Retail Market Area Shape and Structure: Problems and Prospects

J. Barry Mason, The University of Alabama
[ to cite ]:
J. Barry Mason (1975) ,"Retail Market Area Shape and Structure: Problems and Prospects", in NA - Advances in Consumer Research Volume 02, eds. Mary Jane Schlinger, Ann Abor, MI : Association for Consumer Research, Pages: 173-186.

Advances in Consumer Research Volume 2, 1975      Pages 173-186


J. Barry Mason, The University of Alabama

[Joseph Barry Mason is Professor of Marketing and Urban Studies, Graduate School of Business, The University of Alabama.]

The keys to understanding the shape of market areas are found in central place literature. Our concepts of market area structure are anchored in the refinements of the traditional gravity model. Central place theory provides the key assumptions underlying the structure of market areas. Thus, structure emerges as a subset of shape. However, we must ask ourselves the purpose we want predictive mechanisms to serve. If our needs are satisfied by gross decision parameters at the level of the firm, then perhaps our models of shape are satisfactory and our structural requirements are not overly monumental. If, however, we are seeking the basics for a theory of consumer demand at the micro-analytic level, then our structural models particularly are woefully inadequate.

Marketers frequently use various types of spatial analyses in market area planning without understanding the underlying bases of the implicit spatial and temporal relationships in the paradigms used. Most students of consumer behavior are familiar with the contributions of Reilly, Converse, and perhaps one or two other individuals (Schwartz, 1963; Don and Ruth Mulvihill, 1970; Revzan, 1968) such as Huff but their knowledge for the most part does not go beyond this. Perhaps a reason for relative lack of interest is that many researchers do not believe that these paradigms offer the field of marketing explicit means for explaining or predicting the spatial behavior of consumers (Moore and Mayer, 1966). Thus, marketers have turned to a variety of other disciplines in developing useful spatial and temporal constructs for market analysis. Primary contributions have been made by geographers (Berry and Horton, 1970), economic historians (Fite and Reese, 1965), land economists (Hoover, 1948), regional scientists (Isard, 1956), and others.

The explanations offered by these individuals are quite varied. For example, one group of researchers focused on the external relationships of a city to surrounding regions. This thrust includes contributions by such writers as Von Thunen (1966), Weber (1929), Losch (1959), and Greenhut (1952). These writers have been primarily concerned with industrial site location as well as land utilization and spatial supply and demand relationships. Another group of writers, including Fetter (1924), Christaller (1966), and Isard (1960), focused on the intra- and inter-relationships of the city and surrounding regions. Still other contributions have been made by such groups as the human ecologists, whose work is exemplified by R. D. McKenzie and R. F. Park (Mason, 1973), and by the social physicists (Warntz, 1950).

Of particular interest in this paper, however, is a specific focus on the various dimensions of retail market areas. A series of generalizations have emerged on the shape and structure of market areas but gaps still exist in our knowledge. Thus, the specific foci of this paper are (1) to review existing generalizations on the shape and structure of retail markets; (2) to review existing generalizations on consumer behavior and market organization as related to the shape and structure of markets; and (3) to identify existing gaps in our knowledge of the spatial and temporal dimensions of consumer and market behavior and to offer suggestions for further research.


Numerous writers have contributed to the literature on the shape of retail markets. The major theoretical breakthroughs, however, were by Walter Christaller and August Losch (Baskin, 1957), both of whom base their theories on the behavior of retailers and consumers over time and in space.

Christaller's theory begins with the smallest unit of human settlement which provides goods and services for a surrounding region. He termed these central functions and the surrounding region a central place, which he stated would be located at the center of minimum aggregate travel. He further assumes identical consumers, distributed with uniform densities over an unbounded plain with equal accessibility from all points of the surrounding region, and uniform purchasing power. He then determined that a hexagonal market area would require the least average distance for movement to the centers by consumers. He then assumes a hierarchy of settlements with a distinct order of magnitude (size). Each order contains a fixed number, k, of settlements for each settlement of the order above. For instance, in Christaller's model k is assumed to be seven; thus, for each city there will be six surrounding towns (in addition to the town contained within the city) in its direct sphere of influence and for each town six surrounding villages. The assumption of a constant k restricts the number of consumers in a market area. Also, the larger the center the more extensive is the market area and the greater the specialization of services. Lastly, to assign different activities to different markets, Christaller introduces the concept of the "range of a good" which establishes the level below which an insufficient number of consumers exists to support a specified type of activity (Bunge, 1973). Christaller's resulting market areas are shown in Figure 1.

August Losch also starts with the smallest unit of settlement, but proceeds differently from Christaller. He assumes that the cost of transportation increases with distance. Thus, price is higher at the edges of a market and the demand is lower. This result yields a demand cone, as shown in Figure 2, where PQ equals the quantity demanded at the market center. Demand is assumed to decrease along PF as distance increases from Q to F. He then computes the volume of the demand cone as a measure of total demand and shows that when a plain is filled with market areas and the demand curve PF is assumed to be a straight line, a hexagonal based cone as shown in Figure 3 will yield more volume than any other configuration (Bunge, p. 136-137).




Source: William Bunge, Theoretical Geograwhs, Lund Studies in Geography, Series C, General and Mathematical Geography, No. 1. The Royal University of Lund, Sweden (C.W.K. Gleerup, 1973) pp. 136-137.

In a manner comparable to Christaller, Losch assumes uniform distribution of population and hexagonal market areas. However, his system does not have the rigidity of Christaller in that he does not assume, except as a special case, a fixed k. Thus a larger number of market areas may exist. Further, larger settlements do not necessarily contain all of the activities of smaller settlements or the same activities in communities of the same size.

The noted geographer Brian Berry (1967, P. 724 highlights the Christaller and Losch models as follows:

Both Christaller and Losch agree that the triangular arrangement of production sites or retail stores, and hexagonal market areas, represents an optimum for a single good, under the assumption of uniform densities on an unbounded plain, with equal access in all directions. Losch provides explicit proof of this. In the solution, the location of individual firms is as advantageous as possible, every consumer receives service, abnormal profits disappear, market areas are as small as possible, and the boundaries of market areas are points of consumer indifference

Christaller's formulation appears most relevant for understanding the geography of retail and service business, whereas that of Losch provides a framework for analyzing the spatial distribution of market-oriented manufacturing. Christaller's agglomerative requirement, for example, is compatible with the idea of travel-cost minimization by rational consumers on multi-purpose trips, a condition not satisfied by Losch.

An additional refinement of Christaller's work was made by Brian Berry and William Garrison (1958). They removed the limiting assumption of uniform purchasing power which is essential to the arrangement of hexagonal market areas. Their theory was reformulated in terms of threshold and range. Threshold was defined as the minimum purchasing power necessary to support the supply of a good from a center. Christaller earlier defined the range as the maximum distance a consumer would be willing to travel to purchase a good offered at a given place. This limit is of course determined by competition among the centers supplying the same good, as well as other factors.

Berry and Garrison, however, have been criticized for equating threshold functions with the population of central places rather than with that of their market areas (Haggert and Gunawardena). Indeed, much of the criticism of central place theory focuses on its overly narrow concept of demand. Further, various studies have shown that the assumptions of the model are affected by such factors as varying population density, physical isolating mechanisms, intervening opportunities, community size, shopping habits, and differing socio-economic profiles of consumers (Mason and Moore, 1970). Lastly, it has been established empirically that consumers do not necessarily patronize the nearest center, as assumed by central place theory.

Further, the literature on central place theory does not make a major distinction between interurban and suburban markets. One can argue that theoretically the market boundaries established by central place theory are arbitrary. However, consumer patronage in rural areas tends to yield patterns compatible with the theory. As Peter Simons (1973-74, p.72) says, "Results indicate that distance is an important influence on consumer choice in rural areas and that an assumption of rational spatial action may have some relevance in these situations. So it seems reasonable to suggest that, in the interurban case, the shape of the profile derived from central place theory may be an adequate first approximation of the structure of retail market areas."

Finally, Peter Scott (1970, p. 16) has commented as follows in summarizing the criticisms of central place theory as it exists today:

Undoubtedly the most serious limitations of central place theory...stem not so much from its treatment of demand, important though these limitations are, as from its concept of production. Since in retailing the decision-making unit is the firm, and most retail firms sell a variety of goods the range of a good is affected by the product mix and the pricing policy of individual establishments. These considerations are in turn influenced by the organizational structure of firms and the extent to which they enjoy internal economies of scale....But because the central place model is static, deterministic, and retrospective it cannot be used to predict the functions of shopping centers given the differential growth of multi-product firms and the organizational behavior of retailing. Nor can central place theory shed light on the internal arrangements of shops within centers, which necessarily invoke considerations of site, rent, and external economies of scale.

In spite of these criticisms, however, Berry and Pred (1961) conclude that empirical evidence from different parts of the world supports in general terms the concept of a hierarchial structure of retail outlets and centers (also, Olson, 1965).

Based on an overall evaluation of the various studies relative to the shape of trading areas, two well-known marketing geographers, William Applebaum and Saul Cohen (1961), have concluded that the shape of trading areas is not circular in the most general terms, but is elliptical, with the longer axis tending away from the CBD (Applebaum and Cohen, 1961). Simons (1973-74, p.68) states that "if a set of these irregular ellipses is converted to irregular hexagons, the result is a replica of that developed by Isard when he adjusted Losch's regular hexagons."

However, the assumption in central place theory that a central place will have complete and uniform penetration within the defined market area is unrealistic and one must turn to other sources of information for generalizations on consumer behavior within defined market areas. Thus, a focus on the internal structure of markets is necessary for a more nearly complete portrait of retail markets.


The gravity model in one form or another is the basis for most generalizations on the internal structure of markets. Broadly speaking, the gravity concept postulates that an attracting force of interaction between two areas of human activity (perhaps two cities) is created by two population masses and that a friction of movement is created by the spatial separation over which the interaction must occur (Carrothers, 1956). Interaction between two areas of population is a direct function of the size of the masses and an inverse function of the distance between them.

The earliest formulation of this concept was by H. C. Carey (1858). E. G. Ravenstein (1885) presented empirical evidence that migratory movement is to cities of large population and that the volume of movement decreases with distance.

George Zipf (1946) developed a different gravitational concept to determine the "force" of interaction between two concentrations of population. He stated that the number, sizes, and locations of communities theoretically depend on the minimization of the work of transporting mass over distance. Therefore, there are equilibria between opposing forces of unification and diversification. As a result, the interchange of items between communities P1 and P2 will be inversely proportionate to their intervening easiest transportation distance D. Given knowledge of D, the interchange of the masses (given knowledge of price-quantity relationships) will be directly proportionate to P1 P2/D for any two cities in the economy.

Samuel A. Stouffer (1940) modified the gravity flow concept in attempting to measure the mobility of population. The concept, which was empirically studied, assumes no necessary relationship between mobility and distance; rather, the concept of intervening opportunities was introduced. The contention was that "the number of persons going a given distance is directly proportional to the number of opportunities at that distance and inversely proportional to the number of intervening opportunities." [Opportunities must be precisely defined in any use of the theory. The particular definition that is appropriate will depend on the type of social situation investigated, for distribution of opportunities for secretaries would necessarily be different from the distribution of opportunities for unskilled labor.]

Traditional gravity formulations, as is evident from above, however, are inadequate to explain the complexity of factors that determine the economic potential for an intra-city population to support a proposed retail establishment. For example, the gravity concept is based on a notion of ceteris paribus. This restriction allows a concentration only on the two basic variables of distance and mass, and the factors which can be encompassed in these variables. [Carrothers has gone so far as to suggest that the distance exponent itself may be a variable which is inversely related to the size of the population and the distance itself (Carrothers, 1956). He also suggested that populations of different sizes should be raised to variable powers to reflect the effects of agglomeration economies.] This two-dimensional nature thus forces the consideration of the problem in an unrealistic frame.

These models are also designed to account only for the behavior of large groups of people. [Among other problems related to disaggregation and stratification is the problem of attaching exponents as weights to determine the attraction power between and among areas. In fact, this must be experimentally determined and, even though the computer may speed the process, the researcher is still confronted with the "fit" question.] As David Huff (1962[a], p. 64) has stated of the gravity model, "It rests on the assumption that group behavior is predictable on the basis of mathematical probability because the idiosyncracies of any one individual or small group tend to be canceled out." Since disaggregation is at best difficult, making predictions requires that the parameters of spatial interaction must be assumed to be the same for all people (Isard, 1960). The only explicit variations that have so far been given recognition in the literature are those associated with differences generated by different trip types.

When the attempt is made to employ the model as more than a descriptive tool, even more difficult problems are encountered. (Neidercorn and Bechdolt, 1969). Specifically, a lack of theory exists to explain the workings of the model. The results obtained do not explain why observed regularities occur as they do; consequently, one is at a loss when discrepancies occur that cannot be accounted for within the model parameters. [Some studies contend that the yields of the gravity model should be viewed as theory and not as empirical regularity (Neidercorn and Bechdolt, 1969). Other studies have also established that Reilly's law on occasion yields results not in harmony with reality (Jung, 1959).] Finally, examination of choice processes in retail site selection also is not possible, especially in the earlier models which relied wholly on secondary data and essentially administrative markets (Mason and Moore, 1969). Donald Thompson (1966, p. 6) says of the early models that "Such laws must be regarded as little more than historical 'accidents' in absence of tracing out a theoretical connection between their empirically determined weights and exponents and the corresponding behavioral variables on which they rest....Using such models for forecasting or planning is potentially disastrous in absence of knowledge of the true underlying variables." This is particularly true if the forecast doesn't work, and points out the ever present epistemic gap between concepts and operations.

In the early 1960's an attempt was made by Huff to bridge the gap between consumer behavior and the gravity formulation. Huff's model using Luce's choice axiom as the theoretical foundation (Huff, 1963 and 1964; Huff, Huff, Gambini and Jenks, 1968) assumed the following: consumers (1) isolate a subset of alternative shopping center choices from a much larger set consisting of all possible alternatives; (2) calculate a positive measure of utility for each of these perceived alternatives; (3) distribute their retail patronage spatially in probabilistic fashion. (Huff, 1962[b]). The two key operational (empirical) variables in his model are floor space and travel time. One of its primary contributions is the ability to distribute expenditures among more than two centers by the use of probability indifference curves. The model, however, lacks.the richness Huff himself called for in two excellent articles written prior to the publication of the model (1960 and 1961).

Louis Bucklin (1967) raises also the caution flag on the use of travel time in this type of model. His research revealed that travel time to different facilities varies widely by time of day and day of week. He also highlighted the influence of socio-economic factors on consumer travel and the different market areas for different types of goods. Bucklin (Oct. 1967) also gives support to the notion of a curved distance function.

Thompson (1966, p. 8) has stated of the Huff model that "the model is not fundamentally different in terms of calculation of the exponents from the model of Reilly," while Scott (1970, p. 175) also made a similar observation. Thompson (p. 9) further offers the comment that "one may question whether in the consumer choice process implicit in the definition of a subset of alternatives Huff has assumed away one of the critical variables in the choice process, i.e., the less than perfect ability of the consumer to 'see' or perceive the urban or suburban environment in all of its objective complexity."

In commenting on gravity models in general, Simons (1973-74) states as follows

...the 'accuracy' of the model is usually a result of 'calibrating' the model to fit particular situations; that is, the distance exponent is adjusted to the data being analyzed. It is hardly surprising that this kind of procedure has led to large variations in distance exponent values....However, variations in the exponent when estimated in such a fashion are not solely attributable to the independent variable of distance. What is happening, in fact, is that distance operates as a kind of error term for all other independent variables; it is an error term for variables in the equation and for others in the area being studied. Therefore, the supposed 'accuracy' of the gravity model is largely a result of an almost classic example of circular reasoning.

Scott (1970, p. 178) has succinctly summarized the overall problems and shortcomings of the gravity model as follows:

...the retail gravity model continues to pose problems when used to predict retail requirements. The problems include inter alia the definition of the study area and its constituent zones; the availability of data; the need for analysis by type of trade, social structure, and travel mode, the choice for measures of attraction and friction, the calibration of the model given only current data, the implicit assumptions concerning consumer and entrepreneurial behavior, the conversion of sales into floor-space; and the range of technological change and institutional decision-making for which reliable forecasts cannot be made. In short, the model is undoubtedly a valuable tool for preliminary macro-analysis but it remains essentially static, descriptive, and superficial.

Thompson (1966, p. 17) correctly views the state of the literature on retail area markets when he states that "it is not possible to identify a single profile shape [or so many as to be useless], indicative of the structure of retail market areas. The indeterminant nature of the structural dimension is a result of variations in the importance of distance and in the effort consumers are willing to make to purchase goods. Existing theory in this area is either poorly developed, too restrictive, or has conceptual problems."

This paper thus far has focused essentially on the gravity model and central place theory as providing the key thrusts in research on the structure and shape, respectively, of market areas. Meaningful contributions have also been made in terms of various facts of movement theory which offer promise of breakthroughs, particularly in the structural dimensions of trading areas. However, this body of knowledge is not nearly as well developed as is the literature on gravity models. The two are obviously related, however, and movement theory does seem to offer future directions for research.

Harold Hotelling (1921) more than 50 years ago presented a theory of human movement stated in terms of heat flow. He applied his model to human migration in illustrating the historical western migration of population in the United States. Martin Beckmann (1957) has applied hydrodynamic theory to economic and population geography with meaningful results. In his work he related hydrodynamic theory to social physics and the potential of population. Paul Richards (1956) has also applied fluid theory to the movement of automobiles on roads and the friction of space which is encountered. This has yielded promising theoretical constructs on the frictions of spatial interaction.

Kinetic gas theory has also inspired relatively numerous movement theories which have been applied to ecology, to studies of contagious diseases, and to the problems of spatial distribution and spread of animals over time. Neyman and Scott (1957) provide a good literature review on spatial distribution and spread in the context of kinetic gas theory. Torsten Hagerstrand (1952) was the first geographer to develop statistical movement theory. He applied it to peoples and ideas as a foundation for much of his work on the diffusion of ideas. His findings also offer relevance for the study of consumer movement in a spatial and a temporal context. The various ideas embodied in these diverse disciplinary thrusts serve to illustrate the diversity of talent focusing on the spatial and temporal dimensions of human behavior. However, the most immediately promising research is in the micro-analytic dimensions of behavior--particularly imagery research and action space formation as these relate to interaction with the retail structure of an area.


Numerous researchers have built conceptual frameworks using the costs and utilities of travel as a basis for relating consumer search propensities to retail area structure in their efforts to overcome the deficiencies of macro-models of behavior. All of these efforts, however, have been predicated on an "economic man" who objectively evaluates revenues and costs, utilities and disutilities, and who then makes a decision which will maximize these utilities (Cox, 1959). One of the more promising departures from these assumptions is imagery research as applied to the geographic distribution of retail patronage, particularly the work of Kevin Lynch. (Lynch, 1960). Despite the spatial implications of such research, the imagery concept has yet to be applied to the analysis of retail area structure. However, Thompson (1966, p. 17), following his literature review in 1966, suggested the following hypothesis: "the fundamental factor affecting the geographic distribution of retail trade is the manner in which consumers organize their perceptions of the external environment with which they are faced." In a similar vein, John Nystuen (1967),in commenting upon efforts to develop a theory of intraurban consumer behavior, states that "existing...theory is not even adequate for considering the role of customer travel behavior in creating interaction between store types." The general conclusion of Lynch (1960) is that there is a highly subjective orientation of the individual to the urban environment.

An approach in some ways conceptually analogous to image formation is that of action space formation which has been subjected to limited empirical testing. Frank Horton and David R. Reynolds (1970), in a recent report on action space formation, prefaced their work as follows:

Isard has suggested that variations in individual space and time preferences are so great as to preclude any economic rationalization of individual travel behavior. Thus far, Isard's pessimism seems to have been justified in that deterministic economic models, with their built-in assumptions of economic rationality, have been noteworthy for their lack of success in accounting for spatial behavior) except at a highly aggregative level. It would appear appropriate, therefore, to adopt a behavioral approach that examines the formulation of the individual's action space and his resulting travel behavior as a function of his socio-economic characteristics, his cognitive images of the urban environment, and his preferences for travel.

The authors point out that all attempts to use variables useful at the aggregate level in explaining travel behavior have not been useful at the level of individual movement because "Factors that are important conditioners of mass behavior (such as employment rate, median income, etc.) are devoid of behavioral meaning at a less aggregate level. A better understanding of the household's travel behavior demands that more research be directed toward discerning fundamental processes underlying this behavior." (p. 138). Action space formation is one such process. The author concurs with their assessment and supports Thompson's assessment (1966, p. 17) that, in commenting on efforts to blend the macro and micro aspects of behavioral analysis, "running through this literature one finds the twin threads of shallow empiricism and unrelated or unapplied theory. Before further research is undertaken in the former area [macro-analysis], it would seem only logical that an attempt be made first to bridge the gap between the two [macro and micro]."


The gaps in the literature are numerous, but the following suggestions may present the way for at least a limited amount of needed additional research:

1. An effort needs to be made to determine whether the division of consumer patronage between various centers in non-urban areas is distinct or whether it tends to overlap. The key question is whether rational spatial action in terms of distance works to a greater extent in non-urban areas than in urban areas.

2. An independent method needs to be developed for estimating the distance exponents for particular situations as opposed to deriving them for each area and calibrating gravity models in this way.

3. Research needs to be done to determine whether a different profile market shape exists for every commodity in every retail store or whether a single generalized profile shape can be developed.

4. More research needs to be conducted to determine the extent to which market area profiles vary with time.

5. It remains to be determined whether the least effort behavioral strategy which rational spatial action dictates is important in the choice of a particular center in a highly urbanized area. This question becomes particularly relevant given the duplication of retail facilities, the high overlap of market areas, and the high level of accessibility by consumers to retail facilities in highly urbanized areas.

6. A theoretical construct needs to be developed which will reflect the problem of variations in individual effort relative to the search for given types of commodities.

7. Research needs to be conducted to determine the extent to which an individual's travel behavior is in equilibrium with the objective structure of the city, and the effects of such variables as differences in race, social status, education, etc. on action space formation.

8. An effort is needed to develop, in theoretical terms, why the distribution of customers around a center should assume the shape of a normal curve, or perhaps more fundamentally whether such an occurrence actually happens.

9. We need to determine the effects of the consumer's subjective interpretation of the objective landscape on resulting patronage decisions in developing a more viable theory of consumer demand within the context of the spatial and temporal dimensions of market behavior.


Applebaum, W. & Cohen, S. The dynamics of store trading areas and market equilibrium. Annals of Association of American Geographers, 1961, 51, 81-83.

Baskin, C. W. A critique and translation of Walter Christaller's Die Zentralen Orte in Suddeutschland. Unpublished doctoral dissertation, University of Virginia, 1957.

Beckmann, M. On the equilibrium distribution of population in space. Bulletin of Mathematical Biophysics, 1957, 19, 81-90.

Berry, B. & Horton, F. Geographic perspectives on Urban systems. Englewood Cliffs, N.J.: Prentice-Hall, 1970.

Berry, B. & Garrison, W. A note on central place theory and the range of a good. Economic Geography, 1958, 34, 304-311.

Berry, B. Geography of market centers and Retail distribution. Englewood Cliffs, N.J.: Prentice-Hall, 1967.

Berry, B. & Pred, A. Central Place Studies: A bibliography of theory and applications.

Bucklin, L. Shopping patterns in urban areas. Berkeley: University of California, Institute of Business and Economic Research. 1967

Bucklin, L. The concept of mass in intra-urban shopping. Journal of Marketing, 1967, 31 (4), 37-42.

Bunge, W. W. Theoretical geography. Lund Studies in Geography, Series C. General and Mathematical Geography, No. 1. The Royal University of Lund, Sweden: C.W.K. Gleerup, 1973, 136-137.

Carey, H. C. Principles of Social Science. Philadelphia: J. B. Lippincott and Co., 1858.

Carrothers, G.A.P. An historical review of the gravity and potential concepts of human interaction. American institute of planners, 1956, 22, 94.

Christaller, W. Central places in southern Germany. Englewood Cliffs, N.J.: Prentice-Hall. 1966.

Cox, R. Consumer convenience and the retail structure of cities. Journal of Marketing, 1959, 23,

Fetter, F. A. The economic law of market areas. Quarterly Journal of Economics, 1924, 38, 520-529.

Fite, G. X Reese, J. E. An economic history of the United States. Boston: Houghton Mifflin, 1965.

Gambini, R., Huff, D. L., & Jenks, G. F. Geometric properties of market areas. Papers and Proceedings of Regional Science Association, 1968, 20, 85-92.

Greenhut, M. The size and shape of the market area of the firm. Southern Economic Journal, 1952, 19, 37-50.

Hagerstrand, T. The propagation of innovation waves. Lund Studies in Geography, Series B. Human Geography, No. 3. Sweden: Royal University of Lund, 1952.

Haggett, P. & Gunawardena, K. A. Determinants of population thresholds for settlement functions by the Reed-Muench method. Professional Geographer, 1963, 16, 6-9.

Hoover, E. M. The location of economic activitY. New York: McGraw-Hill Book Co.. 1948.

Horton, F. E. & Reynolds, D. R. Action space formation: a behavioral approach to predicting urban travel behavior. Travel Analysis. Highway Research Record 322. Washington, D. C.: Highway Research Board of the National Academy of Sciences, 1970.

Hotelling, H. A mathematical theory of migration. Unpublished masters thesis, University of Washington, 1921.

Huff, D. L. A note on the limitations of intra-urban gravity models. Land Economics, 1962(a), 38, 64.

Huff, D. L. A probabilistic analysis of shopping center trade areas. Land Economics, 1963, 39, 81-90.

Huff, D. L. Defining and estimating a trading area. Journal of Marketing, 1964, 28, 36-38.

Huff, D. L. A probabilistic analysis of consumer spatial behavior. In W.S. Decker (Ed.), Emerging Concepts in marketing. Chicago: American Marketing Association, 1962(b).

Huff, D. L. A topographical model of consumer space references. Papers and Proceedings of the Regional Science Association, 1960, 6, 159-173.

Huff, D. L. Ecological characteristics of consumer behavior. Papers and Proceedings of Regional Science Association, 1961, 7, 19-28.

Isard, W. Location and space economy: A general theory relating to industrial location, market areas, land use, trade and Urban Structure. Cambridge, Mass. The M.I.T. Press, 1956.

Isard, W. Methods of regional analysis. Cambridge, Mass.: The M.I.T. Press, 1960.

Jung, A. F. Is Reilly's law of retail gravitation always true? Journal of Marketing, 1959, 24, 62-63.

Losch, A. The economics of location. Translated by William H. Woglom and Wolfgang F. Stolper. New Haven: Yale University Press, 1954.

Lynch, K. The image of the city. Cambridge: The M.I.T. Press, 1960.

Mason, J. B. Theories of urban development: Comparative regional planning and development. Washington, D.C.: Government Affairs Institute and United States Department of State, 1973.

Mason, J. B. & Moore, C. T. An empirical appraisal of behavioristic assumptions in trading area studies. Journal of Retailing, 1970-71, 46, 31-37.

Mason, J. B. & Moore, C. T. The corridorized concept of household shopping highway travel behavior. Annals of Regional Science, 1970, 4, 69-80.

Mason, J. B. & Moore, C. T. The reliability of census data in trading area analysis and store location studies. Mississippi Valley Journal of Business and Economics, 1969, 5, 68-72.

Moore, C. T. & Mayer, M. L. The uses of gravity models as measures of retail trade area potential and the influence of interstate highways. Paper presented at the Southwestern Social Sciences Association Annual Meeting, Dallas, Texas, Spring 1966.

Moore, C. T. & Mason, J. B. Major retail center patronage decisions. Journal of Marketing, 1969, 33 (3), 61-63.

Mulvihill, D. & Mulvihill, R. Geography, marketing, and urban growth. New York: Van Nostrand Reinhold, 1970.

Neidercorn, J. H. & Bechdolt, B. W. An economic derivation of the gravity law of spatial interaction. Journal of Regional Science, 1969, 9, 273-282.

Neyman, J. & Scott, E. L. On a mathematical theory of population conceived as a conglomeration of clusters. Cold Spring Harbor Symposia on Quantitative Biology, 1957, 22, 109-120.

Nystuen, J. D. A theory and simulation of intra-urban travel. In W. L. Garrison and D. F. Marble (Eds.), Quantitative geography, Part I: Economic and cultural topics and dimensions of micro-behavior. Evanston, Ill.: Northwestern University, Department of Geography 1967.

Olson, G. Distance and human interaction: A review and bibliography. Regional Science Research Institute Bibliography Series No. 2. Philadelphia: Regional Science Research Institute, 1965.

Ravenstein, E. G. The laws of migration. Journal of the Royal Statistical Society, 1885, 48, 167-235.

Revzan, D. A geography of marketing: Integrative Statement. Berkeley: Institute for Business and Economic Research, 1968.

Revzan, D. A geography of marketing: Resource bibliography. Berkeley: Institute for Business and Economic Research, 1968.

Richards, P. Shock waves on the highway. Journal of the Operations Research Society of America, 1956, 6, 42-51.

Schwartz, G. Development of marketing theory. Especially Ch. 2 entitled "Laws of Retail Gravitation." Cincinnati, Ohio: Southwestern Publishing Co., 1963.

Scott, P. Geography and retailing. Chicago, Ill.: Aldine Publishing Co., 1970.

Simons, P. L. The shape of suburban retail market areas; Implications from a literature review. Journal of Retailing, 1973-74, 49, 65-78.

Stouffer, S. A. Intervening opportunities: A theory relating mobility and distance. American Sociological Review, 1940, 5, 845-857.

Thompson, D. Future directions in retail area research. Economic Geography, 1966, 42, 6.

Von Thunen, J. H. Der isoleite staat: In Peter Hall (Ed.), Von Thunen's Isolated State. New York: Pergamon Press, 1966.

Warntz, W. Potential of population and its relationship to marketing. In Reavis Cox and Wroe Alderson (Eds.), Theory in marketing. Chicago, Ill. Richard D. Irwin. 1950.

Weber, A. The theory of the location of industry. Translated by C. J. Friedrich. Chicago, Ill.: The University of Chicago Press, 1929.

Zipf, G. K. The P,P2/D hypothesis: On the inter-city movement of persons. American Sociological Review, 1946, 11, 677-689.