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Testing implications of spatial economics models: some evidence from food retailing.

Testing Implications of Spatial Economics Models: Some Evidence from Food Retailing

A major implication of standard economic theory is that adding firms to a market will increase competition and reduce prices. Adding space to the economic problem complicates the analysis and possibly alters this result. Specific sites are strictly limited in that a site cannot be replicated. If only one firm can occupy a given site, then each firm has locational characteristics that cannot be exactly copied by other firms. Thus, the standard assumption of the ability of identical firms to enter and exit the market does not hold.

One of the interesting questions addressed by spatial economics models is the effect on product price (termed mill price in the models) when new firms enter a given spatial market area. Does product price fall, as predicted by standard (nonspatial) economic theory, or is there a different result? Food retailing is an excellent market in which to study this issue. Consumers make frequent visits to retail food outlets, and location of the outlets is important to consumers' transportation costs.

The purpose of this paper is twofold. First, theories of spatial economics are reviewed for their implications about the effect of new entrants on product price, and application is made to food retailing. Second, the effect of an entrant on retail food prices in a given spatial market is tested using a unique data set from supermarkets located in Raleigh, North Carolina.


The spatial economics problem has been modeled as an oligopolistic market. Due to the small number of firms, it is assumed that each firm must take into account the potential responses of competing firms before settling upon a market strategy.

Two conjectures about the potential responses of rival firms dominate the spatial economics literature: the Hotelling-Smithies (H-S) conjecture (Hotelling 1929; Smithies 1941) and the Loschian conjecture (Losch 1954). H-S assumes that each firm conjectures the prices of competitors to be fixed. (1) Under normal assumptions, the model gives results consistent with standard, spaceless theory: the entry of new firms lowers product price.

Capozza and Van Order (1978) show that entry in the H-S conjecture can have the opposite result of raising, rather than lowering, prices. This occurs when firm density is low and consumer transportation costs are a large proportion of total product price at the edge of the market. Capozza and Van Order (1978) also show that the results of the H-S conjecture are qualitatively unaltered for any price conjectural variation between one and minus one, that is, firms react to the price changes of competitors, but they don't react on a one-to-one basis.

The Loschian conjecture assumes that each firm matches price changes by competing firms on a one-to-one basis. (2) Loschian conjecture results in new entrants raising, rather than lowering, product price for the following reason. The Loschian firm assumes its market area is fixed and consequently sets prices like a monopolist within its market area. Firms are subject to demand elasticities that are net of transport costs. When a linear consumer demand is assumed, price elasticity for any given firm increases when transport costs are subtracted from consumer demand. Higher transport costs result in an increase in price elasticity. As new firms enter the market, each firm loses its most distant customers, resulting in a decrease in average transport costs for consumers, a decrease in aggregate price elasticity, and an increase in product price (Benson and Faminow 1985).

This Loschian result, however, is dependent on the assumption of a linear demand curve. Benson (1980a) shows that when a negative exponential demand curve is assumed in the Loschian conjecture, product price falls as new firms enter.

The H-S conjecture as modified by Capozza and Van Order (1978), in which firms react to the price behavior of competitors but not on a one-to-one basis, would seem to be the more applicable spatial economics model for food retailing. In this case, the effect of new entrants on product price depends on the density of food retailing firms in the spatial market and the level of consumer transportation costs as a proportion of retail food costs. Where firm density is low and relative transportation costs are high, product price is more likely to rise as a result of entry. Conversely, where firm density is high and relative transportation costs are low, product price is more likely to fall as a result of entry.

A corollary should be added to this hypothesis. Consumers do not consider alternative retail stores as perfect substitutes. For this reason, when a new store opens in a market area, consumers will form comparisons between the new entrant and each existing store. For existing stores closer to the new store, consumer transportation costs relative to the new store are small and prices will fall with entry. For existing stores farther from the new stores, consumer transportation costs relative to the new store are larger, and the entry effect will become less negative and, perhaps, positive. Thus, distance of an existing store from the new entrant influences the entry effect. The pattern that should be observed is: a negative entry price effect that dissipates with distance of the existing store from the new store. This feature, also called a distance decay feature, has also been developed by Mulligan and Fik (1988, 1989).

Despite the challenge that spatial economics presents for standard economic theory, little empirical testing of the implications of spatial economic models has occurred. Related work has been done by Mulligan and Fik (1988, 1989) and by West (1981a, 1989b). (3) Other studies have examined the relationship between firm concentration and price (see, for example, Greer 1984, p. 296).

In order to provide one direct test of the effect of entry on product prices, data were collected from a spatial retail food market in Raleigh, North Carolina in which entry occurred. The spatial market is an urbanized area approximately five miles in diameter and, initially, there were six supermarkets serving the market (Figure 1). In 1986 a new store opened in the spatial market (see Figure 1). (4)

In order to test the effects of the entry, retail food prices were collected from the six existing stores in the market area for 32 weeks prior to the new store opening and for 16 weeks after the opening. The price data consist of prices for 22 commonly purchased supermarket products randomly selected from Progressive Grocer's list of the 200 most purchased supermarket and grocery products (Table 1). Identical products in terms of brand size and packaging were surveyed at each store. Furthermore, the price data were collected from each store on the same day of the week and at approximately the same time. All stores, including the new store, are conventionally sized supermarkets and are members of major supermarket chains operating in the Southeast. Descriptive statistics are presented in Table 2.

Of course, factors other than the degree of local competition will affect supermarket prices. First, local supermarket product prices are expected to move in line with national average product prices. To control for this effect, each of the 22 supermarket products was matched with a Consumer Price Index (CPI) product category (see Table 1), and the corresponding CPI index numbers were collected and added to the data set. (5) Unfortunately, the CPI index numbers are only available on a monthly, rather than weekly, basis. Thus, the CPI index number was assumed to be the same for each week of the month. This data constraint obviously reduces the estimated precision of the expected positive association between national prices and local prices. (6)

A second important factor affecting local supermarket product prices is individual store amenities or characteristics. Ceteris paribus, stores with faster checkouts, more accessible parking, and more service, to name a few, will be able to charge higher prices. Examination of the effects of individual store characteristics on product price is beyond the scope of this study. However, it is assumed that the composite effect of store characteristics can be controlled by including store dummy variables in the estimation equations.

The entry effect is measured by two variables. The first variable is ENTRY, indicating that the price observation is from a week after the new store opened (week 33 and after). The second variable is an interaction variable between ENTRY and the inverse of the distance between an existing store and the new store: 1/DIST * ENTRY, where DIST is the driving distance between an existing store and the new store and is an approximation of consumer transportation variable costs. Measured in this way, the interaction variable takes a larger value for existing stores closer to the new store. If the negative effect of entry strengthens as distance from the new store decreases, then the interaction term's parameter estimate should be negative.

Two models can be formed, one that includes both entry variables and one that includes only the entry-distance interaction variable. Call these alternative models A and B:

A: P = + [[alpha.sub.2]] * ENTRY + [[alpha.sub.3]] * 1/DIST * ENTRY, B: P = + [[beta.sub.2]] * 1/DIST * ENTRY,

where P is product price, and the other exogenous variables (discussed above) are omitted for simplicity. Under model A, the total effect of entry is [[alpha.sub.2]] + [[alpha.sub.3]] * 1/DIST. This model assumes that when distance (DIST) is infinitely large, making [[alpha.sub.3]] * 1/DIST close to zero, that an entry effect still remains ([[alpha.sub.2]]). Under model B the total effect of entry is [[beta.sub.2]] * 1/DIST. This model assumes that when distance is infinitely large, no entry effect exists. Both models are estimated. (7)

The estimated equations are thus:

MODEL A: [P.sub.ijt] = [delta] + [[alpha.sub.1]] * [] + [[alpha.sub.2]] * ENTRY + [[alpha.sub.3]] * 1/DIST * ENTRY + [[alpha.sub.4]] * STORE2 + [[alpha.sub.5]] * STORE3 + [[alpha.sub.6]] * STORE4 + [[alpha.sub.7]] * STORE5 + [[alpha.sub.8]] * STORE6, and MODEL B: [P.sub.ijt] = [gamma] + [[beta.sub.1]] * [] + [[beta.sub.2]] * 1/DIST * ENTRY + [[beta.sub.3]] * STORE2 + [[beta.sub.4]] * STORE3 + [[beta.sub.5]] * STORE4 + [[beta.sub.6]] * STORE5 + [[beta.sub.6]] * STORE6,

where [P.sub.ijt] is the price of product i at store j for week t, and [] is the Consumer Price Index number for product i for week t. For [], the null hypothesis is [[alpha.sub.1]] = 0 and [[beta.sub.1]] = 0, and the alternative hypothesis is [[alpha.sub.1]] [is greater than] 0 and [[beta.sub.1]] [is greater than] 0. For the entry variables a two-tailed test is used, with the null hypotheses being [[alpha.sub.2]] = 0, [[alpha.sub.3]] = 0, and [[beta.sub.1]] = 0, and the alternative hypotheses being [[alpha.sub.2]] [is not equal to] 0, [[alpha.sub.3]] [is not equal to] 0, and [[beta.sub.2]] [is not equal to] 0. The store effects are tested against STORE1. The null hypotheses are [[alpha.sub.4]] = 0, [[alpha.sub.5]] = 0, [[alpha.sub.6]] = 0, [[alpha.sub.7]] = 0, [[alpha.sub.8]] = 0, and [[beta.sub.3]] = 0, [[beta.sub.4]] = 0, [[beta.sub.5]] = 0, [[beta.sub.6]] = 0, [[beta.sub.7]] = 0, and the alternative hypotheses are [[alpha.sub.4]] [is not equal to] 0, [[alpha.sub.5]] [is not equal to] 0, [[alpha.sub.6]] [is not equal to] 0, [[alpha.sub.7]] [is not equal to] 0, [[alpha.sub.8]] [is not equal to] 0 and [[beta.sub.3]] [is not equal to] 0, [[beta.sub.4]] 0, [[beta.sub.5]] [is not equal to] 0, [[beta.sub.6]] [is not equal to] 0, [[beta.sub.7]] [is not equal to] 0.

Market basket, or composite, prices were also formed to present the analysis in an aggregate form. Weights for each product were taken from the Consumer Price Index detailed relative importance scales for December 1986. The weights were normalized to sum to 1.0. The weights were applied to the product price and to the CPI national index number (which controls for national product price levels) to form aggregate prices for each store for each week. Three weighting systems and sets of aggregate product prices were formed: for all 22 products, for the 16 food products, and for the 6 nonfood products. The aggregate product price in each case was regressed on the aggregate national price index, the entry variable or variables, and the store dummy variables.


The disaggregated models A and B (individual products) are estimated using Zellner's "seemingly unrelated" regression technique corrected for autoregressive disturbances. This technique controls for the likely correlation of error terms across product price equations caused by association between product prices in the same store. The aggregate models A and B (market baskets) are estimated by OLS.

Table 3 presents the parameter estimates for the disaggregated model A. The system weighted [R.sub.2] is 0.45, which is reasonably good for micro-level data. Fifteen of the 22 parameter estimates for the CPI variable are positive (as expected), and 12 of the positive parameter estimates are statistically significant (one-tail test, 10 percent level or better). Only two of the CPI variable parameter estimates are negative and statistically significant. Given the fact that the CPI data are monthly and the local product prices are weekly, these results are better than expected.

Ten of the 22 parameter estimates for the variable ENTRY are positive and statistically significant (two-tail test, 10 percent level or better), and four of the ENTRY parameter estimates are negative and statistically significant. These results indicate that in half of the product cases, the price effect of entry on an existing store infinitely far from the new store is positive. In contrast, 15 of the parameter estimates for the variable (1/DIST * ENTRY) are negative, and 11 of these estimates are statistically significant (two-tail test, 10 percent level or better). Only one of the distance-entry interaction variable parameter estimates is positive and statistically significant (for the product deodorant). Those results indicate that in 50 percent of the product cases, the entry effect varies with distance of the existing store from the new store with the entry effect being more negative the closer the entrant is to an existing store.

The majority of the parameter estimates for the store dummy variables are negative and statistically significant. Since STORE1 is more centrally located in Raleigh and is closest to a major university and to relatively immobile students, it is reasonable that STORE1 commands higher prices through a location premium.

The aggregate, or market basket, results for model A are given in Table 4. None of the parameter estimates for the entry variables is statistically significant. However, these results are obviously sensitive to the weighting scheme selected, and collinearity between ENTRY and 1/DIST * ENTRY (r = .977) reduces the statistical significance of the parameter estimates.

Table 5 gives the estimates of the total entry effect in model A. The existing stores across the top row are arranged from closest to the new store (left-most) to farthest from the new store (right-most). The F-value indicates whether the sum of the parameter estimates [[alpha.sub.2]] + [[alpha.sub.3]] is statistically significant. Thirteen of the 22 total entry effects are statistically significant, and 10 of these effects show the expected dissipating negative effect with distance from the new store--that is, the entry price effect is negative for existing stores closer to the new store, and the negative effect disappears, and in some cases becomes positive, as the distance of existing stores from the new store increases. Only deodorant has a statistically significant total entry effect, which is positive for closer existing stores and negative for existing stores farther from the entrant.

The parameter estimates for model B are given in Table 6 (disaggregated) and Table 7 (aggregate market basket). The results for CPI and for the store dummy variables are similar to the results in model A. The total entry effect is measured by the single variable (1/DIST * ENTRY). Seventeen of the 22 parameter estimates for (1/DIST * ENTRY) are negative, and 11 of these estimates are statistically significant. In only four cases (bread, tomato juice, dishwashing detergent, and fabric softener) are the entry parameter estimates positive and statistically significant. The market basket results (Table 7) show the entry effect to be negative when all products are considered together and when only food products are considered. However, the entry effect is positive and statistically significant for the nonfood market basket.

Both disaggregated models (A and B) give similar results. Among food products, little evidence of a positive total entry effect exists, whereas in 50 percent of the cases in model A and in 69 percent of the cases in model B, a negative total entry effect, which dissipates with distance from the entrant, was found. Among nonfood products there is much less consistency in the results. Disaggregate model A shows two nonfood products with positive total entry effects for stores closest to the entrant, and disaggregate model B shows two nonfood products with positive total entry effects. In addition, aggregate model B shows a negative total entry effect for foods but a positive total entry effect for nonfood products.

These findings suggest that there may be a different effect of entry for food products and for nonfood products. Three possible reasons are offered for this dichotomy. First, supermarkets may behave as Hotelling-Smithies firms for their major sales product, food, and under conditions of relatively high firm density and low consumer transportation costs, an additional competitor results in lower food prices. However, for nonfood products supermarkets may use the Loschian conjecture. In this case the supermarket assumes that, once consumers are attracted to the store by price competition for food products, consumers consider the store to be a monopolistic seller of nonfood products. Under the assumption of a linear demand curve for nonfood products, entry results in higher prices for nonfood products.

A second explanation is that supermarkets may behave as Hotelling-Smithies firms for both food and nonfood products. The entry of a new competitor results in lower prices for food. However, if food and nonfood products purchased in a supermarket are complements, then the reduction in food prices results in an increase in demand for supermarket nonfood products and an increase in nonfood product prices.

Finally, a third explanation is to consider supermarkets as multiproduct class operations with separate objective functions for food and nonfood. The impact of supermarket entry will be different for nonfood products than for food products because supermarket sales of nonfood products must compete with similar sales by drug stores and department stores. (8)


Introducing space into the standard economic model complicates the analysis and leads to different implications. Spatial economic models have shown that under certain assumptions about the firm's price conjectural variation and the consumer's demand curve, product prices can rise as a result of entry.

A modified spatial economics model was proposed that hypothesized that the price effect of an entrant is negative for existing retail stores closer to the entrant, but the negative price effect dissipates, and perhaps turns positive, as distance of an existing store to the new store increased. Analysis of prices of 22 commonly purchased supermarket products at six retail food stores in a market in which entry occurred lent support to this modified model. Results from two alternative empirical models showed the dissipating negative price effect with distance for half of the products. Most of the other product prices showed no sensitivity to entry. However, there was some evidence that the prices of nonfood products behaved differently in response to entry than food prices, with prices falling for food products but rising for nonfood products.

(1) Other assumptions common to the H-S model and to the Loschian model are: (1) production of a single product with constant marginal and fixed costs, (2) constant transport costs per mile for each unit of product, (3) a homogeneous, unbounded plain occupied by consumers at uniform density, (4) a circular market area, (5) firms enter until profits are driven to zero, and (6) linear consumer demand curves. Variations on the spatial economics models, not explored here, can be developed by altering assumption 5 (Capozza and Van Order 1980). Implications concerning altering the assumption about consumer demand curves are explored in the present study.

(2) A spatial model developed by Greenhut, Hwang, and Ohta (1975) uses a price conjectural variation of -- 1. See Watson (1985) for the conditions under which this conjecture can be derived from profit maximizing behavior.

(3) The Mulligan and Fik papers theoretically examine the degree to which the pricing behavior of a spatial oligopolist is linked to the attributes not only of the closest rival, but also to the attributes of all rivals in the market area. The West papers theoretically and empirically examine the question of whether supermarket firms attempt to preempt rivals in their location and construction decisions.

(4) The new store is part of an existing chain in North Carolina but was the first store of the chain to open in the market area.

(5) Marching producer price (PPI) category indices were also used in place of CPI indices; however, the CPI indices performed better in the empirical tests than the PPI indices.

(6) The empirical analysis was also conducted for monthly averages of the supermarket product prices; however, the results were unimproved.

(7) Model A may seem to be the more applicable, but the application here is to a small finite market. Furthermore, the linked oligopolistic model demonstrated by Benson (1980) and by Mulligan and Fik (1988, 1989) shows that entry, through a linked response, can affect even distant firms. This would argue in favor of model A.

(8) An anonymous reviewer suggested this explanation.


Benson, B. L. (1980a), "Loschian Competition Under Alternative Demand Conditions," American Economic Review, 70: 1098-1105.

Benson, B. L. (1980b), "Spatial Competition: Implications for Market Area Delineation in Antimerger Cases," The Antitrust Bulletin, 25: 729-750.

Benson, B. L. and M. D. Faminow (1985), "An Alternative View of Pricing in Retail Food Markets," American Journal of Agricultural Economics, 67: 296-306.

Capozza, Dennis and Robert Van Order (1978), "A Generalized Model of Spatial Competition," American Economic Review, 68: 896-908.

Capozza, Dennis and Robert Van Order (1980), "Unique Equilibria, Pure Profits, and Efficiency in Location Models," American Economic Review, 70: 1046-1053.

Faminow, M. D. and B. L. Benson (1985), "Spatial Economics: Implications for Food Market Response to Retail Price Reporting," Journal of Consumer Affairs, 19: 1-19.

Greenhut, M. L., M. Hwang, and H. Ohta (1975), "Observations on the Shape and Relevance of the Spatial Demand Function," Econometrica, 45: 669-682.

Greer, Douglas F. (1984), Industrial Organization and Public Policy, New York, NY: Macmillan Publishing Company.

Hotelling, Harold (1929), "Stability in Competition," Economic Journal, 39: 41-57.

Losch, August (1954), The Economics of Location, New Haven, CT: Yale University Press.

Mulligan, Gordon F. and Timothy J. Fik (1988), "Price Variation in Spatial Markets: The Case of Inelastic Demand," Discussion Paper 88-9, Department of Geography and Regional Development, University of Arizona.

Mulligan, Gordon F. and Timothy J. Fik (1989), "Price Variation in Spatial Oligopolies," Geographical Analysis, 21.

Smithies, A. W. (1941), "Optimum Location in Spatial Competition," Journal of Political Economy, 49: 423-439.

Watson, J. K. (1985), "A Behavioral Analysis of Negative Price Reactions in Spatial Markets," Southern Economic Journal, 51: 882-885.

West, Douglas S. (1981a), "Testing for Market Preemption Using Sequential Location Data," The Bell Journal of Economics, 12: 129-143.

West, Douglas S. (1981b), "Tests of Two Locational Implications of a Theory of Market Preemption," The Canadian Journal of Economics, 14: 313-326.

Michael L. Walden is a Professor in the Department of Economics and Business at North Carolina State University, Raleigh, North Carolina.

William Levedahl, Craig Newmark, Ron Schrimper, Walter Thurman, and anonymous reviewers provided helpful comments and guidance without contributing to any remaining errors. Margaret Hale provided research assistance.
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Author:Walden, Michael L.
Publication:Journal of Consumer Affairs
Date:Jun 22, 1990
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