Concluding Remarks

In this chapter, we provide a unified framework towards a thorough understanding of the interplay between the advertising strategies and the channel structure. Specifically, we show that when manufacturers delegate the sales responsibility to dedicated retailers, informative advertising may yield a higher profit for the manufacturers due to its pro-competitive nature.

On the contrary, persuasive advertising should be used more extensively when either the manufacturers sell directly to the end consumers or sell through a common retailer. This is because different advertising strategies allow the manufacturers to adjust the appropriate competition intensity. Consequently, the manufacturers may strategically adopt different advertising strategies in different channel structures, taking into account the competition/

monopoly in the downstream market. We also identify operating regions under which one form of advertising strategy is more favorable than the other, thereby providing a handy guideline for practitioners to design their advertising strategically.

Several extensions are in order. In our model, the manufacturers are endowed with the full bargaining power and consequently are able to determine the wholesale prices in favor of themselves. Nevertheless, there are situations in which it is the retailer that possess a higher bargaining power. In such a scenario, the relative bargaining power may affect how the manufacturers value the advertising strategies and consequently lead to different conclusions from this chapter. Second, one could also consider more complicated channel structures. For example, when there are multiple manufacturers and multiple retailers, the network structure becomes crucial and complex. For example, a manufacturer could sell through only a subset of retailers, and a retailer carries the products from a subset of manufacturers. Strategic interactions in a general channel network deserve further investigations. Finally, this chap-ter focuses exclusively on the manufacturers’ incentive of adopting advertising strategies, whereas in reality the retailers may also be able to advertise by themselves (e.g., to inform consumers the retail store location, price promotion, etc.). This informative advertising may be supported or discouraged by the manufacturers depending on the channel structure, and is clearly a research priority.

Appendix

Derivations of the profits in the pricing games

In the following, we derive the profits in the pricing games under each channel structure (i.e., those profit terms specified in Table 1). Since different advertising strategies only result in different parameters in the effective demands of the manufacturers’ products, these pricing games are similar for a given channel structure. Thus, for ease of illustration, we only present the pricing game for one combination of advertising strategies under each channel structure. Specifically, we present the case of (I, P ) for the integrated channel, (I, I) for

the delegated channel, and (P, P ) for the common retailer channel. The other cases can be derived similarly.

1) (I, P ) under the integrated channel:

Suppose that M₁ adopts the informative advertising and M₂ adopts the persuasive advertising. The demands for M1 and M2 are respectively

q₁ = 5

Given the effective demand functions, we can solve the profit-maximization problems for both manufacturers as follows:

Applying the first-order conditions to these two profit functions simultaneously, we obtain that

p^I₁(I, P ) = 10 + 13γθ

4(5 + 3θ)(1 + γθ) − 3γθ², and p^I₂(I, P ) = 10 + 11θ

4(5 + 3θ)(1 + γθ) − 3γθ². Thus, the corresponding demand functions and the maximum profits for the manufacturers can be expressed as follows: 2) (I, I) under the delegated channel:

When both manufacturers adopt informative advertising, the effective demands for M1

and M2 are

q₁ = 2(1 − p1) + 2θ(p2− p1), and q2 = 2(1 − p2) + 2θ(p1− p2).

Since in the delegated channel, the manufacturers determine the wholesale prices first and then the retailers set retail margins (retail prices) accordingly, by backward induction, we shall first focus on the retailers’ pricing game given the manufacturers’ wholesale prices, and then return to the manufacturers’ pricing game.

Given the wholesale prices, the retailers solve the following profit-maximization problems Having derived the retailers’ optimal retail prices, we now characterize the manufactur-ers’ wholesale prices. Given p1 and p2, the demands for the manufacturers are respectively

q1 = 2 (1 + θ) The manufacturers’ problems are therefore the following:

maxw₁ Π1 = w1

We can apply the first-order conditions simultaneously to solve the wholesale price game, and obtain the optimal wholesale prices as follows:

w₁^D(I, I) = w₂^D(I, I) = 2 + 3θ 4 + 7θ + θ².

The corresponding equilibrium demands and profits for the manufacturers are respectively q₁^D(I, I) = q^D₂ (I, I) = 2 (1 + θ) (2 + 4θ + θ²)

(2 + θ) (4 + 7θ + θ²) ,

Π^D₁(I, I) = Π^D₂(I, I) = 2 (1 + θ) (2 + 3θ) (2 + 4θ + θ²) (2 + θ) (4 + 7θ + θ²)² . 3) (P, P ) under the common retailer channel:

Under the common retailer channel, we focus on the scenario in which both M₁ and M2 adopt persuasive advertising. The effective demands for M1 and M2 are respectively

q1 = 2 − (2 + γθ) p1+ γθp2, and q2 = 2 − (2 + γθ) p2+ γθp1.

By backward induction, we first solve the common retailer’s problem of finding the optimal retail prices. Given the manufacturers’ wholesale prices w1 and w2, the common retailer’s goal is to find the retail prices p1, p₂ to solve the following problem:

maxp₁,p₂ πR= (p1− w1)[2 − (2 + γθ) p1+ γθp2 ] + (p2− w2) [2 − (2 + γθ) p2+ γθp1] . Applying the first-order conditions, we obtain that

p₁ = 1 + w₁

2 , and p₂ = 1 + w₂ 2 ,

and the corresponding demands for the manufacturers are respectively q1 = 1 −

Now we return to the manufacturers’ problem of finding the optimal wholesale prices:

maxw₁ Π1 = w1

Solving them simultaneously, we obtain the equilibrium wholesale prices as follows:

w^C₁(P, P ) = w₂^C(P, P ) = 2 4 + γθ,

and the corresponding equilibrium demands and profits for the manufacturers are respec-tively

q₁^C(P, P ) = q^C₂(P, P ) = 2 + γθ 4 + γθ, Π^C₁(P, P ) = Π^C₂(P, P ) = 2 (2 + γθ)

(4 + γθ)² .

Summary of the results in the advertising games

We now summarize our results in the advertising games under the three channel structures and illustrate them via graphic representations.

1) Integrated channel:

Let us first consider the integrated channel. The profits under different combinations of advertising strategies are summarized below:

Π^I₁(N, N) = Π^I₂(N, N) = 4(2 + θ) (4 + θ)²,

Π^I₁(N, I) = Π^I₂(I, N) = 3(1 + θ)(10 + 11θ)² 2(20 + 32θ + 9θ²)² , Π^I₂(N, I) = Π^I₁(I, N) = (5 + 3θ)(10 + 13θ)²

2(20 + 32θ + 9θ²)² , Π^I₁(N, P ) = Π^I₂(P, N) = 4(2 + θ)(4 + 3γθ)²

[4(2 + θ)(2 + γθ) − γθ²]², Π^I₂(N, P ) = Π^I₁(P, N) = 4(2 + γθ)(4 + 3θ)²

[4(2 + θ)(2 + γθ) − γθ²]², Π^I₁(I, I) = Π^I₂(I, I) = 2(1 + θ)

(2 + θ)²,

Π^I₁(I, P ) = Π^I₂(P, I) = (5 + 3θ)(10 + 13γθ)² 2[4(5 + 3θ)(1 + γθ) − 3γθ²)², Π^I₂(I, P ) = Π^I₁(P, I) = 3(1 + γθ)(10 + 11θ)²

2[4(5 + 3θ)(1 + γθ) − 3γθ²)², Π^I₁(P, P ) = Π^I₂(P, P ) = 4(2 + γθ)

(4 + γθ)².

Note that in the manufacturers’ profits, when both manufacturers do not adopt any adver-tising strategy, both manufacturers receive a higher profit as the product differentiation is more significant (θ is higher). However, this no longer holds if one of the manufacturers adopts the informative/ persuasive advertising.

The three plots a, b, c in Figure 2.4 show the profits of Mj between different advertising responses under different advertising strategies by Mi. The contour is the set of points for which manufacturer Mj is indifferent between adopting informative advertising and adopting persuasive advertising. From Figure 2.4, we observe that Mj’s best response is informative

Figure 4: Advertising Equilibrium Analysis in the Integrated Channel.

advertising if (θ, γ) falls in the left-hand side of the contour, whereas the right-hand side corresponds to the region in which persuasive advertising becomes more favorable. We combine the three plots a, b, and c in d in Figure 2.4 to show that the manufacturers’

dominant strategy is informative advertising in Region 1; consequently, the equilibrium is (I, I). On the other hand, the manufacturers’ dominant strategy is persuasive advertising in Region 3, thereby leading to the equilibrium (P, P ).

2) Delegated channel:

In the delegated channel, the manufacturers’ profits under different combinations of advertising strategies are as follows:

Π^D₁(N, N) = Π^D₂ (N, N) = 4 (2 + θ) (4 + 3θ) (8 + 8θ + θ²) (4 + θ) (16+14θ + θ²)² ,

Π^D₁ (N, I) = 3 (1 + θ) (10 + 16θ + 3θ²) (200 + 590θ + 507θ²+ 105θ³)² 2 (20 + 32θ + 9θ²) (400 + 1280θ + 1249θ²+ 360θ³+ 27θ⁴)², Π^D₂ (N, I) = (5 + 3θ) (10 + 16θ + 3θ²) (2 + 3θ)²(100 + 155θ + 37θ²)²

2 (20 + 32θ + 9θ²) (400 + 1280θ + 1249θ²+ 360θ³+ 27θ⁴)², Π^D₁(N, P ) = (2 + θ) (8 + 4θ + 4γθ + γθ²)kd12

(4 (2 + θ) (2 + γθ) − γθ²)k ² ,

Π^D₂ (N, P ) = (2 + γθ) (8 + 4θ + 4γθ + γθ²)kd32

(4 (2 + θ) (2 + γθ) − γθ²)kd42 , Π^D₁(I, N) = Π^D₂(N, I), Π^D₂(I, N) = Π^D₁(N, I)

Π^D₁(I, I) = Π^D₂(I, I) = 2 (1 + θ) (2 + 3θ) (2 + 4θ + θ²) (2 + θ) (4+7θ + θ²)² , Π^D₁ (I, P ) = (5 + 3θ) (10 + 6θ + 10γθ + 3γθ²) kd52

2 (4 (1 + γθ) (5 + 3θ) − 3γθ²)k_d6² , Π^D₂ (I, P ) = 3 (1 + γθ) (10 + 6θ + 10γθ + 3γθ²) k_d7²

2 (4 (1 + γθ) (5 + 3θ) − 3γθ²)kd82 , Π^D₁ (P, N) = Π^D₂(N, P ), Π^D₂ (P, N) = Π^D₁(N, P ),

Π^D₁ (P, I) = Π^D₂(I, P ), Π^D₂(P, I) = Π^D₁ (I, P ),

Π^D₁ (P, P ) = Π^D₂(P, P ) = 4 (2 + γθ) (4 + 3γθ) (8 + 8γθ + γ²θ²) (4 + γθ) 16+14γθ + γ²θ²
2 , where

k_d1 = 4 (4 + 3γθ) 8 + 4θ + 4γθ + γθ²
+ 2γθ (2 + γθ) (4 + 3θ) , kd2 = 4 8 + 4θ + 4γθ + γθ²
2

− γθ²(2 + θ) (2 + γθ) ,

kd3 = 4 (4 + 3θ) 8 + 4θ + 4γθ + γθ²
+ 2θ (2 + θ) (4 + 3γθ) , k_d4 = 4 8 + 4θ + 4γθ + γθ²
2

− γθ²(2 + θ) (2 + γθ) ,

k_d5 = 2 (10 + 13γθ) 10 + 6θ + 10γθ + 3γθ²
+ 3γθ (10 + 11θ) (1 + γθ) , k_d6 = 4 10 + 6θ + 10γθ + 3γθ²
2

− 3γθ²(1 + γθ) (5 + 3θ) ,

kd7 = 2 (10 + 11θ) 10 + 6θ + 10γθ + 3γθ²
+ θ (5 + 3θ) (10 + 13γθ) , kd8 = 4 10 + 6θ + 10γθ + 3γθ²
2

− 3γθ²(1 + γθ) (5 + 3θ) .

The graphic illustration is given in Figure 5, which follows the same spirit as in Figure 4.

We again observe that in Region 1, the manufacturers’ dominant strategy is informative advertising, and the equilibrium is (I, I); on the contrary, the dominant strategy is persuasive advertising, and the equilibrium is (P, P ) in Region 3.

3) Common retailer channel:

The manufacturers’ profits while delegating to a common retailer under different

com-Figure 5: Advertising Equilibrium Analysis in the Delegated Channel.

binations of advertising strategies are as follows:

Π^C₁(N, N) = Π^C₂(N, N) = 2(2 + θ)

(4 + θ)², Π^C₁(N, I) = 3 (1 + θ) (10 + 11θ)² 4(20 + 32θ + 9θ²)² , Π^C₂(N, I) = (5 + 3θ) (10 + 13θ)²

4(20 + 32θ + 9θ²)² ,

Π^C₁(N, P ) = 16(2 + θ)kc12

(2 + θ + γθ) 4 (2 + θ) (2 + γθ) − θ²(1 + γ)²
kc22, Π^C₂(N, P ) = 16(2 + γθ)kc32

(2 + θ + γθ) 4 (2 + θ) (2 + γθ) − θ²(1 + γ)²
k_c4², Π^C₁(I, N) = Π^C₂(N, I), Π^C₂(I, N) = Π^C₁(N, I)

Π^C₁(I, I) = Π^C₂(I, I) = (1 + θ) (2 + θ)²,

Π^C₁(I, P ) = (5 + 3θ) [(4+4γθ)((5 + 3θ) (10 − 3θ + 7γθ) + 3θ (10γ + γθ − 5θ)) + k_c5]² (5 + 3θ + 5γθ) 4 (5 + 3θ) (1 + γθ) − 3 (1 + γ)²θ²
k_c6² , Π^C₂(I, P ) = 3 (1 + γθ) [4 (5 + 3θ) ((1 + γθ) (10 + θ − 5γθ) + θ (10 + 7γθ − 3γ²θ)) + k_c7]²

(5 + 3θ + 5γθ) 4 (5 + 3θ) (1 + γθ) − 3 (1 + γ)²θ²
k_c8² , Π^C₁(P, N) = Π^C₂(N, P ), Π^C₂(P, N) = Π^C₁(N, P ), Π^C₁(P, I) = Π^C₂(I, P ), Π^C₂(P, I) = Π^C₁(I, P ),

Π^C(P, P ) = Π^C(P, P ) = 2 (2 + γθ) ,

where

k_c1 = 4 (2 + γθ) 4 + θ + 3γθ − θ²+ γθ²
+ θ (1 + γ) 4 + 3θ + γθ + γθ²− γ²θ²
, k_c2 = 16 (2 + θ) (2 + γθ) − θ²(1 + γ)²,

k_c3 = 4 (2 + θ) 4 + 3θ + γθ + γθ²− γ²θ²
+ θ (1 + γ) 4 + θ + 3γθ − θ²+ γθ²
, kc4 = 16 (2 + θ) (2 + γθ) − θ²(1 + γ)²,

kc5 = 3θ (1 + γ) (1 + γθ) (10 + θ − 5γθ) + θ 10 + 7γθ − 3γ²θ

, kc6 = 16 (1 + γθ) (5 + 3θ) − 3θ²(1 + γ)²,

k_c7 = θ (1 + γ) ((5 + 3θ) (10 − 3θ + 7γθ) + 3θ (10γ + γθ − 5θ)) , k_c8 = 16 (1 + γθ) (5 + 3θ) − 3θ²(1 + γ)².

The graphic illustration is given in Figure 6 and the results are similar to those in the integrated and delegated channels.

Comparative Statics for Delegated and Common Retailer Channels

We list our results in Table 2 for both the delegated and common retailer channels.

Table 2: Comparative Statics for Delegated and Common Retailer Channels.

(i) (I, I) Equilibrium

Delegated Channels Monopoly Common Retailer Channel

∂pi

∂wi = (2+θ)(2+3θ)^2(1+θ)2 > ¹_{2 ∂w}^∂pi

i = ¹₂

∂(^pDi (I,I)−wi^D(I,I))

∂θ = _∂θ^∂ (2+θ)(4+7θ+θ^{2+4θ+θ2 2}) <0 ^∂(^pCi (I,I)−w^Ci (I,I))

∂θ = _∂θ^∂ _2(2+θ)^1+θ >0

∂w^D_i (I,I)

∂θ = _∂θ^∂ _4+7θ+θ^2+3θ ₂ <0 ^∂wiC_∂θ^(I,I) = _∂θ^∂ _2+θ¹ <0

∂q_i^D(I,I)

∂θ = _∂θ^{∂ 2(1+θ)}(^2+4θ+θ2)

(2+θ)(4+7θ+θ²) >0 ^∂qCi_∂θ^(I,I) = _∂θ^{∂ (1+θ)}_(2+θ) >0

Note: ^∂qDi_∂θ^(I,I) > ^∂qCi_∂θ^(I,I). The larger value of θ means both products are less differentiated.

(ii) (P, P) Equilibrium

Delegated Channels Monopoly Common Retailer Channel

∂pi

∂wi = (4+γθ)(4+3γθ)^2(2+γθ)2 > ¹_{2 ∂w}^∂pi

i = ¹₂

∂(^pDi (P,P )−w^Di (P,P ))

∂γ = _∂γ^{∂ 2}(^{8+8γθ+γ2θ2})

(4+γθ)(16+14γθ+γ²θ²) <0 ^∂(^pCi (P,P )−wi^C(P,P ))

∂γ = _∂γ^∂ _2(4+γθ)^2+γθ >0

∂w^D_i (P,P )

∂γ = _∂γ^∂ _16+14γθ+γ^2(4+3γθ)2θ² <0 ^∂wiC_∂γ^{(P,P )} = _∂γ^∂ _4+γθ² <0

∂q_i^D(P,P )

∂γ = _∂γ^{∂ 2(2+γθ)}(^{8+8γθ+γ2θ2})

(4+γθ)(16+14γθ+γ²θ²) >0 ^∂qCi_∂γ^{(P,P )} = _∂γ^{∂ 2+γθ}_4+γθ >0

Note: ^∂qiD_∂γ^{(P,P )} > ^∂qCi_∂γ^{(P,P )}. The smaller value of γ means more effective of persuasive advertising.

Chapter 3 Channel Structure, Brand Loyalty, and Advertising

3.1 Introduction

A central issue in the marketing literature is the selection of channel structure. At least dating back to Spengler (1950), there has been a vast discussion on the comparison between the “direct channel,” in which a manufacturer sells the products directly to end consumers, and the “indirect channel,” in which the manufacturer delegates the sales responsibility to the retailer. Spengler (1950) demonstrates that delegation may lead to “a cascade of monopolies:” Since both the manufacturer and the retailer intend to mark up the prices to claim their profits, the retail price is driven upwards away from the socially efficient level and ultimately hurts the entire channel. Consequently, vertical integration may be more favorable than delegation. This is the celebrated “double marginalization” problem.

A remarkable observation made by McGuire and Staelin (1983) is that such preference over channel structure may be reversed if the manufacturer-retailer dyad is confronted with competition from other channels. They demonstrate that, when two channels engage in price competition in the consumer market, delegating to (independent) retailers may relax the price competition. This “retailer buffer ” may be beneficial for the manufacturers if the products are highly substitutable, i.e., if the competition is intense; as a result, it increases manufacturers’ profits even when the channel is not coordinated. Since then, its robustness has been elaborated by a number of researchers, including Bonanno and Vickers (1988), Coughlan (1985), Gupta and Loulou (1998), Moorthy (1988), Rey and Stiglitz (1995), and Trivedi (1998), among others.

Despite its widely accepted position, mitigating price competition does not (immedi-ately) imply higher profits for the manufacturers or less rivalry between manufacturers. On one hand, if the presence of retailers drives up the ultimate (retail) prices the end consumers face, there may be a loss of potential market demand that would otherwise be materialized had the manufacturers/ retailers offered a lower price. In particular, if the high retail price drives away more likely those consumers that are relatively loyal to a manufacturer (and

less willing to purchase from its rival), this manufacturer may actually suffer from such “lost sales” in spite of the reduced price competition. On the other hand, in addition to price competition, there are various forms of non-price competition among manufacturers that might be crucial in different occasions, e.g., advertising, product/ service quality, and R&D expenditure (DeGraba (1987), and Vilcassim et al. (1999)). Delegation may mitigate price competition but at the same time intensify the manufacturers’ competition in other forms.

DeGraba (1987) proposes that though the introduction of most-favored-customer clauses can facilitate collusive behavior among oligopolists, such devices also can lead to a prisoners’

dilemma, in which each manufacturer has a unilateral incentive to make more aggressive non-price decisions.

Built upon these observations, this chapter attempts to address the following research question: When the threat of losing loyal consumers and non-price competition are present, does delegation to retailers remain beneficial for the manufacturers? To this end, we consider a model with two manufacturers, two dedicated retailers, and three groups of consumers with heterogeneous preferences. Among the consumers, there are a group of switchers that are highly price sensitive, and two less price sensitive loyal segments that prefer to purchase from one manufacturer rather than the other. The manufacturers produce horizontally differentiated products, and are confronted with an economic tradeoff: 1) each manufacturer can integrate the (downstream) retailer to bypass the double marginalization problem, which we label as the “direct channel ” scenario; 2) the manufacturers could rather delegate to the retailers to escape from the intense price competition; this is labeled as the “indirect channel ” scenario.

We start with the base case in which the manufacturers compete only on prices. In such a scenario, we find that the manufacturers may prefer the direct channel if the loyal segments are sufficiently large. To understand this result, it is helpful to reexamine the effect of driving up the retail prices. When the retail prices are jointly set high, the manufacturers extract more revenue from the switchers as the price competition is mitigated. However, a higher retail price also makes the loyal consumers less willing to purchase from their own manufacturers; consequently, the actual sales from the loyal segments may be lower if they

are charged a higher retail price. These two conflicting forces therefore determine the equi-librium/ optimal channel structure. In particular, we show that if the loyal segments are sufficiently large, the second force dominates, thereby leading to a preference in favor of the direct channel (from the manufacturers’ perspective).

We then incorporate the possibility of advertising competition between manufacturers.

In this scenario, each manufacturer can choose to spend a lump sum advertising expense to increase consumers’ gross valuation (reservation price) for its own product. This additional model characteristics allows us to examine how the channel structure affects the competition of different forms. We find that in the indirect channel, it may be beneficial for a manufac-turer to advertise if the rival chooses not to do so; moreover, the manufacmanufac-turer suffers from a significant loss if it does not advertise but the rival does. The intuition is as follows. When the manufacturers delegate to the independent retailers, the resulting retail prices tend to be set high (due to the aforementioned double marginalization problem); this in turn dis-suades some loyal consumers from purchasing any product. In this case, it is profitable for the manufacturer to advertise, for it shifts upwards the consumers’ preferences and allows the manufacturer to capture more loyal consumers. However, we also observe that in certain conditions, advertising may make both manufacturers worse off. Collectively, the availability of advertising may drag the manufacturers into the trap of “prisoners’ dilemma”: advertis-ing appears to be an individually dominant strategy, but both manufacturers may be better off if they could commit not to advertise. On the contrary, if the manufacturers sell directly to the consumers, they may stop the temptation of making wasteful advertising.

Our results demonstrate that competition along dimensions other than prices may alter the manufacturers’ preference over channel structures. Naturally, our specific choice of ad-vertising is only one form of non-price competition. Our results are, however, not necessarily limited to this specific form of competition. Potentially, all our results could hold qualita-tively when the manufacturers’ strategies affect directly the consumers’ valuation regarding the product/ service, thereby leading to the belief that the manufacturers may prefer the direct channels occasionally if the nature of competition is complicated/ multi-dimensional.

This chapter contributes to the vast literature on channel management. The majority

of the extant literature suggests that dedicated intermediaries (retailers) can mitigate price competition among manufacturers following McGuire and Staelin (1983). Coughlan (1985) generalizes the demand function to validate the robustness of the result in McGuire and Staelin (1983). Moorthy (1988) argues that whether decentralization dominates vertical integration could also depend on the product characteristics and the nature of strategic interaction. Gupta and Loulou (1998) find that the conclusion of McGuire and Staelin (1983) is not prone to the presence of vertical externality of a manufacturer’s effort reduction in process innovation. Rey and Stiglitz (1995) show that exclusive territories can serve as a device to reduce competition among manufacturers. They further show that intermediaries may be employed when the channel competition is intense. There are other papers that evaluate the connection between price competition and channel structure, see, e.g., Bonanno and Vickers (1988) and Trivedi (1998). In line with this research, we incorporate advertising competition and thus offer further insights into the strategic effects of adopting different channel structures.

Since we investigate the strategic role of channel structure with the presence of adver-tising competition, This chapter is connected to the literature on adveradver-tising strategies. A number of researchers argue that although persuasive advertising is perceived as a powerful means to create manufacturers’ competitive advantage, it could also result in excessive com-petition that ultimately hurts the manufacturers. For example, Alemson (1970), Kelton and Kelton (1982), and Tremblay and Tremblay (2005) report that if a manufacturer increases its expenditure on advertising, its rival manufacturer(s) may increase their expenditure on advertising as well as a counteraction; this could lead to wasteful advertising expenses due to the reciprocal cancellation. In stark contrast with the aforementioned papers, we show that this reciprocal cancellation need not arise if the channel structure is taken into consideration.

We organize the remainder of this chapter as follows: In Section 3.2, we discuss our basic model characteristics, including the consumer preferences, the channel structure, and the manufacturers and retailers’ objective and decisions. In Section 3.3, we analyze how the existence of loyal segments affects manufacturers’ profits under different channel structures.

In Section 3.4, we introduce the possibility of advertising the products and see how it affects

the equilibrium channel structure. Section 3.5 offers some concluding remarks. All the proofs are in the appendix.

3.2 The model

In our model, there are two manufacturers, two dedicated retailers, and three groups of consumers with heterogeneous preferences and single-unit demand. The preference of a consumer is modeled as an ideal point, denoted by x, that lies within a U-shaped line [−a, 1 + a], where a > 0. The two manufacturers, labeled as M1 and M2, are symmetric and located at the endpoints of this line segment: 0 for M1 and 1 for M2. We denote product 1(2) as the product produced by manufacturer M1(M2). The production cost of each manufacturer is assumed to be constant and normalized to zero without loss of generality.

This U-shaped preference space is modified from the widely adopted Hotelling model (Hotelling (1929)) with the typical setting being a line segment. The specific structure of this preference space allows us to classify the consumers into three groups: switchers, the loyal segment of M1, and the loyal segment of M2, which we describe in detail below.

Switchers uniformly reside in the interval [0, 1] with unit density 1. Each switcher obtains a common valuation V from either product 1 or 2, and incurs a transportation cost with a common transportation parameter t. This transportation cost captures the negative utility arising from the discrepancy between her ideal point x and the product position, and the transportation parameter measures her price sensitivity.

In addition to the switchers, there are two groups of loyal consumers that belong to the turfs of the two manufacturers, respectively. Compared to the switchers, these loyal consumers are less price-sensitive with a higher transportation parameter γt, where γ > 1.

The loyal consumers for M1 are uniformly located in the interval [−a, 0] with unit density, whereas those for M2 reside uniformly on M2’s turf [1, 1 + a] with unit density as well (Tirole (1988)). We assume that a loyal consumer obtains a common valuation V upon obtaining one unit of product, irrespective of which manufacturer she purchases from. Thus, the loyalty is entirely captured by the ideal points and the intensified transportation cost. The U-shaped

preference space, the manufacturers’ positions, and the consumers’ price sensitivities are illustrated in Figure 1.

Figure 1: Model Architecture

From the above description, the turf of a manufacturer is composed of a group of con-sumers that are willing to experience a higher price differential between their favorite man-ufacturer and the other manman-ufacturer (compared to switchers), and are also heterogeneous with regard to the tolerance specified by their ideal points. Similar to the discrete model with a group of homogeneous loyal consumers (e.g., Agrawal (1996)), these loyal consumers are in strong favor of their favorite manufacturer. Nevertheless, the heterogeneity among loyal consumers in a manufacturer’s turf leads to an effective demand curve a manufacturer faces in its own turf in response to its pricing decision. This is arguably a more practical situation than the typical discrete setting, since it allows us to capture the heterogeneity among loyal consumers and endogenize their purchasing behavior with a micro-foundation.

As we elaborate later, this demand curve turns out to be crucial for driving most of our results.

Given the model architecture, if a switcher located at x ∈ [0, 1], her utility upon

pur-chasing one unit of product from either manufacturer can be represented as follows:

where p1 and p2 denote the prices for products 1 and product 2, respectively. For a loyal consumer located at x1 ∈ [−a, 0] (in M1’s turf), her utility can be expressed as:

Likewise, a loyal consumer for M2 with ideal point x2 ∈ [1, 1 + a] obtains a utility:

Likewise, a loyal consumer for M2 with ideal point x2 ∈ [1, 1 + a] obtains a utility:

在文檔中 廣告與通路結構關係之探討 (頁 29-0)