Market information and channel price structure

Intern. J. of Research in Marketing 17 Ž2000. 331–351 www.elsevier.comrlocaterijresmar

Market information and channel price structure Abhik Roy ) Department of Business Studies, Hong Kong Polytechnic UniÕersity, Hung Hom, Kowloon, Hong Kong, China Received 1 September 1999; accepted 5 December 2000

Abstract An analytical model is developed that considers the effect of demand information, and the precision with which demand forecasts are made, on channel profitability. Different channel price structures such as Stackelberg and Vertically integrated are considered and comparisons are made of the impact of information precision on channel profits under each structure. Other demand factors such as brand substitutability and share of base level demand are also included in the analysis, and the interaction of information and demand effects is examined. An empirical study is carried out using a sample of firms based in Hong Kong and support is found for the model propositions. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Demand information; Pricing; Channel profitability; Channel structure and coordination; Stackelberg system

1. Introduction A considerable volume of research has been devoted to the study of channel structure and profitability. For example McGuire and Staelin Ž1983., Jeuland and Shugan Ž1983., Coughlan Ž1985. and Moorthy Ž1988. examine the role of competitive price behavior; Shugan Ž1985. the role of implicit understanding; Coughlan and Wernerfelt Ž1989. the impact of collusion between channel members and the effects of non-uniform pricing; Jeuland and Shugan Ž1988. the effect of conjectures on profits; Chintagunta and Jain Ž1992. the role of marketing activities in a dynamic context; Ingene and Parry Ž1995. the profit impact of different channel coordinating and non-coordinating price schemes; Trivedi Ž1998. the effect of horizontal-channel competition, at the retail level, on channel profitability. )

Tel.: q852-2766-7107; fax: q852-2765-0611. E-mail address: [email protected] ŽA. Roy..

Much of this work focuses on competition, either of the horizontal-channel type, between manufacturer and manufacturer, or retailer and retailer, as the major force shaping the distribution channel. Shugan and Jeuland Ž1988. use channel-system competition, which has been referred to as ‘intertype competition’, to study the profits of different channel structures. The role of information, specifically information about market demand, in shaping the institution of distribution channels has received relatively little attention. Most of the economics literature in this area focuses on information sharing between oligopolists ŽRaith, 1996; Vives, 1984; Gal-Or, 1985. and the incentives that firms have to share private information with each other. Information-theory approaches have been used to explain the structure of competition between manufacturers ŽMalueg and Tsutsui, 1996; Raju and Roy, 1998.. We posit that the issue of information sharing within a channel is at least as important as that between competing firms, partly because information sharing is much

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A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

more likely to occur between channel partners than between rival firms. Furthermore, the information about uncertain demand conditions that the channel faces might be related to the structure of the distribution channel. When information exchange between partners in a channel has received attention, it is usually in the context of behavioral relationships between the channel members. For example, exchange of information has been considered as a dimension of influence strategies, which one channel member can use on another ŽBoyle et al., 1992.. Interaction between manufacturers and retailers based on indirect signals of demand has also been examined. To take one example, Krishnan and Rao Ž1989. discuss how the face value of coupons to be issued by a manufacturer might influence pricing strategies of a retailer. Both information sharing and within-channel pricing are types of coordination mechanisms that might be used to ensure that channel members are working towards the same objectives. We extend the literature in the area of competitive pricing behavior and channel structure by introducing imperfect information about uncertain demand as a factor influencing channel profitability. As noted by Shugan and Jeuland Ž1988., research in economics, which complements model-oriented research on channels in marketing, has largely focused on vertical integration. In perfect information models, integration yields the highest channel profits of any system, yet vertically integrated channels are not as prevalent in the real world as one might expect. McGuire and Staelin Ž1983. and Coughlan and Wernerfelt Ž1989. explain this point in terms of softening of price competition. Our findings provide an alternative, information-based explanation for why other channel structures might be preferable to a vertically integrated channel. The alternative structure that we focus on is an implicit leader–follower system. From a practical standpoint, our analysis provides insights that might be useful for those in the business of supplying information, as well as in aiding channel design decisions. The rest of the paper is organized as follows. In the next section we discuss the different channel structures that we consider and provide an overview of the modeling approach. Section 3 includes the formal model. The five propositions that emerge

from the model are presented, together with outline proofs, in Section 4. Derivations of equilibrium prices and profits that form the basis for the comparative statics presented in this section are found in Appendices A and B Ža separate Technical Appendix — available from the author — contains more detailed proofs.. Section 5 contains details of the empirical study conducted to establish some support for the propositions. We conclude with a summary of the findings and discuss some of the managerial implications of this research. 2. Channel structures and demand factors We consider markets in which there are two brands and each brand is distributed through its own channel only. Such exclusive distribution channels might be more prevalent in the case of consumer durables and services. Each channel consists of a manufacturer and an exclusive retailer. In all cases we consider, the retail price of one brand influences consumer demand for the other. The cross-price effects are assumed to be less than self-price effects. We use a modified form of the basic linear duopoly model of McGuire and Staelin Ž1983. and Jeuland and Shugan Ž1988.. Our demand function captures product differentiation through the two coefficients of own price and competitor’s price. In addition we include a market share parameter in the intercept of the demand function for each channel. The intercept represents the ‘base level’ of demand that would be enjoyed by the brand if both brands were distributed freely. The manufacturer and retailer in one channel take the retail price of the other brand as given, before setting prices. Under one form of non-cooperative pricing, there is a Stackelberg leader–follower interaction between channel partners. We will refer to such channels as S type. In response to a given price of a competitor channel, the Stackelberg system yields lower channel profits than the Vertical ŽV. channel, which we consider as the main alternative. The higher price and margin of a Stackelberg channel does not compensate for the loss in volume the high price entails. In this sense, S type channels might be thought to be less enduring ŽShugan and Jeuland, 1988. than the other basic structures. We re-examine this issue in light of the impact of infor-

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

mation on profitability of a Stackelberg channel. Note that we assume that the price leader in the S channel is the manufacturer, because manufacturing firms typically are larger, have greater resources, and are more long-term oriented, compared to their retailers. It is straightforward to show that, regardless of which channel member is the price leader, profits for the channel as a whole are the same. The leader happens to get a larger share of the total channel profits Žas in the perfect information case., so who acts as the Stackelberg leader makes a difference to individual channel member profits. In either case, it does not matter who collects the information, because we assume it is costless. Within a channel, members have the same information about the demand conditions. This last assumption does not necessarily mean that one channel member shares private information with its partner—both channel members might collect identical signals about demand. Vertical channels might include administered vertical systems or contractual systems such as franchises. We do not make any distinctions between these various forms of V channels, which are all likely to use demand information in their marketing decisions. The joint profit maximization objective, we assume, is realistic only for an integrated V channel with common ownership. In a cooperative ŽV. structure, both manufacturer and retailer still condition their prices on the retail price of the competitor’s brand. It has been shown analytically Žsee e.g., Shugan and Jeuland, 1988. that, in the absence of information, and for most forms of between-channel competition, a cooperative or vertically integrated structure ŽV. yields the highest total profits for a channel, of any of the three basic structures, Conventional Žindependent, Nash., S and V. We examine the conditions under which an alternative channel structure, such as a Stackelberg system ŽS., can improve its profitability, close to cooperative levels ŽV.. This has some implications for designing channel structure. If a non-cooperative system, such as Stackelberg, with implicit understanding of the roles of leader and follower, between channel members, can yield profits that approach collusive profits, this weakens the case for costly integration. In other words, we examine alternative mechanisms for improving channel

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profits to near full-coordinated levels, which might yield higher net profit if the fixed costs of vertical integration are also taken into account. Since the retailer in a C channel does not choose its margin, but selects a price given the wholesale price it observes, we focus on a comparison between the S and V type channels in our exposition. We examine the information and demand conditions under which the alternative channel structures, S or V, might yield different profits. The parameter in our model, which captures the information aspects of the decision problem, is the precision with which each channel makes demand predictions, or its historical forecast accuracy. One of the relevant demand parameters is the cross-price effect between the brands sold through each channel, which has been considered in a number of previous studies ŽMcGuire and Staelin, 1983; Coughlan, 1985.. Another demand factor that is considered, uniquely, in our model is the share of base level demand enjoyed by each brand. We examine the interaction between market share and information, and its impact on channel profits under each price structure, V and S.

3. Model We consider a market consisting of two channels, facing an asymmetric demand structure outlined in Eqs. Ž1. and Ž2.. Each channel consists of a manufacturer and an exclusive retailer. The manufacturer in channel i charges a wholesale price of wi and its retailer adds a profit margin of m i to make the retail price pi . The demand functions for channels 1 and 2 are given by: q1 s a a y b 1 p 1 q c1 p 2 ,

Ž 1.

q2 s Ž 1 y a . a y b 2 p 2 q c2 p1 .

Ž 2.

Vives Ž1984. and Roy et al. Ž1994. have shown that linear demand functions of this kind can be derived from a representative consumer’s maximization of a quadratic, concave utility function in q1 and q2 . qi is the demand of channel i, which depends on its own price as well as its rival channel’s price. The effect of own price on demand is moderated by the coefficient bi . Cross-price sensitivities, c1 and c 2 ,

334

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

reflect the degree to which one channel’s price influences demand for the other channel’s product. The c i coefficients together capture the degree of substitutability between the products in this market ŽMcGuire and Staelin, 1983.. We assume that bi 0 c i for i s 1, 2, so that own price effects are greater than cross-price effects Ža weak assumption. and the profit functions are well behaved. The demand functions are assumed to be linear in self- and cross-price effects, which is realistic for a range of prices, and has been adopted before ŽMcGuire and Staelin, 1983; Jeuland and Shugan, 1983.. In the general form of the model, we assume different price coefficients for each channel. In our demand specification, the base level of demand for the industry is a. The share of this base level demand going to channel 1 is a , and that going to its only competitor, channel 2, is Ž1 y a .. We further assume that the base level demand is a random variable, allowing us to capture uncertainty in demand due to changing economic and market conditions. Factors likely to result in uncertainty about total market demand are changes in consumer tastes or demographics, availability of product category substitutes, government policy and the state of the economy. The fact that many firms do monitor these factors on a regular basis is evidence of their concern about the random elements of demand, which are outside their control. More specifically we assume that, a s a q e, where a is the mean level of market demand and e is a random shock in any time period. e is assumed to be distributed normal with mean zero and variance U. In other words, EwŽ a y a. 2 x s U. The normality assumption has limitations because it allows for negative values of base level demand. However, it has been used extensively in the past literature because it simplifies the analysis considerably and allows for closed-form solutions ŽBasar and Ho, 1974; Clarke, 1983; Vives, 1984; Gal-Or, 1985.. We confine demand uncertainty to an unknown additive intercept term in the demand function of each channel. The market shares do not change randomly, and neither do the price coefficients. In other words the slope parameters are stable and known Žsee Malueg and Tsutsui Ž1996. for uncer-

tainty about slopes.. We intend to examine the relationship, if any, between demand uncertainty and channel structure. Since channel structure decisions are made for the long term, it is reasonable to consider changes in demand, which occur over the long run, such as shifts in industry level demand. Short-term fluctuations due to price changes might be less relevant for developing the structure of a channel. Markets for durable products, both consumer and industrial, might be examples of environments in which there is greater uncertainty about total demand for the category than there is about buyers’ response to price changes. For example, demand for household appliances and paint fluctuates with home construction activity, itself dependent on economic and weather factors. The set of major brands in these markets remain stable along with their market shares, while elasticities do not appear to vary much. The toy market is another example of one where tracking fluctuations in demand is probably more important than gauging consumers’ response to price. For example, Mattel, a major toy manufacturer, might be concerned about demand for its line of dolls given that dollsrfigures related to some film or television show might be popular with children in any year. It is confident that its share of the doll market will be steady because it is flexible enough to design products to meet shifting tastes, and price elasticity might be known from historical data. The major uncertainty is about overall market demand in the doll category. Incidentally Mattel does ongoing sales forecasting for its product lines and it does not use vertical channels, while some of its smaller competitors have exclusive distribution agreements with giant retailers like Toys R Us. The channels might improve their accuracy of predicting market demand through market research. Each channel obtains a forecast about unknown industry demand using the information gathering techniques at its disposal. Let us assume that channel 1’s forecast of a is f 1 and that channel 2’s forecast is f 2 . We assume that, fi s a q ei ,

i s 1, 2,

where e i is distributed normal, independent of a, with mean zero and variance si . We further assume that the forecast errors e 1 and e 2 follow a bivariate

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

normal distribution. The covariance matrix of forecast errors is represented by:

ž

s1 s12

s12 , s2

/

where s1 and s2 are the variances as defined earlier, and s12 is the covariance between the forecast errors of each channel. Each channel is privy to only its own forecast, but it recognizes that its competitor proceeds in a similar manner. Better information is defined in terms of the precision of forecasts. Forecast f 1 is more precise than f 2 if s1 - s2 Žand vice versa.. The expected value of the total market demand, given a forecast, is a convex combination of the average demand and the observed forecast ŽCyert and DeGroot 1970; Vives 1984.. More specifically, E Ž a< fi . s Ž 1 y ti . a q ti fi ,

i s 1, 2,

Ž 3.

where ti s

U U q si

,

i s 1, 2,

t i is referred to as the precision parameter and it is inversely proportional to the error variance si . Recall that U is the variance of the random demand intercept. The conditional expectation of one channel’s forecast given the other firm’s forecast can be expressed as follows: E Ž f j < fi . s Ž 1 y d i . a q d i fi , i s 1, 2; j s 3 y i ,

Ž 4.

where di s

Ž U q s12 . , i s 1, 2, Ž U q si .

The proposed structure of the information model also implies that E

Ž fi y a.

2

s E Ž a q ei y a. sE Ž eqe .

2

2

s si q U.

Ž 5.

The members of each channel choose prices and margins to maximize their own expected profits—in this manner the two channels compete. The retail price of the other channel is taken as given. In other words we assume that competition between channels

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is of the independent, Nash type. The optimal wholesale price and retail margin Žand therefore channel price. each depend on the demand function coefficients, and they also depend on the forecast available to the channel. As mentioned earlier, we assume that, within a channel, both the manufacturer and retailer have access to the same forecast about market demand.

4. Propositions

Proposition 1. Channel profits increase with the accuracy of demand information. This holds for all types of channel structures. This is a basic proposition, which ensures that the question of how channel profitability changes with information precision is meaningful. If it does not hold, then further investigation of the relationship between channel profits under different structures, and accuracy of demand information, becomes irrelevant. If, regardless of whether the pricing structure within a channel is leader–follower ŽS. or collusive ŽV., an increase in the precision of the information available to the channel results in an increase in channel profits, then there is an incentive for all types of channels to seek better information. In a general analysis of information sharing between competing firms in an advertising context, Villas-Boas Ž1994. discusses the Adecision-making frameworkB effect, where A . . . more information is better because actions are better adjusted to the current state of the worldB. It might be possible to extend the idea of a decision making framework effect, developed for a single decision maker, to the case of multiple decision makers competing within a market. We can then invoke this positive effect, which favors acquiring and making available more Žbetter. information. Proof. The rate of change of profits with change in precision of information, is examined for all possible combinations of channel structures in the market. A total of four derivatives are examined: two each for channel 1 ŽV or S. when channel 2 is either V or S

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336

type. For exposition purposes, we will focus on the profits of channel 1 throughout our analysis. For example, in a V–S market with a vertical channel 1 and a Stackelberg type channel 2, the equilibrium price equations for each channel are given by: p 1 s AV1 q B1V t 1 Ž f 1 y a . , p 2 s AS2 q B2S t 2 Ž f 2 y a . . The price parameters in each channel’s pricing rule can be expressed as: AV1 s

Ž 4a b 2 q 3c1Ž 1 y a . . a

Ž 8 b1 b 2 y 3c1 c2 . , 4a b 2 q 3c1 d 2 Ž 1 y a . B1V s . Ž 8 b1 b 2 y 3c1 c2 d1 d 2 .

Ž 6. Ž 7.

Num Ž P . s y128 a 2 y 192 a c q 192 a 2 c y 288c 2 t

Similarly channel 2’s price parameters are: AS2 s B2S s

3 Ž Ž 1 y a . a q c 2 AV1 . 4 b2 3 Ž Ž 1 y a . q c 2 B1Vd1 . 4 b2

we adopt throughout in order to examine the signs of derivatives. The directional results for propositions 1 through 3 do not change, even when separate t 1 and t 2 are considered Žsee Technical Appendix.. Let us consider the denominator and numerator of the derivative E P 1VS rEt, which represents the rate of change of channel 1’s profit Žin a V–S market. with information precision. Note that all proofs are in the form of expressions, which are the end result of analysis conducted using Mathematica Žversion 2.2.3 for Windows. software. The denominator is Žy8 q 3c 2 t 2 . 3 which is negative for all c and t. The numerator contains terms multiplied by U. The numerator of E P 1VS rEt is given by the following expression:

q 576 a c 2 t y 480 a 2 c 2 t q 216c 2 t 2 ,

Ž 8.

y 432 a c 2 t 2 q 360 a 2 c 2 t 2 y 432 a c 3 t 2 q 432 a 2 c 3 t 2 q 288 a c 3 t 3 y 288 a 2 c 3 t 3

.

Ž 9.

The general derivation of these parameters is shown in Appendix B. A Technical Appendix Žavailable from the author. contains proofs and a full set of expressions for all four market systems considered, V–V, V–S, S–V and S–S. Since the V–V case corresponds to the Bertrand game studied by Vives Ž1984., we focus our discussion on the other market systems, which include at least one Stackelberg channel. Note that, for exposition purposes, the price parameters for channel 1 are expressed in terms of demand function coefficients, while price parameters for channel 2 are a function of channel 1’s price rule parameters, as well as the demand coefficients. Under this particular market scenario ŽV–S., the rate of change of channel 1’s profit with information precision is E P 1VS rEt, and we can examine the sign of this derivative. Without loss of generality, we can set the values of the self-price coefficients bi in each channel’s demand function to 1, the substitution Žcross-price. coefficients c i both equal to c Žwhere c ( 1., and the information precision parameters t i s t. Market share a is, of course, a fraction with values between 0 and 1. These are the simplifications

y 108c 4 t 3 q 216 a c 4 t 3 y 180 a 2 c 4 t 3 q 27c 4 t 4 y 54a c 4 t 4 q 63 a 2 c 4 t 4 y 27a c 5 t 4 q 27a 2 c 5 t 4 .

Ž 10 . E P 1VS rEt

To examine the sign of the derivative we consider the extreme case when t s 1, c s 1, and substitute these values in the above expressions for numerator and denominator. This corresponds to perfect information and a very competitive market. The derivative is found to be Ž64U q 28 a U q 4a 2 U .r64, which is always positive. When t s 0, c s 1 Žtotally imprecise information and a competitive market. the derivative is Ž81 a U y 27a 2 U .r216, which is positive when a - 0.33. Note that c s 0 corresponds to the less interesting case where there is no competitive effect, and is therefore not considered. Using the graphical simulations outlined in the Technical Appendix, we can show that the sign of the numerator in Eq. Ž10. is positive for all values of a , t and c, when t lies between 0 and 1. With both numerator and denominator negative, E P 1VS rEt is positive. Let us further consider a numerical example in which a s 0.8, c s 1 and t s 0, and examine the values for each of the derivatives which appear in

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

the proofs. These values correspond to a market in which there are two major channels, with channel 1 having a major share of base level demand. There is very little product differentiation, which leads to cross-price effects as high as self-price effects. The value of the information precision parameter follows from the fact that the variance of forecast errors is much greater than the actual variance in demand. It is a symmetric situation in which both channels have very inaccurate information about demand. We retain this, rather extreme, example throughout the propositions, because it highlights the differences between S and V systems on the key ‘rate of change’ expressions. For this example, the value of E P 1rEt for a VS system is 0.22. For a corresponding S–S system Žin both VS and SS markets firm 1 faces a S type competitor. it is a bit lower at 0.21. While magnitudes may differ, we can show that this particular derivative is positive for all pairs of competing channels, and across all values of the demand and information parameters ŽTechnical Appendix.. Proposition 2. The rate of increase of channel profits with information accuracy, increases with the market share of the channel. This holds for Vertical channels across all parameter Õalues. For Stackelberg channels the reÕerse is true: the information effect decreases with market share. This holds oÕer a range of parameter Õalues. There is a caveat to a general rule that higher market share channels benefit more from improved information. When the channel has a Stackelberg structure, the rate of change of its profits with information precision decreases, as its market share increases. This holds in a S–S market system. In this specific market, the sign of the relevant second derivative is negative, over a range of values of demand and information parameters. However, for other market systems, in which the target channel is Vertical, such as V–S and V–V, it is true that profits for channel 1 always increase with information precision at a faster rate Žprofit function is convex., as its share of the market increases. The latter result is consistent with one in Raju and Roy Ž1998., in which horizontal competition between firms is considered. While empirical studies do not always provide evidence that large share firms spend

337

more on activities such as market research and forecasting ŽBuzzell and Farris, 1976; Deshpande and Zaltman, 1982., our results for vertically integrated channels indicate that greater spending on information, by high share marketing firms, is justified. The caveat, mentioned above, is one of a number of analytical results, which suggest that Stackelberg channels are a little different from other types, in terms of their reaction to changes in information about demand. When a channel has a leader–follower structure, it is not automatically true that, if the channel enjoys a higher share of the market, it will benefit more from improved demand forecasting. The profit function is concave and the rate of change of profits with information decreases with market share. In other words, whoever is the ‘leader’ within the channel, enjoying a majority of the profits made by the channel Žwhich in turn enjoys a major share of the market., does not always benefit from improved predictions of total demand. The idea that marginal improvements in information have a greater effect for small firms, which are in a weak position compared to their larger share competitors and have more to gain from better information, appears to hold only in the case of leader–follower channels. We can provide an intuitive argument for this proposition. Individual channel demand should be more volatile Žvariance of a 2 U . for high share Žhigh a . channels in general, causing them to value information more. However, there are some reasons why the information effect for high share S channels might be less. There are two sources of profit for a channel member—margin Žprice. and volume. For a price leader within a S channel, which charges a relatively high price, the impact of contribution margin on its profit is more important than that of sales volume. Volatility of channel sales might be relatively less of a problem for S channel members. Because there is more siphoning off, due to internal competition, of the incremental profits that could be achieved through better information in a S type channel, the value of information might be less in high share S channels compared to low share ones. For V channels, internal competition is not an issue but higher volatility is a problem. A high share V channel would benefit most from better information while a high share S would benefit least. In other words the information effect for V channels is con-

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vex with respect to market share, while for S channels it is concave with respect to share. It is well known that, in a Stackelberg game in prices, it is better to be a follower than a leader. This is the reverse of the first-mover advantage in a corresponding quantity game. Tyagi Ž1999. shows that in a Stackelberg price game, the leader has more incentive to act as such, if its share of the market is higher. While this might be true for competition between channels, our results imply that the information effect mitigates the positive influence of market share on Stackelberg price behavior within the channel. Proof. We shall show one case with a Vertical channel where the second derivative E 2P 1rEtEa is positive over all parameter values, and another case, involving a Stackelberg channel, facing the same type of ŽS. competitor, where the sign of this second derivative is negative over a range of parameter values. In a V–S market, the second derivative E 2P 1VS r EtEa is given by a complex expression ŽTechnical Appendix, Eq. Ž23.., which we examine for the simplified case where c s 1 Žvery competitive. and t s 1 Žperfect information.. E 2P 1VS EtEa

28U q 8 a U s 64

.

high cross-price effect, c s 1, we have E 2P 1SS rEtEa s Ž9U q 2 a U .r4. The RHS of this equation is positive, as in the V–S market. However, when t s 0, which occurs when the demand signal is extremely noisy: E 2P 1SS EtEa

36U y 120 a U s 32

.

Ž 12 .

The RHS of Eq. Ž12. is negative when the market share of the channel is greater than 30%—the proposition that the information effect decreases as the market share of a Stackelberg channel increases, holds in this specific case, for medium to large share channels. Graphical simulations ŽTechnical Appendix, p. 12. indicate that the derivative is negative over a wide range of a and t values. In a majority of cases, the rate of change of the Stackelberg channel’s profits with information precision decreases as the channel’s share of base level demand increases. E 2P 1SS rEtEa is y0.0375 at the point values of our numerical example. Proposition 3. The rate of increase of channel profits with information accuracy, increases with crossprice effects. This holds for all combinations of channel structure.

Ž 11 .

The right hand side of Eq. Ž11. is positive over all parameter values. Using the method described in the Technical Appendix, we find that in all cases the surface described by the numerator of the derivative is below the zero plane—the numerator is negative over all parameter values. The denominator is Žy8 q 3c 2 t 2 . 3, which is always negative.The numerator and denominator both being negative, E 2P 1VS rEtEa is always positive. At the point values of our numerical example, a s 0.8, c s 1 and t s 0, E 2P 1VS rEtEa has a value of 0.175. The result is somewhat different when we examine the corresponding profits of channel 1 Žwith a Stackelberg structure. in a S–S market. The general expression for E 2P 1SSrEtEa is described in Eq. Ž30. of the Technical Appendix. If we consider, as before, the specific case of perfect information, t s 1 and

As the products carried by competing channels become more substitutable, information about the uncertain marketplace can become an important tool for adjusting quantities and prices, and thereby maximizing channel profits. Therefore, it is expected that channel profits should increase with information accuracy, at a faster rate, as cross-price effects increase. When products are differentiated there is some insulation against changes in market demand that might result from changes in industry supply quantities and consumer reaction to price changes. This protection from market forces is much less for undifferentiated products, and improvements in information precision ought to have more of an impact on channel performance, for such commodity-type products. Proof. We examine a S–S market, which is most likely to deviate from the norm, so that a proof for

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351 Table 1 Numerical values of derivatives at point values of model parameters in example E P 1 rEt E 2P 1 rEtEc E 2P 1 rEtEa

V–S

V–V

S–S

S–V

0.22 0.06 0.175

0.20 0.04 0.25

0.21 0.09 y0.038

0.18 0.06 0.075

this market is the strongest evidence for the proposition. To simplify the exposition we consider the extreme case of c s 1, t s 1, and find that the relevant second derivative simplifies to: E 2P 1SS EtEc

112U q 112 a U y 20 a 2 U s 64

.

Ž 13 .

The expression on the right hand side of Eq. Ž13. is always positive. When c s 1, t s 0, the second derivative Žmultiplied by U . is Ž36 a y 36 a 2 .r32, which is also positive. Using the graphical simulations shown in the Technical Appendix, we find that E 2P 1SS rEtEc is positive across all parameter values. In the Technical Appendix, it is also shown that this particular derivative is positive for all four market systems we consider and across all parameter values. The value of the derivative for a ‘typical’ V–V system, E 2P 1VV rEtEc, is 0.04, at the parameter values in our numerical example. For the running, numerical example, the values of derivatives for Propositions 1–3 are summarized, for all four market systems, in Table 1. I Proposition 4. The rate of increase of profits with information accuracy, when substitution effects are small (more differentiated products), is higher in Vertical channels, than in Stackelberg channels, regardless of whether the riÕal channel is of S or V type. This holds oÕer all Õalues of market share and leÕels of information accuracy. The order of the rate of increase of profits with information is the same as that established ŽShugan and Jeuland, 1988. for the ordering of profits in differentiated products markets. The general results regarding profits are obtained in the absence of any information effects and they hold primarily because the lower price charged by Vertical channels is more

339

than compensated for, by higher sales volume. This volume-increasing effect of own price is more pronounced in the case of differentiated than commodity-type products. Proof. The extreme case, when the coefficient Ž c i . is zero and there is no cross-price effect, corresponds to a monopoly pricing scenario. We are more interested in the situation as c ™ 0. When channel 2 is a Stackelberg type and c tends to zero, the difference in expected profits for channel 1, as V compared to S type, tends to: 2

E Ž P 1V y P 1S . s

a 2 Ž a . q 16 a 2 tU 16

.

The rate of change of this difference with respect to t is given by: EE Ž P 1V y P 1S . Et

s a 2 U.

Ž 14 .

When the rival channel is a V type and c tends to zero, the difference in channel 1’s expected profits tends to: 2

EŽ

P 1V y P 1S

.s

a 2 Ž a . q a 2 tU 16

.

The rate of change with t is: EE Ž P 1V y P 1S . Et

a 2U s 16

.

Ž 15 .

The expression on the RHS of Eqs. Ž14. and Ž15. is always positive. Regardless of the structure of the competitor channel, the rate of return of profits with information is greater in a V than S type channel, when products are highly differentiated and there is a negligible cross-price effect. It is straightforward to show, using a graphical method as before, that when the c coefficients have non-zero values, but are much less than the corresponding b coefficients in the demand functions, then the above result still holds. Proposition 5. When the competitor channel is Stackelberg, and when the cross-price effect is high (as in a commodity-type market) a Stackelberg channel’s profits increase with information accuracy, at a faster rate than Vertical channels. This holds oÕer a

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wide range of Õalues of market share and all leÕels of information accuracy. When the competitor channel is V, a V channel benefits more from information precision than S channel, eÕen in commodity-type markets. We provide some intuition for this result. The follower in a S type channel looks to the price of its partner as a signal of demand, especially if the leader is also the collector of information. The follower is able to combine its direct signal of demand with the price signal provided by the leader, and make its margin decision. The leader–follower mechanism allows for better utilization of the two types of signal. It is more difficult to combine price and direct signals of demand in a V type channel. In the latter channel the objective of maximizing total channel profits dominates the pricing decision and inhibits the complex utilization of price and demand signals by both channel members. Hence, the Stackelberg channel benefits more from an incremental gain in direct signal accuracy. This higher benefit is accentuated in commodity-type markets where fine tuned decisions are more important: the effects of pricing are exaggerated because of the high crossprice effects. The more efficient combination of demand and price signals is one reason why the information effect might be greater for channels with Stackelberg pricing structure. The practical impact of sharing of information about demand, within a channel, is the same as that of Stackelberg pricing—it leads to a greater coordination of efforts and ultimately to a better pricing response to demand changes. Such adaptability is more likely to result in higher profits when products are similar to each other. A reason why the information effect might be less in S type channels is that volume changes are less important for such channels. This was a reason put forward for the second part of Proposition 2. When cross-price effects are high the factor discussed above Žefficiency of signal combination. dominates this other factor Žless sensitivity to volume change., and S type channels benefit more from improved information. Why does Proposition 5 hold only when the competitor is S type? To explain this we might consider an effect described in Villas-Boas Ž1994. as the Auncertainty effectB, where A . . . the result of

increased variation on the competitor reactions when there is more information in the system . . . can be positive or negative. It is negative when the competitor is increasingly harmful.B We might claim that the S type competitor, with its relatively higher price, is less ‘harmful’ than a V, especially in a market with high cross-price effects. Hence, there is a positive impact of acquiring more information when the rival is S and a negative effect when it is V. When the competitor is V, even in commodity markets, a V type channel will benefit more from improved forecasts than a corresponding S channel. The effect of market demand information is to reinforce the conclusion that S–S systems ought to be more prevalent in commodity-type markets. Proof. Since this proposition holds for a limited number of market systems only, we describe the profit expressions for the channels in such systems in some detail. For the special case where channel 2 is an S type channel, the total profits for channel 1, under structures S and V, can be expressed as Žsee Appendix A for the general derivation of unconditional profits.:

P 1S s AS1 Ž a a y b 1 AS1 q c1 AS2 . q B1S Ž a y b 1 B1S q c1 B2S . t 1U,

P 1V s AV1 Ž a a y b 1 AV1 q c1 AS2 . q B1V Ž a y b 1 B1V q c1 B2S . t 1U. These are the profit functions we have been using in the proofs of the previous propositions as well. Note that the functional form for unconditional profits is the same in each case, but the exact specification of the price parameters Ž A1 , B1 , A 2 , B2 . depends on the pricing structure of channel 1 and its competitor channel 2. For exposition purposes, we present the price parameters for channel 2 in terms of demand coefficients and the price rule parameters for channel 1. Therefore, the price parameters for channel 2 in a S–S market are: AS2 s B2S s

3 Ž Ž 1 y a . a q c 2 AS1 . 4 b2 3 Ž Ž 1 y a . q c2 B1S d1 . 4 b2

,

Ž 16 . .

Ž 17 .

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

In a V–S market, as shown earlier in Eqs. Ž8. and Ž9., the corresponding parameters are: AS2 s B2S s

3 Ž Ž 1 y a . a q c 2 AV1 . 4 b2 3 Ž Ž 1 y a . q c 2 B1Vd1 . 4 b2

,

Ž 18 .

.

Ž 19 .

As shown in Eqs. Ž6. and Ž7. the price parameters for a channel can be expressed solely in terms of the demand and information coefficients, when the other channel’s price parameters are substituted out. When channel 2 is a type S, we have the following price parameters for a S type channel 1: AS1 s B1S s

Ž 12 b 2 a q 9c1Ž 1 y a . . a Ž 16 b1 b 2 y 9c1 c2 .

,

Ž 12 b 2 a q 9c1 d 2 Ž 1 y a . . Ž 16 b1 b 2 y 9 d1 d 2 c1 c2 .

.

When channel 1 is V, its corresponding price parameters, as shown before in Eqs. Ž6. and Ž7., are: AV1 s

Ž 4 b 2 a q 3c1Ž 1 y a . . a Ž 8 b1 b 2 y 3c1 c2 .

,

with different competencies. Note that making d i s t i means that s12 s 0, but this does not imply that the two forecasts themselves are uncorrelated. It is a weaker assumption, that there is no relationship between the forecast errors that have been made. As before, a and a are the average level of random market demand and the share of this demand enjoyed by channel 1, respectively, while U is the variance in overall market demand. We derive the difference in the profits of channel 1, when it is vertically integrated and when it has a Stackelberg pricing structure Žthe difference between conventional and Stackelberg profits can be shown similarly.. This particular pair of alternatives is selected to illustrate that the vertical structure, while generally yielding higher profits, may not be as profitable as the leader–follower system, under specific demand and information conditions. In particular, we look at the rate of change of channel profits as the precision of demand forecasts changes. For example, taking the derivative of channel profit difference between V and S channels, with respect to the information precision parameter t, EŽ P 1V y P 1S .rEt, we find that the denominator, which is positive for all values of t is: 3

B1V s

Ž 4 b 2 a q 3c1 d 2 Ž 1 y a . . Ž 8 b1 b 2 y 3c1 c2 d1 d 2 .

341

3

8 Ž y3 q t 2 . Ž y2 q t 2 . . .

The price parameters for channel 1 are expressed in terms of the coefficients of the demand function faced by each channel Ž b 1 , c1 , b 2 , c 2 ., as well as the coefficients that describe information accuracy, in particular the correlation between prediction errors of the two channels Ž d1 , d 2 .. Note that the correlation between forecast errors that both firms have made in the past is not the same as the correlation between the forecasts themselves. Without loss of generality, we set the coefficients to the following values: b 1 s 1; b 2 s 1; c1 s 1; c 2 s 1; t 1 s t; t 2 s t; d1 s d 2 and both are equal to t. The equalities involving b and c coefficients imply that cross and price effects are the same, as in the extreme case of a commodity-type market. The equalities with the t coefficients mean that each channel makes forecasts with equal precision. The channels make predictions of their common industry demand, independently of each other, and normally

We also find that the numerator, in which all terms are multiplied by U, is given by: Numerator

ž

EE Ž P 1V y P 1S . Et

/

s y1296 a q 3024a 2 y 432 t q 4320 a t y 9072 a 2 t q 720t 2 y 5004a t 2 q 7740 a 2 t 2 y 360t 3 y 48 a t 3 q 2568 a 2 t 3 y 280t 4 q 3872 a t 4 y 7468 a 2 t 4 q 432 t 5 y 2016 a t 5 q 2718 a 2 t 5 y 120t 6 y 363 a t 6 q 1497a 2 t 6 y 60 t 7 q 568 a t 7 y 1183 a 2 t 7 q 48t 8 y 150 a t 8 q 84a 2 t 8 y 12 t 9 y 8 a t 9 q 101 a 2 t 9 q 9a t 10 y 21 a 2 t 10 .

Ž 20 .

This numerator can have positive or negative values. For a wide range of values of t and a , it is negative, suggesting that, for commodity-type products and this system of competition, profits in a

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leader–follower channel increase with information precision, at a faster rate than profits in a Õertically integrated channel. In the specific case where t s 1, c s 1, E Ž P 1V y P 1S .

y64 y 116 a y 12 a 2 s

Et

64

.

The RHS of the above equation is clearly negative over all parameter values. To illustrate further, if t s 0, as when information is totally imprecise Ž s ™ `. the value of the relevant derivative is: E Ž P 1V y P 1S . Et

y1296 a q 3024a 2 s 1728

.

The RHS of the above equation is negative when a - 0.428. Channels with less than 43% share of the market will benefit more from information if they have a Stackelberg price structure than if they are vertically integrated. Fig. 1 illustrates how, over a range of values of market share and information precision, profits in a Stackelberg channel, in this kind of market, increase

more rapidly with improvements in information accuracy, than do the profits in a corresponding integrated channel. The surface of the 3-D graph, indicating the rate of change of the difference between V and S channel profits with information precision t, is below the zero plane, for lower levels of market share Ž a less than 0.43. and across all t values. This suggests that, especially for lower share channels, in commodity-type markets where the competitor is a leader–follower channel, it is worthwhile to adopt a Stackelberg pricing structure. The benefits of improving predictions about uncertain demand will be greater in such a leader–follower system. Note that we are not claiming that better information in itself makes Stackelberg channel profits higher than Vertical profits, only that the rate of improvement of profit with better demand prediction is higher in leader–follower channels. If improved forecasting, which is likely to come at a much lower cost than vertical integration, causes Stackelberg profits to approach Vertical profit levels then, on the basis of profit net of costs, the Stackelberg model should appear more attractive as a pricing system for a channel.

Fig. 1. Difference between information effect for V and S channels in commodity-type markets: EŽ P 1V y P 1S .rEt over a range of market share and precision values.

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Proposition 5 indicates that, especially for commodity-type markets, Stackelberg channel structures ought to be more prevalent than previously thought. We have considered information to be costless but, as mentioned earlier, the costs of acquiring information Ževen on an ongoing basis. are likely to be much less than the capital and operational costs of vertical integration, adding weight to the inference that there ought to be more Stackelberg channels and fewer vertical channels in the real world. We test the propositions of our model, including the last one, using real world data.

5. Empirical study 5.1. Method A survey of manufacturers was conducted in Hong Kong, in an attempt to find empirical support for the model hypotheses. Note that only the manufacturer’s perspective on information and channel performance was considered, not the retailers. Firms were selected from the Hong Kong Chinese Manufacturers Directory using random sampling. Initial screening of the firms in the directory was carried out, to check whether the business enterprise was likely to use marketing channels, to sell to the local Hong Kong market, and to ensure that the firm was not purely export oriented. The set of businesses that emerged after random sampling Ževery third name in the directory, starting at a randomly selected page. was targeted for a mail survey. Questionnaires were mailed to individuals, identified as senior executives in each enterprise. Each questionnaire was accompanied by a letter, broadly sketching the purpose of the study, without getting into any specifics. As an incentive for participation, we enclosed a token payment and offered to share a statistical summary of the responses with any respondent who was interested. The mailing of the questionnaires was conducted in two waves, separated by a period of 3 weeks. The entire data collection process took nearly 9 weeks to complete. The sample consisted of small and medium scale manufacturers, primarily in industries such as household appliances, toys, furniture, apparel, leather

343

goods. A total of 308 usable questionnaires were returned, out of a mailing list of 1054. This represents a response rate of close to 30%, which is high for a mail survey. Responses were obtained across a range of industries and firm sizes, and there does not appear to be a pattern in the firm characteristics of those who responded to the mailing. The basic question in the survey, about the relationship between market information and channel Žmember. performance, was A To what extent do you think that improÕing the accuracy of your forecasts about industry demand will affect your profits?B A one to seven semantic differential scale was used, with ‘ very little effect’ and ‘ very large effect’ as the end points. This variable we labeled INFOEFFECT. The response to this question, which serves as a dependent variable in a regression model, is a proxy for ‘rate of change of profit with information precision’. We believe it represents a self-report, or perception of a practicing manager, about the term E PrEt in our analytical model. The following are some of the other key questions and independent variables. Ž1. The degree to which the firm’s products and those of its competitors were substitutes for each other. The specific question was A How similar is your product to that made by your competitors in the market?B We labeled this HOWSIM. Two other questions were included as a measure of the extent of product differentiation—A What is the number of similar products in the market?B ŽNUMCOMP. and A how unique is your product compared to your competitors in the market?B ŽUNIQUE.. The response to NUMCOMP was highly correlated Ž0.83. with HOWSIM; the response on UNIQUE was negatively correlated Žy0.79. with HOWSIM and with NUMCOMP Žy0.61.. We combined the three scales NUMCOMP, HOWSIM and the ‘reverse’ score on UNIQUE Ž8 minus the score on UNIQUE. by taking a simple average and named the construct SUBST for substitution effect. Note that although NUMCOMP could obviously have been measured as a number, it was measured on a seven-point scale Žlike the other two measures in the composite., with A Õery fewB and A Õery manyB at the end points of the scale. The Cronbach alpha for SUBST is 0.79. Ž2. A What is your estimate of the share of total sales in the market, enjoyed by your brand?B. This

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self-report of market share was labeled as MKTSHARE. This was a 10-point scale to allow for easy conversion from percentages. Ž3. The extent to which the channel adopted leader–follower pricing. Our measure was partly based on the question A What is your firm’s Ž manufacturer’s . share of total channel profits, relatiÕe to your retailer?B According to analytical results ŽShugan and Jeuland, 1988. the share of channel profits enjoyed by a Stackelberg leader is the highest of the three channel structures considered. The share of channel profits enjoyed by the manufacturer increases on a continuum from vertically integrated to conventional to leader–follower. Therefore, we expected that, for manufacturers acting as price leaders in a channel, the response to this question should be at the higher end of a seven-point scale. Firms using vertical channels should respond in the mid-to-lower range of the same scale. The ‘share of profits’ variable has the advantage of measuring the degree to which a leader–follower structure exists in the channel. We called this variable PROFSHRE. Two other questions regarding channel structure were asked in addition to the ‘share of channel profits’ question. These were A What is the degree of Õertical integration in your distribution channel?B ŽVERTINT. and A What is the extent to which retailer margin is considered in setting wholesale prices?B ŽCONRETMG.. The latter question is a process-based measure of leader–follower pricing, corresponding to the analytical procedure of profit maximization for the leader. The variables PROFSHRE and CONRETMG were found to be highly correlated Ž0.822.. We combined these two, using a simple average, in a construct labeled STACKLF. The VERTINT variable was negatively correlated with each component of the STACKLF construct. VERTINT had a negative correlation with the

PROFSHRE variable Žy0.374. and with CONRETMG Žy0.519., providing a validity check for the construct. In the regression model, which we report later, our construct for channel structure, STACKLF was an independent variable. The alpha reliability for STACKLF is 0.68. The products Žclothes, toys, small appliances. sold by the manufacturers in our sample are not very differentiated Žmean score of 5.8 on the seven-point HOWSIM scale. and the majority of the manufacturers have not integrated their retailers in a vertical system. We estimated a regression model to test the hypotheses which were developed analytically. The descriptive statistics for the constructs in this regression model are presented in Table 2. There are no significant correlations between the independent variables in the model. All the independent variables are significantly correlated with the dependent variable, INFOEFFECT. 5.2. Results In itself, the high mean value of INFOEFFECT Ž5.6 on a seven-point scale. suggests that practising marketing managers agree with Proposition 1, that better demand information leads to higher profits. Results of regression analysis are summarized in Table 3. The dependent variable is the effect of improved information on channel profits, INFOEFFECT. The regression model has an F-statistic of 216.7 and R 2 of 0.782. The significant coefficient of MKTSHARE indicates that there is a positive influence of channel’s share of demand, on the dependent variable, information effect. This supports the first part of the analytical Proposition 2.

Table 2 Descriptive statistics for model constructs Construct

INFOEFFECT MKTSHARE SUBST STACKLF

Mean

5.59 1.88 5.27 4.61

Std. dev.

1.21 0.93 1.14 1.95

Reliability

NrA NrA 0.79 0.68

Correlations INFOE

MKTSH

SUBST

STACK

1.0 0.44 0.56 0.53

0.44 1.0 y0.19 y0.12

0.56 y0.19 1.0 0.04

0.53 y0.12 0.04 1.0

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Table 3 Estimated regression model Variable

Std. coeff.

Coefficient

Std. error

T

Prob ) < T <

INTERCEPT MKTSHARE SUBST STACKLF SUBST)STACKLF MKTSHARE)STACKLF

0.18 0.52 0.49 0.13 y0.10

y3.04 0.38 0.49 0.58 0.19 y0.12

0.95 0.08 0.09 0.17 0.10 0.05

3.20 4.79 5.64 2.85 1.83 y2.40

0.0001 0.0001 0.0001 0.001 0.07 0.001

Dependent variable: INFOEFFECT.

Proposition 3 is supported by the significant coefficient of the substitution variable SUBST. As the cross-price effect increases, the information effect increases. If we compare the magnitudes of standardized regression coefficients and the T values, we find that the influence of the substitution variable on the information effect is the strongest of all the independent variables we consider. There is a main effect of STACKLF that is significant.1 This positive coefficient indicates that as a channel becomes S type, the information effect increases, providing support for Proposition 5. The latter proposition holds only under certain conditions —that substitution effects are high and rival channels are also leader–follower. Judging from the mean values of the relevant constructs, these conditions are apparently met in our sample. The product of the mean-centered MKTSHARE) STACKLF captures the interaction effect of market share and channel structure on the dependent variable. The significant, negative interaction coefficient supports the second part of Proposition 2—that while, as a rule, higher share channels benefit more from better information, the information effect for S type channels increases at a decreasing rate with market share. While high share V channels benefit more from information than low share ones, low share S channels experience a higher information effect than high share S channels. There is evidence from the

1 With a three-item scale, including the direct measure of vertical integration, VERTINT, used for the STACKLF variable, its coefficient estimate is 0.51, with standard error 0.18, significant at 0.05. With a single item construct, and Žreverse of. VERTINT used to measure STACKLF, the corresponding coefficient in the regression model is 0.44, with standard error of 0.21, still significant at 0.05.

INFOEFFECT mean values for the four relevant sub-categories in our sample, to demonstrate this ‘cross-over’ interaction. Another interaction term, measured as the product of the mean-centered STACKLF)SUBST variables was also included in the regression model and found to be marginally significant Ž p - 0.10.. The estimated coefficient has the expected positive sign. This weak evidence of an interaction between substitution effect and channel structure, provides some support for Propositions 4 and 5. The value of information increases as the channel becomes more S type and it is perceived to do so at an increasing rate with the substitution effect. In interpreting our regression results, we should be careful to note that the dependent variable is an indirect measure of the effect of improved information on channel profit, as perceived by marketing managers in manufacturer firms. It is possible to further refine the measures used in this study to make them more consistent with the analytical model. For example, respondents could be instructed to bear in mind that competitors might be aware that they have better information. While the results are encouraging, we reiterate that the empirical analysis does not constitute a formal test of the model, since it does not test alternative explanations for the findings.

6. Conclusions and managerial implications The main contribution of this research is the development of an analytical model, which combines aspects of demand information, such as information precision, with traditional models of channel profit

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under different internal pricing structures. Using this analytical model, we have examined the impact of improved precision of demand information on the profits of distribution channels. We have also studied the influence of factors such as share of uncertain demand and cross-price effects on the ‘information effect’. We have shown how the effect of improved information differs, depending on the pricing structure within the channel. V channels have been implicitly modeled in previous studies of information effects on ‘firm’ profits ŽVives, 1984; Raju and Roy, 1998.. If we compare the results for S type with those for V channels, we find significant differences in the way channel structure interacts with demand information to influence channel profitability. Our linear demand functions, combined with the linear decision rules that follow from our assumptions about the forecast errors, make the analysis tractable, but they also limit the generalizability of our results. Further research is necessary, extending the model to include non-linear demand functions, non-normal distributions of errors and uncertainty about slope coefficients. Another limitation is that we consider the effect of one marketing variable only, price, and our model is static: Chintagunta and Vilcassim Ž1994. demonstrate how the results from static, single variable models might be potentially misleading. We leave it to future research to extend our information-based model to a dynamic, multiple-decision context. In the direction of multiple decisions, a useful extension would be to make both price and information Žamount or accuracy. decision variables. In that case, information would be costly and there could be complex interactions within channels to determine the optimal amount of information. Another possible extension might be to consider administered and contractual vertical systems, and examine how they might benefit from a combination of the S and V structures discussed in this study. We have found support for the propositions generated by our analytical model, using data from a sample of manufacturers who use distribution channels, similar to that we have modeled, to sell their products in local markets. While there may be other explanations for the empirical results, and the ‘soft’ data only reflects the opinions of marketing practitioners, the empirical findings provide some encour-

agement that our model is valid and useful in predicting the directional effects of information and demand parameters on channel profits. A key result of our research is the conclusion that channel structures such as the Stackelberg leader– follower might show higher incremental profit gains from improved demand forecasting than the vertically integrated channel. From a theoretical viewpoint this is important, because in other analyses which consider a channel’s response to a competitor’s price but assume that demand is known with certainty, the implication is that there should be more vertical channels in the real world, since these channels yield highest profits among the three basic structures ŽShugan and Jeuland, 1988.. Inclusion of demand uncertainty and imperfect information in the analytical model changes this conclusion. Our results are also useful because they provide an information-based rationale to support some important strategic decisions made by channel managers. We describe the different market conditions under which demand information is more, or less, valuable to a channel. When products are differentiated, a vertical channel should be willing to pay more for improved demand forecasts, especially if it enjoys a large share of the market. Under a different scenario, when there is little product differentiation and the main Žlarger. competitor is a Stackelberg channel, a channel with a leader–follower price structure should be willing to spend more for better predictions of demand. Firms in the business of supplying information could benefit from the insights provided in this paper. To some extent, the results of our analysis can be helpful in designing channels. If a market is volatile and yet it is possible to track demand shifts with some accuracy, it might be tempting for an organization to adopt a leader–follower, rather than vertical, system, especially if the other conditions are right. Bearing in mind that the cost of information gathering is small compared to the cost of integration, our conclusions about S vs. V channels will not change, even if we assume information is acquired at some cost. In summary, we provide an analytical and empirical framework, which makes it possible for the combined impact of market conditions and demand information to be considered in the study of channel profitability.

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Acknowledgements

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A.1. Equilibrium prices and profits

The paper has benefited from the comments of Jagmohan Raju, Dominique Hanssens, Namwoon Kim, participants at research seminars and conferences at UCLA, INSEAD and Wharton. The work described in this paper was substantially supported by a grant from the Research Grants Council of the Hong Kong SAR ŽProject No. PolyU6r96H..

The first order conditions are obtained by differentiating the conditional expected profits with respect to price: EE Ž P 1 < f 1 . s 0, E p1 EE Ž P 2 < f 2 . E p2

s 0.

Ž A-3.

These yield the following relations: Appendix A. Unconditional profits under independent competition between channels—General equilibria We solve for equilibrium prices and profits in the case of linear, asymmetric demand—different base levels of demand for each channel and different self, cross effects of price on each channel’s demand: q1 s a a y b 1 p 1 q c1 p 2 , q2 s Ž 1 y a . a y b 2 p 2 q c2 p1 .

Ž A-1.

Although each channel enjoys a different base levels of demand, depending on its market share, each is still making forecasts of the industry demand a, and each channel uses the deviation of its forecast from average industry demand Ž f i y a. in its price rule. t i , d i , f i , U and si are as defined in the text. We provide an intuitive explanation for how a channel can arrive at an expectation of its competitor’s demand forecast given its own forecast Žthe formula is shown in the text, Eq. Ž10... In the case of EŽ f 2 < f 1 ., for example, channel 1 might assume that the same deviation from the mean that it observes with its own forecast Ž f 1 y a. applies to channel 2’s forecast. This provides channel 1 with updated information about channel 2’s forecast a q Ž f 1 y a., which it combines with its prior about channel 2’s forecast a, using d1 and Ž1 y d1 . as weights. E Ž f 2 < f 1 . s d1 Ž a q Ž f 1 y a . . q a Ž 1 y d1 . s a q d1 Ž f 1 y a .

Ž A-2.

Using similar reasoning EŽ f 1 < f 2 . s a q d 2 Ž f 2 y a..

2 b 1 p 1 s E Ž a a < f 1 . q c1 E Ž p 2 Ž f 2 . < f 1 . , 2 b2 p2 s E Ž Ž 1 y a . a< f 2 .

Ž A-4.

q c2 E Ž p1Ž f 1 . < f 2 . . Ž A-5. Substituting for p 2 Ž f 2 . from Eq. ŽA-5. in Eq. ŽA-4. we have: c1 Ž 1 y a . 2 b1 p1 s a E Ž a < f 1 . q Ž E Ž E Ž a< f 2 . < f1 . . 2 b2 c1 c 2 q Ž A-6. Ž E Ž E Ž p1 < f 2 . < f 1 . . . 2 b2 There is a double expectation term within parentheses in the RHS of Eq. ŽA-6., which can be expressed as: E Ž E Ž p1 < f 2 . < f 1 . s E Ž p1 Ž E Ž f 1 < f 2 . . < f 1 . s p1 Ž E Ž E Ž f 1 < f 2 . < f 1 . . . We can take conditional expectations operators inside the price function because they are linear in f 1 and f 2 , and because price p 1 is also assumed to be a linear function of f 1. Therefore, we can further express this term as: p1 Ž E Ž E Ž f 1 < f 2 . < f 1 . . s p1 Ž E Ž a q d 2 Ž f 2 y a . < f 1 . . s p 1 Ž a q d 2 Ž a q d1 Ž f 1 y a . . y d 2 a . s p 1 Ž a q ad 2 q d1 d 2 f 1 y d1 d 2 a y ad 2 . s p 1 Ž a Ž 1 y d1 d 2 . q d1 d 2 f 1 . .

Ž A-7.

Assuming that the general equation for the optimal price is the same as that for an optimal decision variable based on a normally distributed state variable Ždemand. and its signal ŽBasar and Ho, 1974; Vives, 1984. we have: p i s A i q Bi t i Ž f i y a . .

Ž A-8.

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We can expand Eq. ŽA-7., and express it in terms of p 1Ž f 1 .:

Under Nash competition, conditional expected profits of 1 are:

p 1 Ž a Ž 1 y d1 d 2 . q d1 d 2 f 1 .

E Ž P 1 < f1 .

s Ž 1 y d1 d 2 . P p 1 Ž a . q d1 d 2 P p 1 Ž f 1 . s A1 Ž 1 y d1 d 2 . q d1 d 2 P p 1 Ž f 1 . .

Ž A-9.

The first order condition for channel 1 can now be rewritten as: c1 Ž 1 y a . 2 bp1 Ž f 1 . s a E Ž a < f 1 . q E Ž E Ž a< f 2 . < f1 . 2 b2 c1 c 2 q d d pŽf . 2 b2 1 2 1 1 c1 c 2 q A Ž 1 y d1 d 2 . . Ž A-10. 2 b2 1

ž

s p 1 Ž f 1 . ) E a a y b 1 p 1 Ž f 1 . q c1 p 2 Ž f 2 . < f 1 . Ž A-14. Substituting the price solutions: E Ž P 1 < f 1 . s a E Ž a < f 1 . y b 1 E Ž A1 < f 1 . yb1 B1 t1 E Ž f 1 y a < f 1 . q c1 E Ž A 2 < f 1 . qc1 B2 t 2 E Ž f 2 y a < f 1 . ) p 1 Ž f 1 . s a a q a t 1 Ž f 1 y a . y b 1 A1 yb1 B1 t 1 Ž f 1 y a . q c1 A 2 qc1 B2 t 2 Ž 1 y d1 . a q c1 B2 t 2 d1 f 1

Collecting terms: c1 c 2 2 b1 y d d pŽf . 2 b2 1 2 1 1

yc1 B2 t 2 a

/

s Ž a a y b 1 A1 q c1 A 2 . qt1 Ž a y b 1 B1 q c1 B2 d 2 . Ž f 1 y a .

s a Ž a q t1Ž f 1 y a . . q

c1 Ž 1 y a . 2 b2

q

c1 c 2 2 b2

aq

c1 Ž 1 y a . 2 b2

A1 Ž 1 y d1 d 2 . .

) Ž A1 q B1 t 1 Ž f 1 y a . . . t1 d 2 Ž f 1 y a .

Ž A-11.

Using the relation t 1 d 2 s t 2 d1 , collecting and simplifying, the Žbest response. Nash equilibrium price for channel 1 is: p 1 Ž f 1 . s A1 q B1 t 1 Ž f 1 y a . ,

B1 s

Ž 2 b 2 a q c1 Ž 1 y a . . a 4 b 1 b 2 y c1 c 2

E Ž P 1 . s E Ž E Ž P 1 < f1 . . ,

Ž 2 b 2 a q c1 Ž 1 y a . d 2 . 4 b 1 b 2 y c1 c 2 d1 d 2

q Ž a a y b 1 A1 q c1 A 2 . B1 t 1 E Ž f 1 y a . q t 1 Ž a y B1 q c1 B2 d 2 . A1 E Ž f 1 y a . 2

q B1 Ž a y b 1 B1 q c1 B2 d 2 . t 12 E Ž f 1 y a . . Ž A-17. Since EŽ f 1 y a. s 0 and E

.

Substituting and solving for channel 2’s Nash equilibrium price, we get a solution which is symmetric to that for channel 1: p 2 Ž f 2 . s A 2 q B2 t 2 Ž f 2 y a . , A2 s B2 s

Ž 2 b1Ž 1 y a . q c2 a . a 4 b 1 b 2 y c1 c 2

Ž 2 b 1 Ž 1 y a . q c 2 d1 a . 4 b 1 b 2 y c1 c 2 d1 d 2

Ž A-16.

E Ž P 1 . s E Ž Ž a a y b 1 A1 q c1 A 2 . A1 .

Ž A-12.

,

Ž A-15.

The unconditional profit for channel 1 is the expected value Žover all f 1 . of its conditional profit:

where A1 s

Ž A1 q B1 t1 Ž f 1 y a . .

Ž A-13. ,

U

2

ž Ž f y a. / s U q s s t 1

1

1

Eq. ŽA-17. simplifies to E Ž P 1 . s Ž a a y b 1 A1 q c1 A 2 . A1 q B1 Ž a y b 1 B1 q c1 B2 d 2 . t 1U.

Ž A-18.

For channel 2 we obtain a symmetric solution to that for channel 1 E Ž P 2 . s Ž Ž 1 y a . a y b 2 A 2 q c 2 A1 . A 2

.

q B2 Ž Ž 1 y a . y b 2 B2 q c 2 B1 d1 . t 2 U. Ž A-19.

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

Note that the exact specification of A1 , B1 , A 2 and B2 depends on the type of channel pricing structure within channel 1 and 2.

a

ž

s w1 a E Ž a < f 1 . y b1w1 y y

c1 2

Appendix B. Equilibrium prices under each channel structure

349

EE Ž P 1 m < f 1 . Ew 1

/

E Ž p 2 < f 1 . q c1 E Ž p 2 < f 1 . ,

s a E Ž a < f 1 . y 2 b1w1 y

B.1. Stackelberg channel

q b1w1 q

a

2

E Ž a< f1 . q

c1

c1 2

b1w1 s

E Ž a< f1 . q

w1 s

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 1 . . .

E Ž P 1t < f 1 .

p1 s

2 b1

Em1

1 2 b1

1 2 b1

s a E Ž a < f 1 . y 2 b 1 m1 y b 1 w 1

m1 s

2 b1

Ž B-1. p1 s s

s

4 b1 3 4 b1 3 4 b1

s w 1 Ž a E Ž a < f 1 . y b 1 w 1 y b 1 m1 q c1 E Ž p 2 < f 1 . . s 4 b1

a E Ž a < f 1 . y b 1 w 1 q c1 E Ž p 2 < f 1 .

/

c1 E Ž p 2 < f 2 . b1

y

w1 2

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 1 . .

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 1 . .

Ž a Ž a q t1Ž f 1 y a . .

Ž a Ž a q t 1 Ž f 1 y a . . q c1 A 2 qc1 B2 t 2 Ž a q d1 Ž f 1 y a . y a . .

3 s

/

Ž B-5.

qc1 Ž A 2 q B2 t 2 Ž E Ž f 2 < f 1 . y a . . . 3

ž

qc1 E Ž p 2 < f 1 .

E Ž p2 < f1 . ,

a E Ž a < f 1 . q c1 E Ž p 2 < f 1 .

y

E Ž P 1 m < f1 .

s w1 a E Ž a < f 1 . y b1w1

q

b1

1

2 b1

Ž B-4.

b1

s

ž

E Ž a< f1 .

Ž a E Ž a < f 1 . y b 1 w 1 q c1 E Ž p 2 < f 1 . . ,

a E Ž a< f1 .

Ž B-2.

Note that we simplified the notation a little, so that EŽ p 2 Ž f 2 < f 1 .. s EŽ p 2 < f 1 .. If the manufacturer 1m, is the price leader within the channel, it incorporates the retailers optimal price in its profit function.

yb1

Ž B-3.

Ž B-6.

Therefore, the retailer’s optimal margin m1 is given by:

a E Ž a < f 1 . y b 1 w 1 q c1 E Ž p 2 < f 1 .

w1

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 2 . .

q

q c1 E Ž p 2 Ž f 2 < f 1 . . s0.

2

Since channel price to customer p 1 s w1 q m1 ,

s m1 Ž E Ž a a y b 2 Ž m1 q w 1 . q c1 p 2 < f 1 . . , EE Ž P 1t < f 1 .

2

2

E Ž p 2 < f 1 . s0,

Let wi be the wholesale price charged by the manufacturer in channel i and m i be the retailer’s profit margin. Let us consider channel 1 and assume that the retailer in channel 1 acts as a Stackelberg follower. Expected profit of channel 1 retailer given demand forecast f 1:

2 1

a

b1

4 b1

Ž Ž a a q c1 A 2 . q Ž a q c 1 B2 d 2 . t 1 Ž f 1 y a . . .

Ž B-7.

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

350

The last identity follows, in part, from the relationship t 2 d1 s t 1 d 2 . Therefore, the price of a Stackelberg channel can be expressed as

Adding the equations for w 1 and m1 to get channel retail price p 1: p 1 s w 1 q m1

p 1S s AS1 q B1S t 1 Ž f 1 y a . ,

2 s

where: AS1 s B1S s

2 b1 3

4 b1 3 4 b1

Ž a a q c1 A 2 . ,

Ž B-14.

Ž B-8.

Ž a q c 1 B2 d 2 . .

Ž B-9.

A 2 and B2 are the intercept and slope coefficients of channel 2’s price rule. Note that the exact form of channel 1’s price depends on whether channel 2 is S or V type.

p1 s

1 2 b1

p1 s

1 2 b1

1

where all terms have been previously defined. E Ž P 1 < f1 . s w 1 Ž E Ž a a y b 1 p 1 q c1 p 2 < f 1 . .

s 2 b1

qc1 B2 t 2 Ž a q d1 Ž f 1 y a . y a . . 1 s 2 b1

Ž a a q c 1 A 2 q Ž a q c 1 B2 d 2 . t 1 Ž f 1 y a . . . Ž B-15.

The last equation follows after collecting terms and using the identity d1 t 2 s d 2 t 1. Therefore, with the channel price expressed as

we have:

s w 1 Ž a E Ž a < f 1 . y b 1 w 1 y b 1 m1 q c1 E Ž p 2 < f 1 . . A1 s

q m1 Ž a E Ž a < f 1 . y b 1 w 1 y b 1 m1

Ž B-11.

Differentiating the expected channel profit with respect to w 1 and m1 , respectively, we have: 1 w1 s Ž a E Ž a < f 1 . y 2 b 1 m1 q c1 E Ž p 2 < f 1 . . , 2 b1 Ž B-12. 2 b1

Ž a a q a t 1 Ž f 1 y a . q c1 A 2

p 1 s A1 q B1 t 1 Ž f 1 y a .

q m1 Ž E Ž a a y b 1 p 1 q c1 p 2 < f 1 . .

m1 s

Ž a Ž a q t1Ž f 1 y a . . qc1 Ž A 2 q B2 t 2 Ž E Ž f 2 < f 1 . y a . . .

The total profit in a channel is the sum of the profits made by the manufacturer and the retailer. Let us consider how a manufacturer sets wholesale price with the objective of maximizing total channel profits, an objective which is applicable in a vertically integrated channel. EE Ž P 1 < f 1 . EE Ž Ž P 1 m q P 1t . < f 1 . s s 0, Ž B-10 . Ew 1 Ew 1

1

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 1 . . .

We can express the retail price of channel 1 as:

B.2. Vertically integrated channel

qc1 E Ž p 2 < f 1 . . .

Ž a E Ž a < f 1 . q c1 E Ž p 2 < f 1 . y Ž m1 q w 1 . . ,

B1 s

2 b1

Ž a q c 1 B2 d 2 . 2 b1

,

Ž B-16.

.

Ž B-17.

Similarly we can show that channel 2’s price parameters are: A2 s

Ž a E Ž a < f 1 . y 2 b 1 w 1 q c1 E Ž p 2 < f 1 . . . Ž B-13.

Ž a a q c1 A 2 .

B2 s

Ž Ž 1 y a . a q c 2 A1 . 2 b2

Ž Ž 1 y a . q c2 B1 d1 . 2 b2

,

Ž B-18.

.

Ž B-19.

A. Roy r Intern. J. of Research in Marketing 17 (2000) 331–351

Note that the prices derived for each channel structure are specific forms of the channel price reaction functions derived by Shugan and Jeuland Ž1988. for the perfect information case, pi s k Ž a q g pj .rb where k takes on the values 3r4 and 1r2 for S and V, respectively. a, b and g in Shugan and Jeuland Ž1988. correspond to a, b and c in our model.

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