Why the Poor May Pay More For Food: Theoretical and Empirical Evidence

Citation:

Howard Kunreuther (1972) ,"Why the Poor May Pay More For Food: Theoretical and Empirical Evidence", in SV - Proceedings of the Third Annual Conference of the Association for Consumer Research, eds. M. Venkatesan, Chicago, IL : Association for Consumer Research, Pages: 660-678.

Proceedings of the Third Annual Conference of the Association for Consumer Research, 1972      Pages 660-678

WHY THE POOR MAY PAY MORE FOR FOOD: THEORETICAL AND EMPIRICAL EVIDENCE

Howard Kunreuther, University of Pennsylvania

[I would like to express my appreciation to Palomona Ferris, Annette Steyer, and Jomo Sunderan for their help in interviewing residents in the New Haven area. William Wells provided helpful comments on an earlier draft of this paper.]

INTRODUCTION

Do the poor pay higher prices for food than their wealthier neighbors? A number of empirical studies have been undertaken in recent years on food price differentials across stores in metropolitan areas and have shed considerable light on this questions (Sexton, 1971). To date the most detailed statistical analysis on whether the urban poor pay more for food than do urban residents with higher incomes is the Alcaly and Klevorick (1971) study of food prices in New York City. On the basis of their statistical regression results for 31 commodities, they conclude that the price of a given commodity in a particular type of store tends to be unaffected by or even rises with an increase in the level of neighborhood income. They also point out, however, that the mean price of each of the items studied is higher in the small independent stores than in the chain stores. To the extent that poor people shop at these smaller stores, they will pay higher prices for the same quality food than if they had purchased their groceries at a chain store.

The Alcaly and Klevorick study has raised a number of interesting questions which deserve further theoretical and empirical study. This paper is an attempt to extend their analysis in both these directions. On the theoretical side, I will suggest a framework for better understanding consumer purchasing decisions by considering grocery items which are packaged in several different sizes. At the empirical level, I will report on the results of a study of household food purchasing decisions undertaken in New Haven during the summer of 1971 which was designed to test these theoretical ideas.

STORE AND SIZE EFFECTS

By standardizing for quality of food items, we should be able to quantify some of the relevant differences in the purchasing behavior of low- and middle-income shoppers. For any given brand, two principal factors to be considered are the "store effect" and the "size effect." The store effect refers to price differentials between stores for the same-sized item. If the price per ounce for any given package size varies inversely with the size of store, then individuals who shop in chains would pay less for identical items than those who patronize smaller grocers. The size effect refers to differences in price per ounce for various sizes of a particular branded item within any given store. If price per ounce varies inversely with size, then poor people who purchase small packages will pay more for the same quantity in the long run than if they had brought a larger size.

It is important to distinguish between these two factors in analyzing purchasing decisions. The store effect provides a measure of the importance of a consumer's location and his mobility on purchasing decisions. We will want to determine not only what price differentials exist between large and small stores but also whether certain offsetting benefits are provided to patrons of a small neighborhood grocer. For example, if shoppers are permitted to charge their purchases then this could partially account for the higher prices in these stores.

The size effect measures the role which budget, storage constraints and costs of holding inventory play in purchasing decisions. If low-income families buy a market basket of goods on their weekly or bi-weekly shopping trip, then they may be forced to purchase smaller sizes as a consequence of a budget constraint. Restrictions imposed by the size of a shopping cart used to carry purchases from the store as well as by limited food storage space in the home will also operate in the same direction. Low consumption rates will discourage large size purchases due to the cost of holding inventory.

To measure the relative importance of store and size effects on purchasing decisions, eight items packaged in at least three different sizes were chosen for detailed study in New Haven. Their prices and availability were tabulated for 11 chain and 11 local neighborhood stores during the week of July 12-16, 1971 (See Appendix A for store descriptions). Table 1 presents the average price per ounce for each of the sizes as well as the differences between t}e large and small stores. For all items surveyed, the average price per ounce declined or remained the same whenever package size increased. Although there were occasional exceptions to this general rule within individual stores, these data indicate the presence of quantity discounts. Looking across all stores surveyed, the percentage savings between purchasing the largest instead of the smallest size ranged from 15 per cent (detergents) to over 50 per cent (mayonnaise), indicating that the size effect may be quite pronounced for packaged goods.

For any given size, there is also a store effect for each of the items, as seen by comparing average price data between large stores and small neighborhood stores. These data are consistent with all of the recent surveys on food-price differentials (Bureau of Labor Statistics, 1966; and Federal Trade Commission, 1969). Table 1 also shows that the smaller neighborhood grocers stock fewer larger-sized items relative to the chain stores. This is undoubtedly due to a combination of their own space constraints and their shoppers' preferences for smaller sizes. Individuals shopping in smaller stores thus pay higher prices than the chain shoppers for identical items, while also having a narrower range of choice. [Store owners of the small independents did indicate that they provided credit to their regular shoppers but did not state the explicit terms, perhaps because they had no formal rules of behavior.]

A MODEL OF HOUSEHOLD FOOD PURCHASING DECISIONS

The data from the New Haven stores suggests that there are significant store and size effects which should affect the family's food purchasing decisions. A simple model incorporating both these factors will now be developed using concepts from the theory of consumer demand.

Consider a family who has a choice of purchasing a combination of n different food commodities. Defining qj to be the consumption rate of item j per unit of time the family's function for the n commodities is

U(q₁, ..., q_n).   (1)

We will make the simplifying assumption, which from our New Haven consumer survey results does not appear unrealistic, that the household has a fixed food budget (B) per unit of time. If pj is the price for item j, the budget constraint can be written as

EQUATION   (2)

TABLE 1

GROCERY STORE PRICES IN NEW HAVEN STORES (JULY, 1971) FOR 11 CHAIN AND LARGE INDEPENDENTS AND 11 SMALL NEIGHBORHOOD STORES

We can derive a demand curve for item j by holding all prices constant except pj and maximizing (1) subject to the budget constraint of (2). [For a standard treatment of this problem, see J. R. Hicks, Value and Capital (Second Edition, London: Oxford University Press, 1957).]

The size effect on consumer purchasing decisions can be incorporated into the analysis by deriving an implicit "supply" schedule for each good. To see this more clearly, assume that the jth item is packaged in m different sizes, 1 being the smallest and m the largest. Let size i contain kij ounces and size at a price per ounce pij. If a quantity discount phenomenon exists, then pi+1/i < pi/j. Since the package size i lasts for ki/j / qj time units, there is an inventory cost associated with storing the unused portion of the good. Let h represent the percentage cost per dollar per unit of time. [There is no reason that h must remain the same for each item. Items which deteriorate more rapidly in quality could have a higher value of h reflecting the spoilage factor. A more detailed discussion of inventory costs as it affects consumer demand appears in H Kunreuther, "The Effect of Quantity Discounts on Consumer Demand: An Application of Inventory Theory," Center for Mathematical Studies in Business and Economic Report No. 7009, University of Chicago, Graduate School of Business, 1970.] The cost per ounce of the ith size per unit of time is then given by

EQUATION    (3)

For each item j the household will want to choose the size i which minimizes C1. From (3) we see that if a quantity discount phenomenon exists, then optimal package size increases as the consumption rate (q.) increases. For a given value of h we can trace out a supply schedule for item j which shows the lowest economic cost per ounce as a function of qj. For specificity, let the unit of time be one year and h = .1. The sold line in Figure 1 represents the supply curve, SS, for catsup based on price data from a chain store in the New Haven area which stocked five different sizes. The points of discontinuity indicate that another package size has become optimal, based on (3). [Equation (3) indicates that it would never be optimal to purchase size 3 for the set of catsup prices in this particular store.] The choice of package size for item j is determined by the intersection of the consumer's demand schedule for catsup, DD, with SS as illustrated by point E1 in Figure 1. Such an intersection will represent a stable equilibrium if the demand schedule cuts the supply schedule from above.

Several implications of the size effect on consumer purchasing decisions can be derived from this model. From (1) ant (2) it can easily be shown that a decrease in B will cause a leftward shift in the demand curves for goods which have a positive income elasticity of demand. If quantity discounts exist, then the optimal purchase size of these items will vary directly with B. A constraint on the amount of space for food can be incorporated through h, which will increase to reflect both the opportunity cost of money as well as a marginal value of extra storage space. From (3) we see that an increase in h will shift the supply curve upward and yield the same or smaller optimal package size for any given value of qj. If low-income families have the most severe storage and budget restrictions, then the above analysis would predict that for any given qj they will purchase the same or smaller packages than middle-income families.

The store effect is reflected in different values of pij across stores and will lead to a shift in the supply curve. To illustrate, consider the dashed supply curve, S'S', in Figure 1 based on prices of catsup in a small local store in New Haven which only stocked three sizes. The price per ounce is higher for each size relative to the chain store, providing a clear illustration of the store effect. In this case, the equilibrium point for the demand curve given by DD is at E2 indicating that size 3, rather than size 4, would have been the optimal one to purchase.

FIGURE 1

OPTIMAL PURCHASE DECISION AS A FUNCTION OF SIZE AND STORE EFFECT

What factors determine the choice of store at which a consumer will purchase his goods? The costs associated with travelling to and from a store may play an important role in the shopper's selection process. Looking at a specific trip, low-income families who have limited mobility will have much higher transportation costs per mile for long-distance travel than middle-income families with automobiles. They are thus more likely to shop at the neighborhood store than to travel some distance to chain stores. In formal terms, suppose a consumer has the choice of shopping at r different food stores. If Fk is the transportation cost per unit of time associated with travelling to and from store k then (2) becomes

EQUATION    (2')

To illustrate how (2') may operate, consider a simple example where r = 2, with store 1 being the nearest chain store and store 2 the local grocer (assumed to be much closer to the household than store 1). If F1 is sufficiently greater than F2, it would be optimal for the poor family to shop at store 2 since the decrease in transportation cost would more than offset the higher food prices at the local store.

EMPIRICAL TESTS OF THE MODEL

To better understand consumers' purchasing decisions and test these theoretical ideas we undertook a survey of 159 households in the New Haven area. A 25% random sample of New Haven residents had been undertaken in 1967 to pretest the 1970 U. S. Census, and for this purpose the city was divided into 13 cap districts with each cap then subdivided into a number of subcaps. Figure 2 details these boundaries and the six subcaps we surveyed. Some of the detailed economic data which were collected in 1967 are summarized in Table 2. As can be seen from the income data the first three subcaps (2-2, 3-2, 14-1) are relatively well-to-do areas of the city while the other three (7-8, 1-1, 5-4) are relatively poor sections. By combining these subcaps to form an upper-middle-income group and a low-income group it is possible for us to make preliminary comparisons as to differences in food purchasing patterns as a function of income.

We interviewed between 25 and 30 families chosen on a quota sampling basis in each of the subcaps to better understand their shopping patterns and their purchase size decision (See questionnaire in Appendix B). Except for subcap 2-2 (where a number of residents were reluctant to answer doorbells), approximately 90 per cent of the housewives were willing to be interviewed. A Malaysian student interviewed in the black areas and two white female graduate students covered the other subcaps. The final sample comprised 78 housewives in the middle-income group and 81 in the low-income bracket .

Based on the above consumer purchasing model, two hypotheses, one related to the store effect and the other to the size effect. were formulated:

FIGURE

1967 CENSUS

TABLE 2

ECONOMIC DATA ON SIX SUBCAPS IN NEW HAVEN

Store Effect Hypothesis. Low-income families will be more limited in mobility than middle-income families and hence will be more prone to shop in stores close to their homes. Given the relatively few chain stores in these areas the percentage of low-income consumers shopping at small neighborhood stores will be significantly higher than for middle-income consumers.

Size Effect Hypothesis. Consider a low- and middle-income household each with identical family size and identical per capita consumption rates for a given item. Due to more stringent budget and storage constraints, the low-income family will tend to purchase a smaller-sized package than will a middle-income family. As family size increases we would expect to find a higher total consumption rate per unit of time for most items and hence a preference for larger-sized packages.

Table 3 presents summary data on the store effect for the two m come groups, Only five per cent of middle-income families shop at small neighborhood stores while over 60 per cent of the low-income families do their primary shopping at the small local grocer. One reason for this difference in shopping patterns is provided by the data on mode of transportation and distance travelled to the store. A sizable proportion of low-income families use public transportation or walk to their local grocery store while practically all middle-income families drive automobiles to a chain. This is also reflected in figures on the average distance travelled: 1.9 miles for the low-income group and 3.6 miles for the middle-income group. [If there were fewer stores per square mile in the middle-income area in comparison with the low-income sections, then this would provide an alternative explanation with respect to differences in distance travelled.]

Due to the limitations of the questionnaire data we were only partially successful in measuring the magnitude of the size effect. Our own budget and time constraints prevented us from making detailed pantry checks so that we had to rely on perceptual answers regarding "number of sizes available in your store," "size of purchase" and "frequency of purchase." Interestingly enough, Table 4 indicates that for the eight items chosen for detailed study the average low-income family perceived at least the same number of available sizes as the middle-income shopper did. Despite the larger average family size in low-income households, their ratio of actual purchase size to number of sizes perceived was lower than for middle-income families on all items except applesauce.

Table 4 also shows that low-income families purchased all eight items more frequently than middle-income families. This could be due to the presence of budget and storage constraints and/or different consumption rates for the two groups. From Table 4 we can see that low-income families had more restrictive per capita food budgets on the average than middle-income families and a greater percentage of them perceived inadequate storage space. In this sense, the evidence from the questionnaire supports the size effect hypothesis and suggests that the poor may pay more because constraints force them to buy smaller sizes on a more frequent basis than middle-income shoppers.

How do the New Haven results compare with other surveys on consumer behavior? To my knowledge the only study which explicitly examines the choice of store by consumers is one undertaken by Goodman (1968) in a low-income area of Philadelphia where there were no large or modern food retailing facilities. In contrast to the New Haven survey, he found that approximately 92 per cent of the 520 families interviewed did their principal grocery shopping outside of their neighborhood and most of these families shopped at supermarkets or medium-sized independents, using the local stores as supplementary sources of food. With respect to mode of transportation, approximately 45 per cent of the sample used automobiles, an additional 14 per cent used public transportation and the remainder walked to the store. Since over 40 per cent of the residents shopped by foot, these data imply that larger stores were located relatively close to the low-income area, in contrast to New Haven. [A study by Sexton may also yield data on the store effect. He restricted his analysis to a comparison of mean prices of three products purchased in the same type of store (e.g., chain, independent) by approximately 220 black and 600 white families. No analysis was made of choice of store by income group but it should be possible to obtain these figures from his dissertation. See Donald E. Sexton, Jr., "Do Blacks Pay More? A Comparison of Prices Paid for Grocery Store Commodities by Black and White Families," unpublished doctoral dissertation, University of Chicago, Chicago, Illinois, 1970.]

TABLE 3

COMPARISON OF STORE EFFECT BETWEEN MIDDLE- AND LOW-INCOME GROUPS IN NEW HAVEN

TABLE 4

COMPARISON OF SIZE EFFECT BETWEEN LOW-AND MIDDLE INCOME GROUPS IN NEW HAVEN

Empirical evidence on the size effect has been presented by Frank Douglas and Polli (1967) based on 491 households from the Chicago Tribune 1961 consumer panel survey. Multiple regression techniques were utilized to explain the per cent of purchases made of small package sizes by the ith household for each of 31 different grocery products. Among the 11 variables which they found to be statistically significant, purchase size was positively correlated with income and family size and negatively related to building size. All these relationships are consistent with the predictions from the theoretical model of consumer behavior developed in the previous section.

SUGGESTIONS FOR FUTURE RESEARCH

This paper should be viewed as a first effort in developing a formal framework for understanding consumer purchasing decisions. The questionnaire administered in New Haven uncovered a number of other factors which appear to play an important role in the choice of store and package size.

Value of Time. Consumers' value of time may play a role in purchase size decisions. Schraier (1972), building on the work of Becker (1965), has investigated this question. He suggests that shoppers who have a high value of time will tend to purchase large-sized items and make relatively few trips to the store. It is likely that these families will have an automobile and can thus easily transport large packages to their residences. Those who must walk to the store are limited with respect to the amount they can carry, and will thus be less prone to take advantage of quantity discounts. It is likely that these families will have a relatively low income, and hence a low value of time, which also suggests that they would make more frequent trips to the store

Cost of Search. A closely related factor is the cost of search and differences in behavior between income groups. High-income families may have greater mobility than poor families which facilitates their searching process, but this comparative advantage may be offset by their higher value of time.

Price Comparisons Across Sizes. Many stores have recently posted the price per ounce on packaged goods either voluntarily or due to legislation. Proponents of unit pricing legislation claim that burdensome arithmetic computations prohibit shoppers from making meaningful price comparisons when "price per ounce" figures are not posted. If this is true then many individuals are unaware of the extent of quantity discounts and hence may make uneconomical purchases. It should be possible to test this hypothesis by seeing whether or not there are significant differences in the total sales of each size of an item before and after the change to "unit pricing" by a particular store. These data would provide some measure of the value of this additional pricing information to the consumer.

Brand Effect. What differences exist between income classes with respect to the types of brands they purchase? If low-income families purchase nationally advertised brands because their local stores do not stock any house brands, then they may be paying more per ounce for the same quality product.

Market Basket Effect. We have implicitly assumed that each household allocates a proportion d its income for food and then determines a market basket of goods to purchase with this fixed amount. More research is needed to test the realism of this assumption. If an individual were not constrained by a short-run budget, then presumably he could buy a few large packages each shopping trip rather than a market basket of goods unless limited storage space prevented him from making these purchases.

Consumption Rate Effect. We have also assumed in this analysis that the household's consumption rate did not vary with purchase size. One low-income housewife in New Haven claimed she purchased the medium size box of corn flakes on her weekly shopping trip because she could not afford to have her children finish a large size box each week. It would be interesting to determine whether, in fact, poor families purchase some items in small sizes as a way of reducing their consumption rate and hence meeting a long-run income constraint.

APPENDIX A

NEW HAVEN GROCERY STORES

APPENDIX B

NEW HAVEN QUESTIONNAIRE ON GROCERY STORE PURCHASES

REFERENCES

Alcaly, R. & Klevorick, A. Food Prices in Relation to Income Levels in New York City, Journal of Business, 1971, 44, 40-46.

Becker, Gary S. A Theory of the Allocation of Time, Economic Journal, 1965. 75, 493-517.

Bureau of Labor Statistics. Prices Charged in Stores in Low and High Income Areas of Six Large Cities, February, 1966. Special Studies in Food Marketing, Technical Study No. 10, National Commission on Food Marketing, Washington, D. C., June, 1966, 121-144.

Federal Trade Commission, Economic Report on Food Chain Selling Practices in the District of Columbia and San Francisco Washington, D. C., 1969.

Frank, R., Douglas, S., & Rolli, R. Household Correlates of Package-Size Proneness for Grocery Products. Journal of Marketing Research, 1967, 4, 381-384.

Goodman, Charles S. Do the Poor Pay More? Journal of Marketing, 1968, 32, 18-24.

Hicks, J. R. Value and Capital. Second Edition, London, Oxford University Press, 1957.

Kunreuther, H. The Effect of Quantity Discounts on Consumer Demand: An Application of Inventory Theory. Center for Mathematical Studies in Business and Economics Report No. 7009. University of Chicago, Graduate School of Business. 1970.

Sexton, D. E., Jr. Do Blacks Pay More? A Comparison of Prices Paid For Grocery Store Commodities by Black and White Families. Unpublished doctoral dissertation, University of Chicago, 1970.

Sexton. D. E.. Jr. Comparing the Cost of Food to Blacks and to Whites--A Survey. Journal of Marketing, 1971, 35, 40-46.

Shraier, S. A Theory of Household Behavior in Purchasing Frequently Bought Goods. Mimeograph, January, 1972.

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