Selling vertically differentiated products under one channel or two? A quality segmentation model for differentiated distribution channels

Abstract Many manufacturers have adopted differentiated distribution channels to market vertically differentiated products. However, there is scant literature addressing the quality differentiation in the presence of differentiated channel policies. We, therefore, examine whether (how) differentiated channel policies affect manufacturers’ quality differentiation and all parties’ performance. Specifically, we consider a manufacturer who produces high- and low products together, but with two marketing options: (1) distributing both products through one retailer (Model O), or (2) providing high quality products through one channel but low-tier products through another (Model T). Our results show that the manufacturer is more likely to decrease the level of quality differentiation in Model T than in Model O. Moreover, we show that “quality distortion” is not limited to low-tier products but can occur with high-tier products. We also comment on how the additional horizontal consumer heterogeneity affects our results and the implications of the competition at the manufacturer level.


Introduction
In the past two decades, with improving living standards and accelerating globali-13 sation of economies, consumer demands have become more diversified and personalised 14 (Ma et al. 2012). To cater to a broader and more heterogeneous mix of consumer groups, 2. Relevant literature two approaches. The first is an emphasis on quality differentiation under the assump-111 tion that product quality is exogenous. Mussa and Rosen (1978)  low, then adding the direct channel raises the unit wholesale price and retail price in the 120 indirect channel. In contrast to these studies, in both of our models we consider that 121 quality is an endogenous decision made by the manufacturer.

122
There are also many studies, beginning with Spengler (1950), that assume that prod-123 uct quality is endogenous and that customers have heterogeneous preferences for quality.
124 Rhee (1996) notes that manufacturers should offer a product of similar quality when 125 consumer heterogeneity is not sufficient; otherwise, offering identical qualities is opti-126 mal. Ha et al. (2016) show that a manufacturer offering differentiated products through 127 two channels prefers to sell its high-tier product through a direct channel. Several other 128 papers have studied endogenous quality in supply chain coordination (e.g., Bacchiega 129 and Bonroy (2015), Yang et al. (2015), brand value (e.g., Choi and Coughlan (2006) and demand functions for high-and low-tier products from the consumer utility functions 201 as follows: 3 203 Based on the inverse demand functions in equation (1), we can now consider our two  outputs of high-and low-tier products (q h , q l ) to maximise his profit. That is, taking the 211 wholesale prices of high-and low-tier products (w h , w l ) as given, the retailer's problem 212 is:

Equilibrium analysis
where the first term is the retailer's revenue from selling high-tier products, the second 214 term is the retailer's income from marketing low-tier products, and the remaining two 215 terms are the retailer's cost of wholesaling high-and low-tier products.

216
Anticipating the retailer's response to the wholesale prices she sets, the manufacturer 217 chooses the wholesale prices (w h , w l ) and quality levels (u h , u l ) to maximise her profit: Backward induction is employed to determine the subgame perfect equilibrium in 219 each model. Specifically, we first determine the retailer's optimal quantities from (2) 220 and then substitute them into (3), which provides the equilibrium wholesale prices and Proposition 1. In Model O, the equilibrium quantities, wholesale prices, quality levels, 224 and profits can be summarized as follows: .

234
Proposition 1 is partly consistent with previous studies (e.g., Chung and Lee (2014) In Model T, the manufacturer can reach consumers by adopting a two-channel policy, in which high-tier products are distributed through one channel and low-tier products are sold by another. More specifically, Retailer One chooses his output of high-tier products (q h ) and Retailer Two chooses his output of low-tier products (q l ).
Anticipating the retailer's optimal strategies, the manufacturer chooses the optimal 241 wholesale prices (w h , w l ) and quality levels (u h , u l ) to maximise her profit, that is: ity level and profits using backward induction:

244
Proposition 2. In Model T, the equilibrium quantities, wholesale prices, quality levels, 245 and profits, respectively, are: .

256
From Proposition 2, compared with proposition 1, we find that the quantities of

265
To ensure the comparison of the interior point solutions to both models, as in Gilbert 266 and Cvsa (2003), Savaskan et al. (2004) and Yan et al. (2015), we derive the following 267 assumption: in both models, the cost of selling a high-tier product is not sufficiently 268 large; that is, 0 < c < min( 1 36k , 1). As in the rest of the subsection, we consider only the 269 intersection of the two models.

270
6 All channel members independently seek to maximize their own profit, resulting in higher retail prices and lower sales quantities and profits than in a vertically integrated channel (Spengler 1950).

277
A major concern of this paper is to examine the strategic consequences of canni- Remark 1 shows that, compared to that in Model O, the optimal policy of the 306 manufacturer would reduce the difference between the two products in Model T. Remark 307 2 further indicates that the competition between downstream agents may affect both 308 the high-tier and low-tier products: On the one hand, in a high-valuation market, the 309 optimal quality of high-tier products in Model T is always lower than that in Model O.

310
On the other hand, in a high-valuation market, when c > 162 10000k , the optimal quality 311 of low-tier products in Model T is always lower than that in Model O; otherwise, the 312 opposite is true. Taken together, these two remarks suggest that, when confronting the 313 competition between downstream agents, the manufacturer is more likely to reduce the 314 difference between the two products by unduly downwardly distorting the quality of the 315 high-tier products; however, she may downwardly or upwardly distort the quality of the 316 low-tier products.

317
As mentioned earlier, selling products through a two-channel policy, in which two 318 downstream agents independently seek to maximise their own profit, results in stronger 319 competition than in Model O. If the high-tier products were not counterbalanced by 320 setting a lower price through downwardly distorting quality, then the cannibalisation 321 from low-tier products would unduly reduce the demand for the high-tier products and 322 thereby reduce the profits. Thus, although the downward quality distortion for high-323 tier products reduces the marginal revenue from them, it increases profits by supporting 324 their substantial demand through offering lower prices. Note that the manufacturer's 325 profits come from two sources: selling high-and low-tier products. When the selling 326 cost disadvantage for high-tier products is sufficiently pronounced (i.e., c > 162 10000k ), the 327 manufacturer's profitability from high-tier products decreases. Thus, in order to earn 328 more profits, the manufacturer has little concern about cannibalisation from the low-329 tier products and would increase the availability of low-tier products by downwardly 330 distorting their quality. However, when the selling cost disadvantage for high-tier prod-331 ucts is not pronounced (i.e., c < 162 10000k ), the manufacturer is greatly concerned about 332 cannibalisation from the low-tier products. To avoid reducing the marginal revenue from 333 high-tier products, the manufacturer would upwardly distort low-tier products, resulting 334 in a lower cannibalisation problem from those low-tier products.

335
companies the downward quality distortion of a low-tier product, while the high-tier 337 product is immune to quality distortion. In particular, Villas-Boas (1998) concluded 338 that, in general, the downward quality distortion of a low-tier product becomes mag-339 nified, leading to quality degradation and increased differentiation in the product line.

340
However, Remark 2 reveals that, when confronting competing downstream agents, a 341 manufacturer is more likely to reduce the quality difference by unduly downwardly dis-342 torting the quality of the high-tier products. Although a similar modelling approach is 343 adopted in Villas-Boas (1998), our model differs due to its focus on whether (how) dif-344 ferentiated channel policies affect manufacturers' quality differentiation and all parties' 345 performance. It is also inconsistent with the results of Chung and Lee (2014), who show 346 that channel decentralisation does not necessarily lead to quality distortion of low-tier 347 products, but that this can happen to high-tier products.  349 We can now address the second question posed at the beginning of this paper: Which 350 scenario is beneficial for the manufacturer, the retailer(s) and the supply chain: selling 351 differentiated products under one channel or two? Based on Propositions 1 and 2, we 352 are able to summarise several key differences between the two models:

Remark 3. i) The manufacturer is always better off in Model T than in Model O; that
iii) The profit of the total supply chain in Model T is higher than that in Model O; Remark 3i) shows that the manufacturer always benefits from the two-channel policy

Remark 4. i) As the selling cost of high-tier products (c) increases, the levels of quality
ii) The difference in the retailer's profit between the two models is the highest for the iii) As the cost of selling high-tier products (c) increases, the difference in the prof-399 itability for the manufacturer and the supply chain between the two models decrease; that the cost of selling high-tier products. Recall that an increase in the cost of selling 403 high-tier products means that retailers have a greater disadvantage in marketing high-404 tier products, which can reduce the competition between high-and low-tier products.

405
Note that increased competition among retailers contributes to the profitability of the 406 manufacturer. Hence, in Model T, as the disadvantage from selling high-tier products 407 increases, the manufacturer tries to increase the difference between the products. How-408 ever, in Model O, when confronting a monopolist retailer who distributes both products 409 together, as the disadvantage of selling high-tier products increases, the manufacturer 410 is more likely to reduce the difference between the products.

411
Remark 4ii) shows that the cost of selling high-tier products plays an interesting and 412 intuitive role in the retailer's profits: in addition to cannibalisation of high-tier products 413 by low-tier ones, as the cost of selling high-tier products decreases, the competition 414 between the two channels intensifies and causes the profitability of both retailers to 415 decline. Conversely, the cost of selling high-tier products increases and the retail cost 416 disadvantage for the high-end store is too great, which causes the high-end store to 417 derive less revenue from high-tier products and results in the retailer's profitability to 418 decrease. Therefore, the difference between the two models in the retailer's profit is 419 highest for a medium sale cost of c ∆ .

420
As Remark 4iii) shows, the difference in profits for the manufacturer and the total 421 supply chain reduces between the two models. This can be interpreted as follows: as    O, when confronting a monopolist retailer who distributes both products together, as 479 the selling cost, c, decreases, the manufacturer is more likely to reduce the difference 480 between the products; this is to maximise his own profit and to mitigate the canni-481 balisation between both products. Figure 2(b) illustrates that, as Remark 4 ii) and iii) shown, the difference in the retailer's profit between the two models is the highest 483 for the medium selling cost of c ∆ . However, the difference in the profitability for the 484 manufacturer and the supply chain between the two models decrease with the cost of c.

Model Generalizations 7 486
In this section, we analyze two relevant extensions and discuss: 1) How does the We can use backward induction to solve both models and obtain the following result.
and achieves minimum at x ∆ ; 497

ii) Both the industry and the manufacturer are better off in Model T than in Model
we can conclude that Remark 1, which indicates that the levels of quality differentia-511 tion decline in Model T relative to Model O, is robust, regardless of whether there is 512 a customer search problem and/or transaction costs between different channels. Fur-513 thermore, the difference in the levels of quality differentiation under both models is a 514 concave function for the transaction costs x, and reaches its maximum at x ∆ . Sec-515 ond, Figure 3(b) shows that the manufacturer's profit is always higher under Model

516
T than under Model O. This difference increases with the transaction costs x; that is, Figure 3(b) shows that, from the retailer's perspective, 518 selling differentiated quality products through two channels can still lead to a loss in 519 profitability; that is, π T * r < π O * r . This is consistent with Remark 3ii). Finally, Figure   520 3(b) shows that selling differentiated quality products through two channels can still 521 lead to a higher profit for the supply chain; that is, π T * s > π O * s . This is consistent with 522 Remark 3iii).

Manufacturer-level competition 524
Our analysis until now has assumed that the manufacturer is the monopoly supplier 525 in the market. This is inconsistent with the practice where multiple manufacturers 526 compete with each other to distribute products through a common retailer in the same 527 market. Thus, in this subsection, we consider the scenario in which two manufacturers 528 compete with each other for providing differentiated products. Comparing these results 529 from those in the preceding section allows us to focus specifically on the implications of 530 competition at the manufacturer level.

531
Let q i , and Q i , be the units of products made by two manufacturers, where i = h, l 532 denotes the type of product (high-or low-quality, respectively) of manufacturer 1 or 2.

535
Focal Firm: Competitor: Where 0 < e < 1 represents the degree of competition between the two manufacturers.

536
The higher the value of e, the more intense is the competition between them.

537
Solving both competitors' problems with backward induction, we can obtain several 538 interesting characteristics under competition at the manufacturer level.  that Remark 6 counterparts of our main results in the preceding sections (see, e.g.,  To gain additional insight into quality segmentation in the impact of market-related 576 factors, such as differentiated distribution channels, we develop two channel models for a 577 manufacturer who produces two types of products (high-and low-tier products) together 578 but with two options for marketing them: (1) marketing both products through one 579 retailer (one-channel policy) or (2) providing high-tier products through one retailer 580 but low-tier products through another (two-channel policy). Our main analysis and 581 discussion is of interest to product and marketing managers, as quality segmentation 582 is characterized by a close relationship with differentiated distribution channels. We 583 discuss managerial implications of our key results and make suggestions for further 584 research below.

585
First, our study suggests that the manufacturer is more likely to decrease the level 586 of quality differentiation in Model T than in Model O. That is, our first result points to 587 the fact that cannibalization in product lines design is not an "evil" to prevent, but an 588 effective strategy that leads financial growth. This is no surprise, on the one hand, as 589 previous research has argued that, as the competition among the retailers increases, the 590 profitability of the supplier increases. Taking the reasoning one step further, we demon-591 strate that the manufacturer is more likely to increase the substitutability of products, 592 which leads a more intense competition between downstream agents. On the other 593 hand, although many believe that the cannibalization is detrimental to manufacturer, 594 and, thus, should be prevented through a selection with multi-distribution channels, 595 our results are in line with the work of Nijssen (1999), who provided empirical support 596 for this theoretical result when they conducted a survey of 95 product and marketing 597 managers from 21 fast-moving consumer goods companies. In particular, they argued 598 that the manufacturer would prefer to line extensions involve cannibalization problems 599 due to "cannibalization is very much positive related to a line extension's success".

600
Second, our analysis reveals that "quality distortion" is not limited to low-tier prod-601 ucts, but can occur with high-tier products, an argument supported by Robertson (1998) 602 who showed that, although the taste of consumers have dramatically improved, rather 603 releasing those products with radical innovation, many firms are more likely distort 604 downward the quality of high-tier products by sharing components in commonality with 605 those low-tier ones. For example, Toyota motor offered several model of Lexus (high-tier 606 products) based on the same platform and engine as that of the Camry line (low-tier 607 ones). Similarly, the premium Honda Acura car is nothing but "Honda Accord: same 608 perfume, different bottle" (Desai et al. 2001). Similar case also appears in a variety of industries, such as Mobile Phones, Personal Computers, and Electronics and Appli-610 ances, where high-tier products usually share basic-common with the existing low-tier 611 units.

612
Finally, it should be noted that, we have shown a conflict internal to the supply chain 613 between the upstream agents (i.e., manufacturers) and downstream agents (i.e., retail-614 ers): The two-channel policy benefits the manufacturer but hurts the retailer. During 615 the 1980s, in order to generate asymmetric bargaining power, manufacturers used dis-616 tributing quality differentiated products through multi-channels to create an advantage 617 of sharing revenue from the sale process (Aaker et al. 1994). However, the situation 618 has now changed. In particular, the retailing industry today is increasingly dominated 619 by centrally managed "power retailers" who are more sophisticated and manage their . Thus there is a unique global optimal (q O * h , q O * l ). By applying FOCs to it with respect to q , q l , we can obtain Plugging (1) .

773
Solving the first-order condition yields one root of is sufficient to above conditions, that is, it will be a maximum point.

775
Substituting of q h , q l , respectively. By applying FOCs to it with respect to q h , q l , we can obtain .

782
Plugging (1), q T * h and q T * l into the manufacturer's profit (5) and π T M is jointly concave 783 in (w h , w l ). Thus there is a unique global optimal (w T * h , w T * l ). Solving the first-order Plugging (1), w T * h , w T * l , q T * h and q T * l into the manufacturer's profit (5) and solving 786 the first-order condition yields one root of After simplification, this reduces to 0 < c < 2 49k , for the sales of both products to be positive, 0 < c < 1 36k with this restriction, After simplification, this reduces to 0 < c < 1 20k . Since 1 36k < 1 20k , that is to say for . 803 We can easy find that For the sales of both products to be positive 0 < c < 1 36k . With this restriction, for the sales of both products to be positive 0 < 814 c < 1 36k . With this restriction, π T * r < π O * r is always holds.
his optimal outputs of high-and low-tier products (q h , q l ) to maximise max q h ,q l π O r = (p h − w h )q h + (p l − w l )q l 10 , to establish optimal quantities as q h = 1+u h −x−w h +w l −u l −x 2(u h −u l ) and 839 q l = xu l +u l w h −u h (1−x)−w l u h 2u l (u h −u l ) . Substituting these into Equation (3)  , respectively. In the last stage, the 841 manufacturer's problem is to design product qualities to maximise the profit in Equation

851
As before, we can obtain the equilibrium outcomes using backward induction, in 852 particular, To enable clear analysis of the effect of transaction cost, we assume that the retailer's unit marketing costs for high-and low-tier products are identical, i.e., c h = c l = c, and normalised to zero, i.e., c = 0.
. Substituting these into Equation (5)  2−e , respectively. In the last stage, the manufacturer's problem is 885 to design product qualities to maximise the profit in Equation (3); accordingly, we can 886 determine that u h = 9 23k and u l = 6 23k .

887
The details are omitted here and all equilibrium decisions and profits in the following 888 Table. 889