Abstract
We examine how product and pricing decisions of retail gasoline stations depend on local market demographics and the degree of competitive intensity in the market. We are able to shed light on the observed empirical phenomenon that proximate gasoline stations price very similarly in some markets, but very differently in other markets. Our analysis of product design and price competition between firms integrates two critical dimensions of heterogeneity across consumers: Consumers differ in their locations and in their travel costs, as in models of horizontal differentiation. They also differ in their relative preference or valuations for product quality dimensions, in terms of the offered station services (such as pay-at-pump, number of service bays or other added services), as in models of vertical differentiation. We find that the degree of local competitive intensity and the dispersion in consumer incomes are sufficient to explain variations in the product and pricing choices of competing firms. Closely located retailers who face sufficient income dispersion across consumers in a local market may differentiate on product design and pricing strategies. In contrast, retailers that are farther apart from each other may adopt similar product design and pricing strategies if the market is relatively homogeneous on income. Using empirical survey data on prices and station characteristics gathered across 724 gasoline stations in the St. Louis metropolitan area, and employing a multivariate logit model that predicts the joint probability of stations within a local market differentiating on product design and pricing strategies as a function of market demographics and local competitive intensity, we find strong support for the central implications of the theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Some other papers which model the joint consideration of vertical and horizontal differentiation are Rochet and Stole (2002), Desai (2001) and Schmidt-Mohr and Villas-Boas (2008) in the context of product line competition, and Iyer (1998) in the context of quality screening by a manufacturer of competing retailers in a market, and Coughlan and Soberman (2005) in the context of selling through multiple channels.
The equal size assumption is made to simplify the analysis. Assuming unequal sizes does not change any of the results presented in this section.
While we assume two consumer types, the equilibrium results of the paper generalize to a continuum of consumer types whose valuations θ are uniformly distributed. Also given the spatial model we consider two firms and not multiple firms. But in alternative formulations using, for example, the representative consumer model (Perloff and Salop 1985) we could consider multiple firms and we would expect the effect of greater number of firms to be akin to lesser differentiation between the firms.
This representation of consumer preferences is in the spirit of Mussa and Rosen (1978). Consider a quasi-linear direct utility function U(X, α(Y(θ i ))q j ) + X 0, where X is one unit or none of the focal product, X 0 is a numeraire commodity which is measured in the same units as income, Y(θ i ) is consumer i’s income (which is increasing in θ i ), q j is the quality level at retailer j, and α(Y(θ i )) is an income-based scale on the product \(\big(\frac{\partial\alpha(Y(\theta_{i}))}{\partial Y(\theta_{i})} > 0\big)\). Consumers choose their optimal bundle by maximizing utility subject to the budget constraint p j X + X 0 ≤ Y(θ i ) − τ(Y(θ i ))x ji , where p j is the price paid per-unit of the product, τ(Y(θ i )) is the travel cost such that \(\frac{\partial\tau(Y(\theta_{i}))}{\partial Y(\theta_{i})}>0\) and x ji is consumer i’s distance from retailer j. Assuming small income effects, the consumer’s optimization problem will yield an indirect utility form which can be specialized to (1).
Both price and quality are increasing in θ l as well, because as θ l increases, the average quality valuation in the market goes up.
These conditions imply that for every υ as long as t is small enough, there is an unique asymmetric outcome. And as long as t is large enough, there will be a unique symmetric outcome.
From this point onwards, product design and product quality will be used inter-changeably.
The survey data was collected by a marketing research firm, New Image Marketing Limited, based in Fort Myers, Florida.
Each census tract has multiple – typically one or two, and sometimes three – block groups, and the census tracks demographics at the level of block group within each census tract.
We can alternatively operationalize local markets by observationally classifying stations into different mutually exclusive markets by using a subjective, but consistent, heuristic. For example, in previous research, markets have been defined based on stations that fall within a circle of half a mile or one mile radius. We use census tracts on account of their objective definitions in the U.S. census. However, in an earlier version of this paper we had constructed markets using a subjective heuristic that involved markets with a half mile radius and the qualitative results are similar to what are reported here.
One question pertaining to the use of the census tract as a measure of local markets is whether stations within a census tract compete more with each other than with stations in adjoining census tracts. Since this is more likely to be a problem for stations at the periphery of census tracts, we conducted the following analysis: For each census tract i, we calculated the centroid of the locations of stations within the tract. Denote this centroid by C(i). We then calculated the average distance of stations within census tract i from C(i). Denote this average distance by be d(i). We then identified the peripheral station of census tract i as the station which was farthest from centroid C(i). Denote this peripheral station by P(i). Last, we calculated the distance of P(i) from the centroid of the nearest census tract outside census tract i. Denote this distance by D(i). We found that for 156 out of 186 census tracts in our dataset, d(i) < D(i). We could reject the null hypothesis that a peripheral station is just as likely to be correctly classified as it is to be wrongly classified, in terms of whether the station’s rightful market is its own census tract or not, at the 0.01 level of significance.
For example, suppose a local market has 3 stations. The theoretical maximum visibility is 3*2 = 6.
An alternative measure of locational differentiation is VIS, which represents the effects of relative visibility of these stations from each other.
Note that the multivariate logit model is used to explain multiple correlated binary outcomes, as opposed to the multinomial logit model that is used to explain single multinomial outcomes. Another model that applies to correlated binary outcomes is the multivariate probit model (Ashford and Sowden 1970). However, unlike the multivariate logit, it does not have a likelihood function with an analytical closed-form, which renders it computationally unattractive.
The index GINIOPER for a local market is calculated as \(\sum\limits_{q=1}^{4} Pr(OPER=q)^2\), where Pr(OPER = q) represents the fraction of stations within the market with OPER = q. Similarly, GINIBLDG is calculated as \(\sum\limits_{q=1}^{5} Pr(BLDG=q)^2\), where Pr(BLDG = q) represents the fraction of stations within the market with BLDG = q.
Png and Reitman (1994) document the importance of the number of pumps as a quality differentiation variable.
These results are reported in the Appendix.
These results obtained using VIS are available from the authors.
References
Anderson, S. P., de Palma, A., & Thisse, J. F. (1996). Discrete choice theory of product differentiation. Cambridge: MIT.
Ashford, J. R., & Sowden, R. R. (1970). Multivariate probit analysis. Biometrics, 26(3), 535–546.
Bresnahan, T. F., & Reiss, P. C. (1991). Entry and competition in concentrated markets. Journal of Political Economy, 99(5), 977–1009.
Chan, T. Y., Padmanabhan, V., & Seetharaman, P. B. (2007). An econometric model of location and pricing in the gasoline market. Journal of Marketing Research, 44(4), 622–635.
Coughlan, A. T., & Soberman, D. (2005). Strategic segmentation using outlet malls. International Journal of Research in Marketing, 22(1), 61–86.
D’Aspremont, C., Gabszewicz, J. J., & Thisse, J. F. (1979). On hotelling’s stability in competition. Econometrica, 47(5), 1145–1150.
Dasgupta, P., & Maskin, E. (1986). The existence of equilibrium in discontinuous economic games. The Review of Economic Studies, 53(1), 1–26.
Davis, P. (2005). The effect of local competition on retail prices: The US motion picture exhibition market. Journal of Law and Economics, 48(2), 677–708.
Desai, P. (2001). Quality segmentation in spatial markets: When does cannibalization affect product line design. Marketing Science, 20, 265–283.
Draganska, M., & Jain, D. C. (2006). Consumer preferences and product-line pricing strategies: An empirical analysis. Marketing Science, 25, 164–174
Grizzle, J. E. (1971). Multivariate logit analysis. Biometrics, 27(4), 1057–1062.
Hill, M. S. (1985). Patterns of time use, in time, goods and well-being. In F. Thomas Juster & F. Stafford (Eds.), Survey research center (pp. 133–176). Ann Arbor: University of Michigan.
Hotelling, H. (1929). Stability in competition. Economic Journal, 39(153), 41–57.
Iyer, G. (1998). Coordinating channels under price and non-price competition. Marketing Science, 17(4), 338–355.
Maurizi, A., & Kelly, T. (1978). Prices and consumer information: The benefits of posting retail gasoline prices. Washington DC: American Enterprise Institute.
Mazzeo, M. J. (2002). Product choice and oligopoly market structure. The RAND Journal of Economics, 33(2), 221–242.
Moorthy, K. S. (1988). Product and price competition in a duopoly. Marketing Science, 7(2), 141–168.
Mussa, M., & Rosen, S. (1978). Monopoly and product quality. Journal of Economic Theory, 18(2), 301–317.
Neven, D., & Thisse, J. F. (1990). On quality and variety competition. In J. J. Gabszewicz, J. F. Richard, & L. A. Wolsey (Eds.), Economic decision-making: Games, econometrics and optimization, Chapter 9. Amsterdam: North Holland.
Niraj, R., Padmanabhan, V., & Seetharaman, P. B. (2008). A cross-category model of households incidence and quantity decisions. Marketing Science, 27(2), 225–235.
Perloff, J., & Salop, S. (1985). Equilibrium with product differentiation. Review of Economic Studies, 52, 107–20.
Pinkse, J., Slade, M. E., & Brett, C. (2002). Spatial price competition: A semiparametric approach. Econometrica, 70(3), 1111–1153.
Png, I. P. L., & Reitman, D. (1994). Service time competition. The RAND Journal of Economics, 25(4), 619–634.
Rochet, J. C., & Stole, L. A. (2002). Nonlinear pricing with random participation. Review of Economic Studies, 69, 277–311.
Schmidt-Mohr, U., & Villas-Boas, M. J. (2008). Competitive product lines with quality constraints. Quantitative Marketing and Economics, 6(1), 1–16.
Seim, K. (2004). An empirical model of firm entry with endogenous product-type choices. Working paper, Graduate School of Business, Stanford University.
Shaked, A., & Sutton, J. (1982). Relaxing price competition through product differentiation. The Review of Economic Studies, 49(1), 3–13.
Slade, M. E. (1986). Exogeneity tests of market boundaries applied to petroleum products. The Journal of Industrial Economics, 34(3), 291–303.
Slade, M. E. (1992). Vancouver gasoline price wars: An empirical exercise in uncovering supergame strategies. The Review of Economic Studies, 59(2), 257–276.
Acknowledgements
The authors thank Bart Bronnenberg, Tat Chan, Glenn MacDonald, Frank Mathewson, Jack Mintz, Andy Mitchell, Chakravarthi Narasimhan, Amit Pazgal, J. Miguel Villas-Boas, Ralph Winter, and seminar participants at INSEAD, HKUST, SUNY-Buffalo, and University of Houston for their comments on earlier versions of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
1.1 A.1 Symmetric equilibrium
The second-order conditions \(\frac{\partial^2\pi_{j}(\cdot)}{\partial q_{j}^2} < 0\) imply that \(t > \frac{2\upsilon \theta_{l}}{9(\upsilon + 1))}\). In this range, the reduced-form profit functions are strictly quasi-concave and continuous in q j . From Dasgupta and Maskin (1986), the strict quasi-concavity and the continuity of the reduced-form profit functions are sufficient for the existence of a pure-strategy equilibrium. Consider the range \(t > \frac{2\upsilon \theta_{l}}{9(\upsilon + 1))}\). Simultaneously solving the reaction functions results in the unique symmetric equilibrium reported in the paper.
1.2 A.2 Asymmetric equilibrium
Here we solve for the asymmetric equilibrium of the model, which involves one firm (say, Firm 1) offering higher quality and price and selling to the higher valuation segment, while the other firm offers lower quality and price and sells to the lower valuation segment. Consider the individual rationality and the incentive compatibility constraints for this asymmetric equilibrium shown in Eqs. 6–9. First, it can be noted that given that each firm is selling to one complete segment of consumers, if the incentive compatibility constraint for a firm is binding, then the individual rationality constraint for that firm should be slack. Similarly, if the individual rationality constraint for a firm is binding, the incentive compatibility constraint for that firm must be slack.
Consider now the case when Eqs. 7 and 8 are the binding constraints, while Eqs. 6 and 9 are slack. From Eq. 7, we have p 2 = θ l q 2 − tθ l and p 1 = p 2 + θ h (q 1 − q 2) − tθ h . The profit functions of the two firms are \(\pi_{1} = \frac{p_{1}}{2} - \frac{q_{1}^2}{2}\) and \(\pi_{2} = \frac{p_{2}}{2} - \frac{q_{2}^2}{2}\), from which the equilibrium quality choices are \(q_{1}^* = \frac{\theta_{h}}{2} = \frac{\upsilon \theta_{l}}{2}\) and \(q_{2}^* = \frac{\theta_{l}}{2}\). Therefore, the equilibrium prices are \(p_{1}^* = \frac{\theta_{l}^2}{2}[1+\upsilon(\upsilon-1)]-\\t\theta_{l}(\upsilon+1)\) and \(p_{2}^*=\frac{\theta_{l}^2}{2} - t\theta_{l}\). To identify the condition for the existence of this equilibrium, we use the slack constraints. Specifically, from Eq. 9 we have that \(t < \frac{\theta_{l}}{2} \frac{(\upsilon-1)^2}{\upsilon + 1}\). For the equilibrium quality and price levels, the inequality in Eq. 6 is strictly satisfied. Also we require that the equilibrium prices be positive, which implies that \(p_{2}^*>0\) which implies that \(t < \frac{\theta_{l}}{2}\).
We now have to check to ensure that there is no profitable deviation from the equilibrium strategy for either firm. Let us first look at possible deviations for Firm 2 (the low quality, low price firm), given that Firm 1 is at the equilibrium strategy. Consider a general deviation in which Firm 2 serves 0 < y 2d < 1 high type consumers closest to it, and some 0 < x 2d < 1 low type consumers. Then y 2d is determined by \(\theta_{h} q_{2d} - p_{2d} - t\theta_{h} y_{2d} -[\theta_{h} q_{1}^* - p_{1}^* - t\theta_{h} (1- y_{2d})] = 0\) and x 2d is given by θ l q − p − tθ l x 2d = 0. The deviation profits are \(\pi_{2d} = p_{2d}\big(\frac{y_{2d}+x_{2d}}{2}\big)-\frac{q_{2d}^2}{2}\). We solve first for the optimal p 2d and then substitute it in the profits to then solve for the optimal q 2d . The second-order condition for a maximum with respect to q 2d implies \(t > \frac{9 \upsilon}{8(1+ 2 \upsilon)}\), otherwise π 2d will be at a minimum of zero. Comparing π 2d to the equilibrium profits, it can be shown that when \(t > \frac{9 \upsilon}{8(1+ 2 \upsilon)}\), the equilibrium profits are always higher and, therefore, this deviation cannot be profitable. Next, consider a deviation in which Firm 2 abandons the low type segment and competes only in the high type segment. Again, if 0 < y 2d < 1, high type consumers along the line closest to it buy from Firm 2, then y 2d is given by \(\theta_{h} q_{2d} - p_{2d} - t\theta_{h} y_{2d} -[\theta_{h} q_{1}^* - p_{1}^* - t\theta_{h} (1- y_{2d})] = 0\). The profit for Firm 2 is \(\pi_{2d} = \frac{p_{2d}y_{2d}}{2}-\frac{q_{2d}^2}{2}\). The second-order condition for a maximum is \(t > \frac{\upsilon}{8}\), and in this range the deviation profits are greater than the equilibrium profits. But for \(t < \frac{\upsilon}{8}\) the equilibrium profits are greater than the deviation profits. Finally, there can be a possible deviation in which Firm 2 sells to all the consumers in the market and an analysis similar to that above shows that this deviation is also not possible.
Next we check for possible deviations by Firm 1, i.e., the high quality firm (given that Firm 2 is adopting the equilibrium strategy). Consider a general deviation in which Firm 1 serves 0 < x 1d < 1 low type consumers closest to it and some 0 < y 1d < 1. Then x 1d is determined by \(\theta_{l} q_{1d} -t \theta_{l} x_{1d} - p_{1d} - (\theta_l s_2^* - t\theta_{l} (1-x_{1d})-p_2^*)=0\) and y 1d is given by θ h q 1d − tθ h y 1d − p 1d = 0. Calculations can show that the deviation profits for this case will be lower than the equilibrium profits. Finally, we must check the possible deviation for Firm 1 in which it sells to the entire market. We can show that this deviation is not profitable if \(t < \frac{\upsilon^2 - 2\upsilon-2}{4(\upsilon-3)}\).
Next, for r = 0 and θ l = 1 we need that \(t < \frac{\upsilon^2 -2\upsilon +2}{4(\upsilon +1)}\) for Firm 1’s equilibrium profit to be positive, and \(t < \frac{1}{4}\) for Firm 2’s equilibrium profit to be positive. Collecting all the constraints reported above and identifying the binding constraints we have that the asymmetric equilibrium exists when \(t < \min\{ \frac{(\upsilon-1)^2}{2(\upsilon + 1)} ~,~ \frac{\upsilon^2 - 2\upsilon-2}{4(\upsilon-3)} ~,~ \frac{\upsilon^2 -2\upsilon +2}{4(\upsilon +1)} ~,~ \frac{1}{4}\}\).
The asymmetric equilibrium for the case when Eqs. 6 and 9 are the binding constraints can be solved in a similar fashion.
1.3 A.3 Coefficients of control variables from the trivariate logit model
1.4 A.4 Results from the linear regression model
Rights and permissions
About this article
Cite this article
Iyer, G., Seetharaman, P.B. Too close to be similar: Product and price competition in retail gasoline markets. Quant Mark Econ 6, 205–234 (2008). https://doi.org/10.1007/s11129-008-9038-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11129-008-9038-8
Keywords
- Vertical differentiation
- Horizontal differentiation
- Product competition
- Price competition
- Spatial models
- Multivariate logit
- Retail gasoline markets