Brand-supermarket demand for breakfast cereals and retail competition.

One of the most influential market equilibrium models for differentiated products is that of Berry, Levinsohn, and Pakes (1995; hereafter, BLP), who use a random coefficients logit demand approach at the product brand level. The BLP approach, originally applied to automobiles, has also been applied at city or national levels to a limited number of food products including breakfast cereals (Nevo 2001), frozen foods (Mojduszka, Caswell, and Harris 2001), and ketchup (Rennhoff 2004). By conducting their analyses at the city or national levels, these studies neglect a critical component of the food system: grocery stores. Not only are consumer purchases and food-pricing decisions ultimately made at the grocery store level but supermarkets can exert market power of their own, resulting in significant markups. This study tries to fill this gap by being the first to apply BLP at the supermarket chain level. (1)

Focusing on thirty-seven brands of ready-to-eat breakfast cereals (hereafter, RTECs) at the supermarket chain level in Boston allows us to look more closely at the nature of consumer choices and retail competition. (2) Empirical results show that taste parameters vary considerably across consumers and that although consumers are quite responsive to prices with respect to their chosen cereals, they exhibit a strong degree of brand and supermarket loyalty. Our estimated supermarket markups average approximately 28% of the retail price although they vary substantially across supermarkets and RTEC brands. Retail markups increase and marginal costs decrease with grocery market shares, attesting to oligopoly power with efficiencies. Markups decrease with the own-price elasticity of demand, with Corn Flakes (arguably the most basic RTEC) having the highest markups and lowest price elasticities across supermarkets. By extending the BLP model to the supermarket chain level, a more detailed picture of consumer demand and retail competition emerges than previously provided for RTECs.

The Model

Demand

In the BLP model (summarized here for expository purposes), the consumer chooses one brand among competing products, maximizing utility driven by brand characteristics as well as the consumer's own characteristics. The indirect utility of consumer i from buying brand j([U.sub.ij]) is given by

(1) [U.sub.ij] = [[alpha].sub.i][p.sub.j] + [[beta].sub.i][x.sub.j] + [[epsilon].sub.ij], i = 1, ... n; j = 1, ..., J

where [x.sub.j] is a vector of the observed product characteristics of brand j, [p.sub.j] is the price of brand j, [[alpha].sub.i] and [[beta].sub.j] are taste parameters unique to each consumer, and [[epsilon].sub.ij] represents the distribution of consumer preferences around the unobserved product characteristics with a probability density function f([epsilon]).

Following BLP, let [[alpha].sub.i] and [[beta].sub.i] be decomposed into fixed and variable components that change with consumers' observable and unobservable characteristics. That is,

(2) [[alpha].sub.i] = [alpha] + [lambda][D.sub.i] + [gamma][v.sub.i],

(3) [[beta].sub.i] = [beta] + [phi] [D.sub.i] + [rho][v.sub.i]

where [D.sub.i] denotes observed consumer characteristics (e.g., demographics) with a probability density function h(D); [v.sub.i] denotes the unobserved consumer characteristics with a probability density function g(v), assumed to be normally distributed N(0, 1); and [alpha], [beta], [lambda], [phi] [gamma], and [rho] denote fixed parameters.

Substituting equations (2) and (3) into (1) yields

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The indirect utility can be decomposed into two parts: a mean utility term [[delta].sub.j], which is common to all consumers, and a brand-specific and consumer-specific deviation from that mean, [u.sub.ij], which includes interactions between consumer and product characteristics.

To complete the model and to define the market (and, hence, market shares) an outside good is included to give the consumer the possibility not to buy any of the brands included in the choice set. As each consumer purchases a unit of the brand that yields the highest utility or the outside good, aggregating over consumers, the market share of the jth brand corresponds to the probability that the jth brand is chosen. That is,

(5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [theta] = ([alpha], [beta], [lambda], [phi], [gamma], [rho]) is a vector of consumer taste parameters in equation (4); k = 0 denotes the outside good; and H(D), G(v), and F([epsilon]) are cumulative density functions for the indicated variables, assumed to be independent from each other.

Using equation (5), the price elasticities of the market shares for individual brands are

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Note that substitution patterns are not constrained by a priori segmentation of the market as in the multiple-stage budgeting approach (e.g., Cotterill and Haller 1997; Hausman, Leonard, and Zona 1994). Also note that the commonly used logit model delegates consumer heterogeneity to the error term [[epsilon].sub.ij] (equation 4), which is assumed to follow an i.i.d, type I extreme value distribution. (3)

Retail Markups

The RTEC market channel in Boston consists of manufacturers at the national level and retailers at the local level. Because manufacturers compete nationally and we are interested in the brand-supermarket level, this study focuses on markups at the retail stage, taking manufacturers' wholesale prices and physical RTEC brand attributes as given. Furthermore, it is assumed that a brand (e.g., Kellogg's Corn Flakes) sold at a given supermarket chain is different from the same brand sold at another supermarket chain, the difference in demand and markup reflecting the supermarket effect. (4)

Consider then the case where a retailer chooses the retail price for each brand it sells to maximize his own profits in a horizontal Nash-Bertrand model of competition. The rth retailer's problem is then given by maximizing

(7) [[pi].sub.r] = [summation over (j [member of] [S.sub.r])] ([p.sub.j] - [c.sub.j])[S.sub.j](p)M

where [S.sub.r] is the set of brands sold by the rth supermarket; [p.sub.j] is the retail price, [c.sub.j] is the retailer's constant marginal cost, and [s.sub.j](p) is the share of the market of brand j; p is a vector of retail prices at all supermarkets; and M is market size that includes sales of all brands in the choice set in all supermarkets and the outside good. Note that all market shares are defined relative to M. The first-order conditions are given by

(8) [s.sub.j] + [summation over (k)] ([p.sub.k] - [c.sub.k) [partial derivative][S.sub.k]/[partial derivative] [p.sub.j] = 0, j, k [member of] [S.sub.r].

Repeat the procedure for each supermarket and stack the solutions to obtain the RTEC retailers' equilibrium price-cost margins as

(9) p - c = - [[DELTA].sup.-1] s(p)

where c is a vector of retailers' costs at the brand-supermarket level and [DELTA] is a block diagonal matrix of first derivatives of the market shares with respect to all retail prices (its elements are equal to [partial derivative][[S.sub.k]/[partial derivative]/[p.sub.j] if brand j combination is sold by the same supermarket and are 0 otherwise). (5) The Lerner indices of oligopoly power at the brand-supermarket level are then given by [L.sub.j] = ([p.sub.j] - [c.sub.j])/[p.sub.j]. Note that by estimating equation (9) one can easily obtain retail marginal costs at the brand-supermarket level as retail prices are observable.

The Data

We use data for thirty-seven brands of breakfast cereals over thirty-five four-week periods between April 1995 and December 1997 at five supermarket chains in Boston, including Stop & Shop, Shaw's, DeMoulas, and Star Market. The fifth "chain" combines all smaller residual supermarkets. Although used in the calculations, the results for the latter are not reported. Thus, in total 6,475 observations were assembled (37 brands x 5 supermarkets x 35 time periods). The data used consist of product characteristics (including sales data and brand attributes) and consumer characteristics at the Boston level (including observable demographics and unobservable characteristics).

The sales data, which came from the Information Resources, Inc. (IRI) Infoscan database at the Food Policy Marketing Center of the University of Connecticut, consist of dollar sales, volume (in pounds) sold, and the percentage volume sold under promotion. The retail prices were computed by dividing the dollar sales of each brand by the number of servings sold and then deflating by Boston's Consumer Price Index (December 1997 = 1). Data on brand attributes, collected by examining the nutrition labels on breakfast cereal boxes, included sugar content, fiber content, calories per serving, and a dummy variable to indicate "kids' cereals." (6) The potential market size is assumed to be one serving per capita per day, as in Nevo (1997), times the Boston population. Market shares are obtained by converting volume sales into number of servings sold and dividing by potential market size. This is done by using the serving weight found on each box of cereal. The share of the outside good is then one minus the aggregate share of the thirty-seven brands.