) mechanisms. The part research has typically built into their approach an operationalization and measure of these variables by, for instance, relating perceived risk to behavior or the effect of changes in certain marketing variables to product selection. It is the purpose of this approach to treat these internal and external mechanisms as part of a total system of interacting forces - a Gestalt. Thus, the focus here is not to measure each of these components but rather to measure the resultant output from these interacting mechanisms (see Figure 2). That is, given a present set of variables describing a situation at a particular point in time, what is the consumer's perception of the market? Given a set of inputs, what is being measured is simply the output from the consumer's black box.



The task thus lies in measuring consumers' perception of product substitutes given the set of total available products. This task or research problem should be approached from two perspectives (as previously stated): a demand and a supply dimension. The supply dimension is relatively easily measured, as firms produce what they perceive and believe consumers want. The output on the supply side is clear - a product(s). The demand side is not so clear. Given the above illustrated input stimuli and interacting internal mechanisms, it is difficult to measure their output or perception of product substitutes. The difficulty lies mainly in the fact that investigators have relied largely upon surrogate measures of this product substitution phenomenon. The present technique uses a more direct route by simply asking consumers which products they perceive as substitutes. These subjective Judgements are taken to be direct measures of a consumer's perception of product substitutes. They then serve as maximum likelihood estimators of the underlying parameters for the market delineation task.

A Two Consumer P-Product Market

Before expanding the model to a whole population, it may be easier to show an example for the case where we would have simply two consumers and P products (see Figure 3).



The P set represents that group of products offered by all producers; these are thought, by producers, to be the total set of products satisfying a need. In fact, in this two consumer population, C1 perceives nine products (P1...P4, P11...P15) as substitutes, while C2 perceives ten products (P1...P10) as substitutes. In this simple case, each consumer could form separate market segments. But, if one were to define a MARKET for this situation, it would be that sub-set of products which is perceived similarly by both consumers, or in set notation:



Some products are neither part of the market nor of market segments. This would be the set of products in:

(C1 U C2)' or P - (C1 n C2)

These products are not perceived as being in either the market or market segment and thus should not be produced for this particular market; if they are, they should be satisfying some "other" need. The present market is therefore defined as the set of those four available products being perceived as substitutes by the two consumers. We may say that we are 100% certain that these four products are in the same market, since both consumers of this two consumer population perceive them as such. On the other hand, products P5 . . . P15 are not as clearly defined. For instance, we could say that we are only 50% certain that each of the groups of products P5...P10 and P11...P15 forms separately a market, since these are respectively perceived as being in a market by only one of two consumers. In probabilistic terms:

EQUATIONS  (1)   and  (2)

A Three Consumer P-Product Market

A second example will be given to illustrate the problem. Let us suppose that our population was made up of three individuals with the same set of products as in the above example.

In the same fashion, as earlier derived, we may state the following:




There are obviously other product combinations but the above combination serve to illustrate the basic concept of a delineated market and its associated confidence level. The decision maker is then in a position to define his relevant market with a predetermined level of confidence.

A Statistic for the General Case

The previous two simple examples serve to illustrate the procedure to be followed. In the general case, we wish to identify a group of products which are perceived as substitutes by (1-a) of the consumers. For instance, the decision maker may decide that he wishes to delineate a set of products which are perceived as similar by at least 80% (i.e., e = 0.20) of the population. If he were to draw a random sample of the population, the suggested method would yield objective and statistical conclusions for the choice of his market.

The statistic is derived from the information provided by each respondent. This information consists of a set of classes (groups of products) for each respondent for each usage situation. That is, the statistic is based on a measure of substitutability and is derived on the basis of each usage situation. These two dimensions have been suggested earlier by Massy (1975) and later emphasized by Day and Shocker (1976). The initial total list of products could be generated using Srivastava, Shocker and Day's (1977) suggested methodology. That is, each respondent presents his perceived markets (product substitutes) from a given set of P products. This could be represented by the following three dimensional data matrix:


From the observed data we can define the following statistic:


In the case where k (number of products in the supplied product set) is small, the calculation of all possible Pk's becomes quite arduous. That is, if one wishes to see how k products out of P products could be combined to form various market definitions, then (Pk) comparisons must be made before choosing that combination of k products which is most likely to occur.

For instance, if one had a total set of 40 products while considering delineating a market with 10 of these products, one would have to evaluate 847,660,528 (or P!/(k!(P-k)) combinations before choosing the most likely combination, that is, that combination with the greatest P10. In many cases, the exercise would probably be repeated for P9, P8, . . .P2. This would require the calculation of other likelihoods. It is obvious from this simple (and not abnormal) example that the computer time involved in calculating such probabilities would be prohibitive. Given these real constraints, a heuristic is needed which could shorten the time required to calculate each of these likelihood estimators. The following heuristic is seen as a proper approximation.


The great advantage with this approximation, besides that of being expeditious, is that we need only the initial probability matrix (i.e., the similarity measure for all pairs of products). A disadvantage is that it is an approximation and that it would tend to understate the actual Pk. On the other hand, it is only an estimator and the calculation of the "actual" Pk would then be obtained following the selection of the proper combination of products, which meets the 1-a predetermined level. The selection of the proper combination of products is that group of k products with the largest Pk. The actual selection is made by choosing the greatest Pk. In order to verify for possible selection errors, given that we are using an estimator, one could calculate the actual Pk for those Pk neighboring Max {Pk} and then select the maximum value of Pk.


Groups start forming in pairs of products. The degree of substitution between any two products is directly related to, and calculated from, the number of times any two products appear in the same class across all of the individuals. These are likelihood estimators for the proportion of people who see two products as being substitutes. These estimators are stored in a similarity matrix. Each element in this matrix is in fact an actual P2 for each pair of products.

The first group is formed by selecting the largest P2 element. The decision maker would have already set his confidence level at the a level; we would then compare our maximum P2 to this 1-a level. If Max {P2} equals or exceeds 1-a, we continue our search for additional members; if Max {P2} is below the predetermined level, the procedure ends and we conclude that we have a homogeneous group of products at our predetermined confidence level.

If the procedure is allowed to continue, the two products with maximum P2 are chosen as a departure node for increasing the market size until we reach the desired cut-off point. Thus, the next product most likely to join the market will be that product which produces Max{Pk }. For instance, if we assume that product number 5 will be chosen, among 40 products, to join products 11 and 23, then we have:


Generally, we have in the k = 3 case:

EQUATIONS  (6)   and  (7)

This procedure is extended to include whatever number of products the researcher requires in a marker or until the cut-off point is reached, whichever occurs first. Thus, new members to the market are added while maintaining a predetermined level of market homogeneity.

Once a market is completely defined, the procedure involves going back to the original similarity matrix and choosing the next pair of products which are most similar. From this point, we repeat the above procedure This iterative process is carried out until all pairs have been exhausted or until the next highest substitution index is less than the critical level (1-a).


The preceding discussions have attempted to present a framework with which to examine the problem of determining the relevant market and a methodology with which this framework may be implemented. It is expected that this will have contributed to a reduction in the problem of identifying competitive market boundaries, and that the methodology presented will provide a defensible approach to defining a market. The true test of the proposed approach lies in its application - our following task.

The relevance of such research, for instance, to advertising is well illustrated by those anti-trust cases which have appeared before the courts. Advertising's role in the competitive process underlying our free market system has been a matter of controversy for many years. The importance of this subject for anti-trust regulations did not really emerge until the filing, by the FTC, of charges against the four leading ready-to-eat (RTE) cereal manufacturers (Kellogg's, General Mills, General Foods, Quaker Oats) under section 5 of the FTC act. It was claimed that their advertising practices result in high barriers to entry and is the main reason for the monopoly situation in this industry.

The case being made actually makes two basic and very important assumptions. First, it assumes that advertising can be a barrier to entry into the market. Second, implicitly assumed is a "defined" market. Depending upon how narrowly or broadly the market is being defined, the case for barriers to entry is more or less valid and thus the entire case actually lies in properly delineating the relevant market. Thus, it was the purpose of this paper to provide an objective means to operationalize this delineation task, while the implications of such research could be broadened to other areas of concern such as: evaluation of market share, product positioning, new product development, legal suits involving monopoly cases and the effective use of advertising.


F. M. Bass, E. A. Pessemier, D. J. Tigert, "Complementary and Substitute Patterns of Purchasing and Use", Journal of Advertising Research, 9 (June, 1969), pp. 19-27.

J. R. Bettman, "Decision-Net Models of Buyer Information Processing and Choice: Findings, Problems and Prospects", in Buyer/Consumer Information Processing, C.D. Hughes and M. L. Ray (eds.), Chapel Hill, North Carolina: U. of North Carolina Press, 1974, pp. 59-74.

J. R. Bettman, "The Structure of Consumer Choice Processes", Journal of Marketing Research, 8 (Nov., 1971), pp. 465-471.

J.C. Bourgeois, G. H. Haines Jr., M. S. Sommers, "Defining an Industry", presented at the joint national conference of the Operations Research Society of America (ORSA) and The Institute of Management Sciences (TIMS), Las Vegas, Nevada (Nov., 1975).

Business Week, "Making the Switch to Something Else", Sept. 14, 1974, pp. 67-70.

G. S. Day, A. D. Shocker, "Identifying Competitive Product-Market Boundaries: Strategic and Analytical Issues", Working Paper 156, Graduate School of Business, University of Pittsburgh (1976).

J. N. Dean, "Product-Market Definition Under the Sherman and Clayton Acts", University of Pennsylvania Law Review, 110 (April, 1962), pp. 861-878.

G. H. Haines Jr., "Process Models of Consumer Decision-Making", paper presented at the Association for Consumer Research Workshop in Information Processing, University of Chicago, 1972.

G. H. Haines Jr., "Process Models of Consumer Decision-Making", in G. D. Hughes and M. L. Ray, Buyer/Consumer Information Processing, Chapel Hill, N.C.: University of North Carolina Press, 1974.

J. A. Howard, J. N. Sheth, The Theory of Buyer Behavior, Wiley, 1969.

D. Krech, R. S. Crutchfield, Theory and Problems of Social Psychology, McGraw-Hill, 1948.

W.F. Massy, "Some Thoughts About the Definition of 'Relevant Market' in Antitrust Cases", Working Paper, Stanford University, 1975.

W. T. Moran, "Why New Products Fail", Journal of Advertising Research (April, 1973).

W. G. Nickels, Marketing Principles - A Broadened Concept of Marketing, Prentice-Hall, 1978.

R. K. Srivastava, A. D. Shocker, G. S. Day, "An Exploratory Study of the Influences of Usage Situation on Perceptions of Product Markets", Working Paper No. 239, Graduate School of Business, University of Pittsburgh, 1977.

V. Stefflre, New Products and New Enterprises: Report on an Experiment in Applied Social Science, University of California, Irvine, California, 1971.

P.O. Steiner, "Markets and Industries", in D. L. Sills (ed.), International Encyclopedia of the Social Sciences, New York: Free Press, 1968 (pp. 575-581).

R. H. Strotz, "The Empirical Implications of a Utility Tree", Econometrika, 25 (April, 1957), pp. 269-280).

R. H. Strotz, "The Utility Tree - A Correction and Further Appraisal", Econometrika, 27 (July, 1959), pp. 482-488.

R. W. Wreth, "Determination of the Relevant Product Market", Ohio State Law Journal, 26 (Spring, 1965), pp. 241-293.