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Pricing strategy & practice
Product categories, returns policy and pricing
strategy for e-marketers
Ruiliang Yan
School of Business and Economics, Indiana University Northwest, Gary, IN, USA
Abstract
Purpose – The purpose of this paper is to provide a framework to help e-marketers to find an optimal returns policy and pricing strategy in order to
maximize their profits.
Design/methodology/approach – A profit-maximization model is developed to determine the optimal returns policy and pricing strategy for
e-marketers.
Findings – The author demonstrates that an optimal returns policy and pricing strategy exists when firms sell products through an e-market. When a
firm uses an e-market to sell its product, its optimal returns policy and pricing strategy is to offer a more generous returns policy and to charge a higher
price when the product web-fit is strong. Furthermore, the results also show that while the returns policy always is valuable for the e-marketer, the
value of returns policy increases with the product web-fit.
Research limitations/implications – The present study assumed that all consumers have perfect information. However, information to the
consumers could be incomplete. It is recommended that future research explores returns policy and pricing strategy under an incomplete information
setting.
Practical implications – This paper provides a very useful model framework, returns policy and pricing strategy for business managers who are using
or planning to use the e-market to sell their products.
Originality/value – This paper fills a conceptual and practical gap for a structured analysis of the current state of knowledge about returns policy and
pricing strategy in e-business. The paper provides practical, solid advice and examples that demonstrate the application of the optimal strategies for
e-business managers.
Keywords Marketing, Returns, Pricing policy, Marketing decision making, Electronic commerce
Paper type Research paper
1. Introduction
According to Comscore Networks, online retail spending in
2006 was $102.1 billion; this was a 24 percent rise over the
previous year’s $82.3 billion (www.webmarketcentral.com).
Also, according to Forrester Research, European e-commerce
will surge to e263 billion in 2011, with travel, clothes,
groceries, and consumer electronics all moving above the e10
billion per year mark (www.forrester.com/Research/
Document/Excerpt/0,7211,38297,00.html). As a result, the
rapid development of commerce on the internet has made
e-market sales attractive for many firms and individuals. From
thecustomer’spoint-of-view,theonlinepurchaseis
advantageous because it drastically reduces the search cost
and is convenient since the online market operates 24 hours a
day, seven days a week, and the customers can purchase
online at any time (Wu et al., 2004).
There is a substantial body of literature (e.g. Chiang et al.,
2003), which indicates that when the same product is
purchased over the internet, it is of less value to the consumer.
There can be several reasons for why consumers perceive
products purchased on the web to be less valuable as
compared to an identical product purchased through a
traditional physical market. One reason could be that many of
the product attributes that are transparent to a consumer in
the traditional physical market, such as the fit of a pair of
trousers, are hidden on the web. Another reason might be that
on the web, possession and gratification is delayed, whereas
they are instant for purchases made through the traditional
physical market. When customers purchase online, they have
to sacrifice the benefit of a physical inspection of the product,
which increases the likelihood of customers who have some
dissatisfaction with the product. This results in the customer’s
desire to return the product. In a survey conducted by Rogers
and Tibben-Lemke (1999), 63 percent of respondents
indicated that a generous returns policy is one significant
tool to draw customers. A generous returns policy can
effectively increase sales volume by inducing more customers
to purchase online. However, a generous returns policy can
also increase the quantity of returned product and lead to
substantially higher costs. According to Rogers and Tibben-
Lemke (1999), returned products could take range from 2 to
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1061-0421.htm
Journal of Product & Brand Management
18/6 (2009) 452– 460
qEmerald Group Publishing Limited [ISSN 1061-0421]
[DOI 10.1108/10610420910989776]
452
50 percent of total sales revenue. Therefore, the returns policy
is a tradeoff.
In this paper, we study this trade-off. We expect that the
optimal returns policy would allow the e-marketer to maximize
its profit. We also know that the pricing strategy is very
important for the e-marketer and is closely related to the
returns policy. Thus when a firm sells product through an
e-market, an important question is how the returns policy and
pricing strategy should be set so that the e-marketer can
optimize its profit. In our research we focus on the pressing
question of an optimal returns policy and pricing strategy under
the consideration of product web-fit. We use a profit
maximization model to specifically study the following
questions: what is the optimal pricing strategy when there is
no returns policy? What is the optimal returns policy and
pricing strategy when the e-marketer offers a returns policy?
What is the value of a returns policy to the e-marketer,
particularly when the product is more suitable for the e-market?
The rest of our paper is organized as follows. Section 2
provides a summary of the relevant literature. Section 3
presents our profit maximization model under two different
scenarios: when the e-marketer does not offers a returns
policy to customers, and when the e-marketer does offer a
returns policy to customers. Section 4 presents our main
results regarding optimal policies and a sensitivity analysis.
Section 5 presents the results of our numerical analysis to
provide some further insights for e-marketers. Conclusions
and managerial implications are presented in section 6.
2. Literature review
In this section, we review the relevant marketing literature to
position our paper.
2.1 E-market pricing
Some of the studies specifically focus on e-market pricing
strategies. See Table I for a summary.
As regards online price dispersion, see Table II for a
summary.
However, all papers mentioned above did not address the
strategic value of a returns policy in the e-market.
2.2 Returns policy
First, a considerable amount of research has been done
regarding the manufacturer’s returns policy. See Table III for
a summary.
The literature also examines the retailer’s returns policy.
See Table IV for a summary.
However, these papers all did not address the strategic
importance of product categories in the e-market, since
product categories always play an important role in the
returns policy, pricing strategy, sales volume and profit of
e-marketers.
2.3 Product categories sold through e-market
Since e-business is becoming more and more popular, optimal
returns policies and pricing strategies are becoming important
issues to the success of e-marketers. Our paper fills a
conceptual and practical gap for a structured analysis of the
current state of knowledge about returns policies and pricing
strategies for e-marketers. In this paper, we use a profit-
maximization model to obtain optimal strategies for an
e-marketer under different scenarios: when e-marketer does
not offers a returns policy to customers, and when e-marketer
does offer a returns policy to customers. Finally, we contrast
and compare these two scenarios to determine policy
decisions. Based on our results, we propose the optimal
strategies for the e-marketer to adopt (Table V).
3. Model framework
3.1 Pricing strategy without a returns policy
In this section, we consider a simple supply chain system
consisting of two players: the e-marketer who sells a product
and customers who buy the product. We introduce the basic
demand model and the pricing decision when a product is
sold through an e-marketer without a returns policy. The
schematic representation of this e-market model is shown in
Figure 1.
When a firm sells products through an e-market, the
product category has an important impact on the customers’
buying decision. This factor-product web-fit,
u
, measures the
extent of synergy between the characteristics of a product and
the internet. Its value varies from zero to one, where zero
signifies no compatibility with the e-market and one stands for
complete compatibility with the e-market. In a similar vein,
Balasubramanian (1998) assumes that product fit with the
e-market varies across product categories. A product has a
value vto a certain customer when it can be physically
inspected and immediately owned. However, the same
product, purchased through an e-market, can only be
virtually inspected and thus be worth
u
v(
u
v#v).
Therefore, in this market, all consumers with valuations in
the interval ½p;
u
v(i.e.
u
vis greater than price to be paid) will
buy this product. So, consumer demand for this product
through the e-market is the following:
d¼
u
v2p;0,p,
u
vð1Þ
We assume that the marginal cost for the product sold
through the e-market is c. To simplify the exposition, we also
assume the marginal cost c¼0 without affecting the basic
results. Thus the profit function of the e-marketer is the
following:
p
¼pð
u
v2pÞð2Þ
Given the above profit function, we obtain the e-marketer’s
pricing strategy with no returns policy. Proof is given in
Appendix 1.
T1. Suppose the e-marketer sells a product without a
returns policy. Then, there exists an optimal pricing
strategy,pN¼
u
v
2, which increases with product web-fit.
Theorem 1 (T1) shows that when there is no returns policy,
the optimal pricing strategy for the e-marketer to adopt is
(pN). In other words, the e-marketer will charge a higher price
for a product with a stronger web-fit. Balasubramanian
(1998), Johannes (2000), and Chiang et al. (2003) show that
such a pricing strategy can effectively maximize a firm’s profit
through e-marketing.
3.2 Pricing strategy with a returns policy
We now modify the above model by considering a returns
policy. A customer pays a price pto purchase a product from
e-marketer. After receiving and trying this product, the
customer may return this product to the e-marketer. The
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
453
e-marketer then gives a refund of f(0 ,f#p) dollars back to
the customer. A higher fmeans that a more generous returns
policy is being provided by the e-marketer. We assume that
the e-marketer will generate higher demand from his more
generous returns policy. Thus, the demand of the product will
take the following form:
d¼
u
v2pþ
b
fð3Þ
b
(
b
.0) is the customer’s sensitivity with respect to the e-
marketer’s returns policy, which measures the efficacy of the
returns policy in stimulating consumer demand. One might
anticipate that the greater the value of
b
, the more the returns
policy contributes to the demand.
In our model, the e-marketer allows the customer to return
the product for a refund of fdollars. Although this returns
policy will generate more demand; it will also generate more
returns from consumers. We model this by the following
equation: q¼b
b
f
Where, qis the returned quantity, and parameter b(b.0) is
the product return rate with respect to the returns policy f.
Thus, the profit function with a returns policy can be written as:
p
¼pð
u
v2pþ
b
fÞ2b
b
f2þsð4Þ
Where sthe total salvage value from returned products. In
order to simplify the computation without losing any
generality (because the salvage value is not a decision
variable in our model), we normalize the salvage value of
returned product to zero (s¼0). From the profit function of
an e-marketer with a returns policy, we find that the profit
function of e-marketer is a concave shape under the condition
4b.
b
(proof is given in Appendix 2). Thus, there exist an
optimal returns policy and pricing strategy for the e-marketer.
In the next proposition, we obtain the optimal solutions for
a returns policy and pricing strategy for the e-marketer. Proof
is given in Appendix 3.
P1. Suppose the e-marketer sells a product with a returns
policy. Then, there exist an optimal returns
policy,fr¼v
u
4b2
b
, and pricing strategy, pr¼2bv
u
4b2
b
, which
increase with product web-fit.
P1 shows that when the e-marketer sells a product with a
returns policy, the optimal returns policy and pricing strategy
for the e-marketer to employ are (fr;pr). The returns policy is
positively related to the product web-fit. The rationale is that
when the product is more suitable for e-market sales, more
customers would like to purchase the product online. Thus a
more generous returns policy would draw many more
customers to the e-market. The e-marketer also can charge
a higher price for the product with a stronger web-fit when the
e-marketer offers a more returns policy to customers.
Table I Review of related research in the pricing strategy of e-marketing
References Addressed research
Dolan and Moon (2000) Studied pricing and market making on the internet and found that it is optimal for the firms to use a different
pricing mechanism on different channels
Baker
et al.
(2001); Kung
et al.
(2002) Conducted research to show that the e-markets do not drive prices down and may help firms to design better
pricing strategies
Ancarani and Shankar (2004) Did an empirical study to reveal that multi-channel retailers have the highest prices and pure play e-marketers
may have the lowest prices in the e-marketing if shipping costs are included
Kurata and Bonifield (2007) Used an analytical model to determine the optimal pricing strategy of the e-business in the hotel and airline
industries and showed that e-business can improve its profit by taking into account customer segmentation
Zhang and Jasimuddin (2008) Studied the different levels of pricing strategies for an online knowledge market and examined how a firm can
use various posting prices to regulate the knowledge market
Table II Review of related research regarding online price dispersion
References Addressed research
Bailey (1998); Clemons
et al.
(1998); Erevellers
et al.
(2001) All found that online price dispersion is the same or higher than offline price dispersion
Brown and Goolsbee (2000); Morton
et al.
(2001) Showed that online price dispersion is lower than price dispersion through traditional
channels
Tang and Xing (2001) Found that price dispersion for pure play e-marketers is lower than price dispersion for
multi-channel retailers
Scholten and Smith (2002) Found that price dispersion for retail and e-tail markets is persistent over time and
across channels
Ratchford
et al.
(2003) Showed that online price dispersion is persistent for eight product categories: books,
CDs, DVDs, PDAs, computers, software and consumer electronics
Ancarani and Shankar (2004) Found that online price dispersion in the books and CDs industry has higher levels if
shipping and handling costs are charged
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
454
4. Analysis
The following proposition shows how the pricing strategy is
affected by a returns policy. Proof is given in Appendix 4.
P2. In an e-market where the price with a returns policy is
higher than the price without a returns policy.
The result in proposition P2 is intuitive. The rationale is that
when the e-marketer offers a returns policy, the return
allowances increase; thus, price with a returns policy should
be higher. Much of the previous researches (i.e. Marvel and
Peck, 1995; Padmanabhan and Png, 1995; etc.) provides
Table IV Review of related research in the retailer’s returns policy
References Addressed research
Davis
et al.
(1998) Used an analytical model to identify potential causes for a retailer’s return policy and found certain conditions for
offering a low-hassle returns policy
Sarvary and Padmanabhan (2001) Showed that a returns policy is an efficient tool for the retailer to reduce demand uncertainty when accurate
demand information is not available
Wood (2001) Did an experimental study to investigate the effects of a retailer’s returns policy on a customer’s purchasing
decision when the customer purchased from remote settings, and found that the probability of a customer’s
purchase is positively related to a generous returns policy.
Mukhopadhyay and Setaputra (2004) Studied the optimal price and returns policy for reverse logistics in e-business and found that a returns policy is
welcomed by the customers and the retailer
Table III Review of related research in the manufacturer’s returns policy
References Addressed research
Pasternack (1985) Used the newsboy model to examine possible pricing strategies and return policies for perishable commodities, and
showed that full credit return or no return for unsold products are suboptimal, while a partial credit returns policy for
unsold products can achieve channel coordination
Marvel and Peck (1995) Incorporated the uncertainties of customers’ arrival and customers’ valuations to examine pricing strategies and return
policies for firms, and found that offering a returns policy raises the retail price
Padmanabhan and Png (1995) Used a game theoretical approach to show that a full returns policy can increase the manufacturer’s profit when retail
competition increases
Emmons and Gilbert (1998) Examined the performance of a retailer in the presence of a returns policy and uncertainty of demand and showed that
uncertainty can increase retail price and under certain conditions, both the manufacturer and the retailer can benefit
from the manufacturer’s generous returns policy
Webster and Weng (2000) Modeled a simple supply chain with one manufacturer and one single retailer for unsold inventory at the end of the
season for perishable product and identified the conditions for the manufacturer’s returns policy
Lee (2001) Explored the role of pricing strategies and returns policies in the channel coordination with a two period newsboy
problem and found that the joint optimal model (JOM) and the individual optimal model (IOM) are comparable to
maximize the supply chain profit
Choi
et al.
(2004) Studied an optimal returns policy for a two-stage supply chain where the manufacturer could sell the returned products
at a higher price through the e-market and identified conditions under which a unique solution to the problem exist
Yao
et al.
(2005) Examined the role of the returns policy in the coordination of a manufacturer and two competing retailers, and found
that provision of a returns policy is based on the market conditions the retailers faced
Chang and Pao (2006) Studied the relationship between the quantity discount strategies and the return policies and showed that the quantity
discount could be negative when the buyback price under a returns policy is too high
Chesnokova (2007) Studied the effect of a returns policy on market outcomes and showed that consumer welfare decreases with product
reliability
Lu
et al.
(2007) Studied channel coordination from a firm’s rebate, returns and price protection policies and identified conditions under
which the supply chain could be coordinated to guarantee a win-win situation
Ding and Chen (2008) Studied how to coordinate a three-level supply chain with flexible return policies and showed that appropriate contracts
can effectively coordinate the three-level supply chain
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
455
further evidence that a more generous returns policy should
be accompanied by an increase in price.
As we know, the bottom line in business is profit, not price.
Profit always is the first consideration for all firms. Therefore,
it is critical to find out under which policy the e-marketer can
derive more profits. This can be determined by comparing the
profits under two scenarios: when the e-marketer does not
offers a returns policy to customers, and when the e-marketer
does offer a returns policy to customers. Accordingly, we
obtain proposition 3. Proof is given in Appendix 5.
P3. The e-marketer’s profit with an optimal returns
policy,
p
r¼bv2
u
2
4b2
b
, is higher than its profit without a
returns policy,
p
N¼v2
u
2
4, and the value of the returns
policy increases with product web-fit.
P3 indicates that the e-marketer always profits more from an
optimal returns policy than from no returns policy, and when
the product web-fit is strong, the e-marketer will profit more.
Therefore, the important managerial guideline is that business
managers should use any operational means to offer a more
generous returns policy to customers under any circumstance
when they sell strong web-fit products through the e-market.
Next, we analyze the effect of any change in the sensitivity
parameters on the value of a returns policy when an e-
marketer sells a product with a strong web-fit. The objective
of this study is to generate some important managerial
guidelines that can be used for making decisions regarding
returns policy.
We first study the effect of the customer’s sensitivity of the
returns policy on the value of the returns policy when the
e-marketer sells a product with a strong web-fit. We obtain the
following proposition. Proof is given in Appendix 6.
P4. In a market where product web-fit is strong, the value
of the returns policy increases with the customer’s
sensitivity of a returns policy (larger
b
).
P4 gives an important managerial guideline. When the
e-marketer sells a product with a strong web-fit, a larger
customer’ sensitivity to the returns policy is desirable because
it increases both product demand and profitability for the
e-marketer. Therefore, the business manager should employ
any possible means to increase customer sensitivity to the
returns policy in the e-market when the product has a strong
web-fit. For example, the clothing e-marketer can use
marketing promotions to inform customers of its generous
returns policy, which thus increases the customer’s sensitivity
to the returns policy.
Next, we study the effect of the product return rate on the
value of the returns policy when e-marketers sell product with
a strong web-fit. We obtain the following proposition. Proof is
given in Appendix 7.
P5. In a market where product web-fit is strong, the value
of the returns policy increases when the product return
rate decreases (decreasing b).
P5 also gives an important managerial guideline. If the e-
marketer can enhance its product quality and improve
customer online support to help customers to select the
right product in the purchase, then more customers would be
more likely to keep the product rather than returning it. Then
there will be a reduction in the product return rate. For
example, when the e-marketer sells digital products, which
have a strong web-fit and are known as sensitive to the
product return rate, e-marketers should actively improve
product quality and support customers’ purchases to decrease
the return rate.
5. Numerical examples
While our findings in propositions can be derived analytically,
the analytical expressions are too complex to provide
meaningful insights. Thus we now present some numerical
examples to illustrate the effect of changes in product
Table V Review of related research in the product categories of e-market
References Addressed research
Hughes (2006) Showed that prominent among the drivers for the adoption of new channels are pricing and product type
Kwak
et al.
(2002) Conducted an empirical study to show that computer-related products and services and books, information, and magazines were
the most frequently purchased products, whereas electronics and entertainment were least frequently purchased online
Bhatnagar
et al.
(2000) Identified some of the product characteristics that decrease the value of a product when it is purchased on the web as compared
to when it is purchased from a traditional retail channel, and found that consumers perceive a high degree of risk when a
product is technologically complex, satisfies ego-related needs, has a high price, and when “touch and feel” is important
Lal and Sarvay (1999) Found that consumers would be less willing to buy products with a high proportion of non-digital attributes. Additionally, it is
also difficult to return products purchased online
Wood (2001) Found that consumer purchases through the web are more risky because of a lack of experiential information about product
returns policies
Korgaonkar
et al.
(2006) Showed that credence products are less likely to sell on the web as compared to search or experience products
Figure 1 The e-marketing diagram
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
456
category,
u
, on the optimal strategies and to illustrate the
value of a returns policy to the e-marketer’ profit. Kacen et al.
(2002) did an empirical study to show that the web-fit of
some products, which is based on actual empirical analysis of
data, turns out to be larger than zero and less than one
(Table VI).
For our simulation, the values we used for the various
parameters are shown in Table VII.
We vary the value of
u
from 0 to 1, and substitute these
values into the optimal strategies under the two scenarios:
when e-marketer does not offer a returns policy to
customers, and when e-marketer does offer a returns policy
to customers.
Figure 2 shows that the returns policy and pricing strategy
is positively related to the product web-fit. In the other word,
the returns policy and pricing strategy always increases when
the product web-fit is stronger. Also, we observed that the
price with a returns policy is higher than the price without a
returns policy. This is exactly matching with what we
analytically found in propositions 1 and 2.
Figure 3 shows that the e-marketer’ profit always increases
when the product web-fit is stronger. The gap between the
cases of an e-marketer without a returns policy and an e-
marketer with a returns policy reflects the value of the returns
policy. This gap shows that as product web-fit increases
(increasing
u
), the value of the returns policy increases for the
e-marketer. This result confirms our analytical observation
obtained in proposition 3.
6. Conclusions and managerial implications
The contributions of this study are both theoretical and
substantive in nature. In this paper, we demonstrate that an
optimal returns policy and pricing strategy exists for the firm
when it sells products through the e-market. We first derive a
returns policy and pricing strategy, and then we do
comparative statistics to determine an optimal strategy
decision. Our results indicate that a firm using an e-market
to sell its product should offer a more generous returns policy
and charge a higher price when its product has a strong web-
fit. Furthermore, our results show that a returns policy is
always valuable for the e-marketer and the value of the returns
policy increases when the product web-fit is stronger. From
our results, we also derive important managerial guidelines
about how business managers can use marketing and
operational strategy to influence the customer sensitivity to
the returns policy and to the product return rate in order to
increase profit. Our numerical examples further illustrate and
verify our analytical findings. Next we summarize the
managerial implications of our research.
The findings in our research are of immense managerial
significance. Our findings can help firms identify the values of
product categories, returns policy, and the corresponding
price strategy when they do business in the e-market.
Additionally, these businesses may be able to use insights
from our research to improve their marketing decisions to
improve profit.
In today’s business environment, with the rapid
development of e-marketing, companies and individuals
are increasingly using the internet to sell directly to
Table VII Parameters values and range of values used in our numerical
analysis
Parameters Base values and range of values
v
2
u
0-1
b
1
b
1
Table VI Product web-fit index
u
for e-market
Category Book Shoes Toothpaste DVD player Flowers Food items
Acceptance 0.904 0.769 0.886 0.787 0.792 0.784
Note: All product categories have
u
below 1.0 at the 1 percent significance
level
Figure 2 The impact of product web-fit on the returns policy and pricing strategy of the e-marketer
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
457
customers. The growing e-business environment provides a
motivation for many firms to better understand the sales
and profit implications of e-marketing. Since e-business is
becoming more and more popular, it is managerially
important to develop an optimal strategy for e-marketers.
This is an intuition-based conclusion. In our paper, we use
profit-maximization model to show that this intuition can be
made objective by selling products with a strong web-fit and
employing optimal returns policies and pricing strategies. By
strategically implementing these strategies, the e-marketer
can maximize its profit efficiently. For example, when e-
marketers are selling strong web-fit products, such as mobile
phones (perishable products), clothing (durable products),
cosmetics (fast moving consumer goods), and curtains
(household appliances), they need offer a generous returns
policy and charge an optimum price for their products. In
the business market, Amazon, Overstock, and Kohl’s e-
channel are some typical examples of companies that have
successfully applied these strategies in their businesses.
The research contained in this study may be updated in a
number of different ways. First, in this paper we assumed that
consumers have perfect information. However, information to
the consumers could be incomplete, and we can explore
returns policies and pricing strategies under an incomplete
information setting. Second, our analysis is based on a single
period model. Future research could examine returns policies
and pricing strategies in a dynamic multi-period environment.
Finally, competition can be explicitly incorporated into our
model, thus allowing analysis of demand not only on a single
firm’s returns policy and pricing strategy but also on the
decision of the competitors.
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Figure 3 E-marketer’s profit with different returns policies
Product categories, returns policy and pricing strategy for e-marketers
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Journal of Product & Brand Management
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458
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Appendix 1
When there is no returns policy,
p
¼pð
u
v2pÞ:
We differentiate
p
on pand let ð
›
p
=
›
pÞ¼0, then we
obtain:
pN¼
u
v
2
Substituting pN¼
u
v
2into profit function, we obtain
p
N¼v2
u
2
4
Appendix 2
When there is a returns policy, d¼
u
v2pþ
b
fq¼b
b
f
p
¼
dp 2qf þsand we assume s¼0.
Thus
p
r¼pðv
u
2pþ
b
fÞ2b
b
f2
Hessian matrix for our profit function is:
22
b
b
22b
b
"#
:
Thus, H1is 22 and H2is 4b
b
2
b
2. Since H1¼22,0, so
if H2¼4b
b
2
b
2.0or4b.
b
, then profit function is
strictly concave.
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
459
Appendix 3
Since
p
r¼pðv
u
2pþ
b
fÞ2b
b
f2
We differentiate
p
ron prand
p
ron frand let ð
›
p
r=
›
prÞ¼0
and ð
›
p
r=
›
frÞ¼0. Then, we obtain:
fr¼v
u
4b2
b
pr¼2bv
u
4b2
b
Substituting fr¼v
u
4b2
b
and pr¼2bv
u
4b2
b
into profit function, we
obtain:
p
r¼bv2
u
2
4b2
b
Appendix 4
Because pN¼
u
v
2and pr¼2bv
u
4b2
b
.
Then we obtain pr2pN¼
b
v
u
8b22
b
.0, thus pr.pN.
Thus, poposition 2 is proved.
Appendix 5
Because
p
N¼v2
u
2
4and
p
r¼bv2
u
2
4b2
b
So we obtain
p
r2
p
N¼
b
v2
u
2
16b24
b
.0
Furthermore, we obtain
›
ð
p
r2
p
NÞ
›
u
¼
b
v2
u
8b22
b
.0
Thus, proposition 3 is proved.
Appendix 6
Because
p
r2
p
N¼
b
v2
u
2
16b24
b
.
Furthermore, we obtain
›
›
ð
p
r2
p
NÞ
›
b
=
›
u
¼2bv2
u
ð4b2
b
Þ2.0
Thus, proposition 4 is proved.
Appendix 7
Because
p
r2
p
N¼
b
v2
u
2
16b24
b
:
Furthermore, we obtain
›
›
ð
p
r2
p
NÞ
›
b
=
›
u
¼22
b
v2
u
ð4b2
b
Þ2,0
Thus, proposition 5 is proved.
Corresponding author
Ruiliang Yan can be contacted at: yanr@iun.edu
Product categories, returns policy and pricing strategy for e-marketers
Ruiliang Yan
Journal of Product & Brand Management
Volume 18 · Number 6 · 2009 · 452 – 460
460
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