lower cost or higher quality? product enhancement ... · cost reduction and quality improvement...
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Lower Cost or Higher Quality? Product EnhancementDecisions When Consumers Are Strategic
Sang-Hyun KimYale School of Management, Yale University, New Haven, CT 06520, [email protected]
Robert SwinneyGraduate School of Business, Stanford University, Stanford, CA 94305, [email protected]
December, 2009
Abstract
Firms developing new products must often make a trade-o¤ between production costs andproduct quality: higher quality products are more valued by consumers, but also more costlyto manufacture. We analyze the impact of activities that increase consumer value (qualityimprovement e¤orts) and activities that decrease production costs (cost reduction e¤orts) onthe pro�t of a �rm. We demonstrate that when demand is deterministic, an increase in consumervalue and a decrease in production cost of the same amount have an identical e¤ect on �rm pro�t.When demand is stochastic, however, the two strategies di¤er. In particular, if consumers arenon-strategic, cost reduction is always more valuable to the �rm than quality improvement (ofthe same amount). On the other hand, if consumers are strategic (i.e., anticipate future pricereductions and time their purchasing decisions), quality improvement may be more valuableto the �rm, in stark contrast to the non-strategic consumer case. Surprisingly, with strategicconsumers, the �rm does not necessarily prefer the greatest degree of cost reduction or qualityimprovement possible, even if it is costless to achieve. We conclude that demand uncertaintyand consumer purchasing behavior greatly in�uence a �rm�s choice of a product enhancementstrategy.
1 Introduction
For a �rm designing a new product, among the many decisions made during the development process
is whether to focus �nite resources on activities that reduce manufacturing costs or on activities
that increase consumer willingness-to-pay for the product, both of which potentially result in an
increase in the product�s pro�t margin. The decision of which strategy to pursue (if any) is typically
based on an economic analysis of the costs and bene�ts of each approach. For instance, adapting
an example from Ulrich and Eppinger (2008), consider a �rm which has already �nalized the basic
architecture and function of a new product, and is in the process of evaluating possible changes
to the product�s design or manufacturing process. The �rm may conclude that the R&D expense
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associated with reducing marginal production costs by $1 while holding the product�s selling price
constant is $10,000, while the R&D expense of increasing consumer willingness-to-pay (and hence
the selling price) by $1 while holding manufacturing costs constant is also $10,000. Both approaches
increase the product�s margin by $1; thus, all else being equal, the �rm would seem to value both
strategies equally.
While most managers would undoubtedly cite a desire to pursue both strategies simultaneously,
thereby minimizing production costs and maximizing consumer value for the product, it is often
the case that �rms are either unable or unwilling to do so (Rust et al 2002). For example, because
of the high costs involved with either approach, resource-constrained �rms (e.g., limited by budget,
technical expertise, the number of employees, etc.) may be forced to pursue one strategy or the
other, but not both. Thus, in this paper, we analyze the value of these mid- to late-stage product
design activities, which we call product enhancement e¤orts, in order to determine how a �rm
should value them and choose between them.
While product design and development encompasses myriad decisions and potential choices,
we abstract our focus to the two basic approaches discussed above. The �rst, which we call
cost reduction, decreases expenses by minimizing production costs while maintaining the quality
of the product perceived by the consumers. Cost reduction may be enabled by a variety of
activities, including process innovation (e.g., changes in the manufacturing process which result
in lower defect rates and more e¢ cient usage of materials), product redesign (e.g., modifying the
product architecture to maintain the same consumer functionality while lowering the number of
components), and sourcing from more e¢ cient or lower-cost suppliers. The second approach, which
we call quality improvement, increases revenues by generating greater consumer willingness-to-pay.
Quality improvement includes all activities that may result in increased consumer value, and may
be enabled by adding new features to the product, improving the performance of existing features,
or increasing the durability of the product by upgrading raw materials or components.1
The choice between cost reduction and quality improvement arises not only with �rm designing
new products, but also with �rms revising existing products. For example, faced with high manu-
1We note that in the operations management literature, the term �quality improvement�is frequently synonymouswith �cost reduction�and refers to process quality improvement. Throughout the paper, we use �quality improve-ment�to refer instead to the distinct strategy of an increase in end-user (consumer) value resulting from improvementto the functionality, features, or intrinsic quality of the product.
2
facturing costs on its popular PlayStation 3 video game system, Sony chose to focus its e¤orts on
cost reduction, lowering the unit production cost by 50% in 13 months by simplifying the design,
reducing the number of components, and shrinking the processor size using new manufacturing
technologies (Hall 2008). These changes, while resulting in substantial costs savings, caused little
or no change in product functionality from the consumer standpoint (i.e., the device continued to
play the same games). In the same industry and during roughly the same time period, Nintendo,
a chief rival to Sony, chose the opposite strategy, releasing an enhanced version of its DS portable
gaming system, called the DSi, with a larger screen, more memory, and the capability of playing
new types of games, raising the selling price by more than 30% (Buckleitner 2009). Thus, Sony
pursued a cost reduction strategy while Nintendo followed a quality improvement approach.2
Substantial academic and practical debate persists as to which strategy should be employed
under what circumstances. At a basic intuitive level, however, there is no reason to believe
that one strategy is superior to the other. In fact, as Spence (1984) argues, all else being equal
(in particular, the total demand), the two approaches are equivalent. To see why, consider a
generalization of our example above: suppose that, midway through the development stage after
the basic design has been �nalized, the �rm determines that it can set the product price such that
all surplus is extracted from consumers who have homogeneous valuations v for the product and
that it can manufacture the product at marginal cost c. If the �rm invests in quality improvement
activities to increase consumer valuations from v to v + � while keeping the marginal production
cost at c, the net bene�t is � per unit sold. On the other hand, if the �rm invests in cost reduction
activities to reduce the production cost from c to c� � while maintaining consumer valuation, the
net bene�t is again � per unit sold. By this reasoning, ceteris paribus, the two strategies bring
identical value to the �rm.
In this paper, we challenge this simple argument that quality improvement and cost reduction
are equivalent by demonstrating that two important factors � uncertain demand and forward-
looking consumer behavior �greatly in�uence the �rm�s preference between the two strategies. To
obtain these insights, we analyze a stylized model in which a �rm makes a investment decision
2 It is worth noting that while Sony and Nintendo are competitors, the two products mentioned here do not directlycompete with one another: the Sony product is a non-portable home unit while the Nintendo product is a handheld,battery operated game system. Hence, the opposing strategies of the �rms in this case do not appear, at leastdirectly, to be the outcome of competition.
3
Figure 1. The six potential product development interactions, with our focus highlighted by the shadedfactors and bold interaction arrows (�gure adapted from Ulrich and Eppinger 2008).
to either lower manufacturing costs or raise product quality at a mid-to-late stage in the product
development stage. Both cost reduction and quality improvement incur �xed, up-front R&D
costs initially, but eventually bring the bene�ts of lower production costs and greater consumer
willingness-to-pay (and hence prices), respectively. The �rm must decide whether the �xed costs of
cost reduction and quality improvement justify the marginal changes in the product�s manufacturing
cost and consumer valuation, and if so, which product enhancement strategy should be adopted.
In making this decision, the �rm has to consider potential impacts on the selling price, the optimal
quantity to be produced, the strategic incentives of the consumers who may delay purchasing to
take advantage of a clearance sale, and ultimately, pro�tability to the �rm. Put another way, we
consider three of the six potential product development interactions as discussed by Ulrich and
Eppinger (2008); see Figure 1.
We �rst show that, in the absence of demand uncertainty, the �rm is in fact indi¤erent between
the two strategies if the amount of cost reduction equals the amount of value increase to consumers,
thereby agreeing with the informal argument outlined above. If, however, demand is uncertain and
production leadtimes are long (leading to potential supply-demand mismatches), the �rm strictly
prefers a cost reduction of � per unit to a value increase of an identical amount. Intuitively, this
is because cost reduction is enjoyed on each unit the �rm produces, while an increase in consumer
value is only enjoyed on each unit the �rm sells; facing demand uncertainty, average sales are less
than the production quantity, leading to a preference for cost reduction.
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We then examine the impact of forward-looking (or strategic) consumer behavior on the �rm�s
preference between cost reduction and quality improvement. Strategic consumers anticipate that at
the end of the product�s lifecycle, excess inventory will be cleared at a reduced price, and they take
the potential future price reduction as well as the chance of a stock-out into account when choosing
whether to buy the product at the full price or wait for the clearance sale. We demonstrate that,
when consumers are strategic and demand is uncertain, the value of both strategies to the �rm is
reduced. Interestingly, the �rm may prefer quality improvement of � per unit to cost reduction
of the same amount when it faces strategic consumers, directly contrasting with the case of non-
strategic consumers. The reason for this result is that a higher quality product makes consumers
less willing to wait for a clearance sale by increasing the downside risk of a stock-out (i.e., the
foregone utility if a consumer waits for the sale but is unable to obtain a unit). The �rm can
exploit this fact to raise price and increase the pro�tability of the product more than it can with
cost reduction, leading to a (possible) preference reversal when the consumer population exhibits
strategic behavior.
Generally speaking, the choice between cost reduction and quality improvement may be in�u-
enced by a variety of other factors, including branding issues (e.g., whether the �rm o¤ers �bargain�
products or �premium�products), technical expertise (the �rm may be better at driving costs down
than improving the product, or vice-versa), and market characteristics (e.g., the market for a high
quality product may simply not exist). However, our results show that, looking purely from an
operational standpoint and holding all else equal, the two strategies are not generally equivalent,
and moreover, the values of the two strategies depend critically on whether the consumer popula-
tion exhibits forward-looking behavior and how such behavior interacts with demand uncertainty.
This, in turn, demonstrates that important product enhancement decisions �speci�cally, whether
to manufacture high-cost, high-quality products or low-cost, low-quality products � are a¤ected
both by demand uncertainty and inter-temporal consumer purchasing behavior.
The remainder of the paper is organized as follows. §2 discusses the related literature, and §3
introduces the basic model. §4 analyzes cost reduction and quality improvement in the presence of
non-strategic consumers. §5 discusses strategic consumers and the �rm�s preference between cost
reduction and quality improvement in their presence. §6 concludes the paper.
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2 Related Literature
There are three streams of research that bear particular relevance to this paper. The �rst is the
marketing and economics literature on revenue expansion and cost reduction. Rust et al. (2002)
provide an excellent survey and empirical analysis of this issue. Rust et al. (2002) consider both
strategies to be rooted in the concept of quality: cost reduction is an internal manifestation of
quality (e.g., process quality, the minimization of waste, Six Sigma programs, etc.), while revenue
increase (which we refer to simply as �quality improvement�) is an external manifestation of quality
(i.e., quality as it relates to the consumer�s needs). Rust et al. (2002) consider �rm-wide emphasis
on cost reduction or quality improvement, and perform an extensive survey-based and empirical
examination of which strategy performs better. They �nd that revenue expansion (a focus on
increasing quality from the consumer point of view) generally is associated with better long-term
stock market performance than a focus on cost reduction. Furthermore, they �nd little value
results from attempting to focus on both strategies simultaneously, referred to as a �dual empha-
sis�approach, and indeed this simultaneous approach is associated with negative long-term stock
returns. In contrast to Rust et al. (2002), we focus not on a �rm-wide culture of cost reduction or
quality improvement, but on the more salient issue of where to focus development resources for a
single product.
Spence (1984) considers the value of investment into research & development that ultimately
results in cost reduction, analyzing �rm incentives for R&D spending in a competitive market in
which investment into R&D causes some spillover e¤ects (i.e., R&D spending impacts the quality
or cost of a competitor�s products). As previously mentioned, Spence (1984) brie�y argues that
cost reduction and consumer valuation increase are equivalent. Speci�cally, Spence (1984) claims
equivalence in the following manner: if a product is thought of in terms of the services it delivers
to consumers, increasing the quantity of services per unit of the product (and hence consumer
willingness-to-pay) while maintaining the total production cost is equivalent to reducing the mar-
ginal cost of each service provided to consumers. This is a similar, but not identical, argument to
the one we presented in the introduction. In contrast, Levin and Reiss (1988) also consider R&D
spillovers but model quality improvement and cost reduction as distinct forms of R&D. Related to
this literature, but distinct in its underlying mechanism, is the learning curve literature in which
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the degree of cost reduction is a function of total output �see, e.g., Spence (1981). In our model,
by contrast, cost reduction and quality improvement are the result of costly investment during the
product development phase rather than endogenous process learning during the production phase.
The second relevant area of research is the operations literature on process quality improvement
and cost reduction. Motivated by the surge of quality improvement programs in the 1980s typi�ed
by the Toyota Production System (Ohno 1988) and Six Sigma, the papers in this stream focus on
the economic value of operational quality improvement (that is, internal quality as it relates to
process and production, resulting in operational cost reduction). For example, Porteus (1985) and
Porteus (1986) consider the impact of reducing set-up costs in manufacturing systems with �xed
cost components. More recently, a stream of research has emerged that examines incentives to
invest in quality across �rms in the supply chain, e.g., Zhu et al. (2007). Unlike our paper, the
papers in this area typically do not consider external quality, i.e., quality of the product as perceived
by the consumer, as opposed to internal quality, which is related to the �rm�s production process.
An exception is the literature on product design and development; however, even in this literature,
the potential operational di¤erences between cost reduction and consumer quality improvement
have not been fully explored. For example, in discussing the economics of product development,
Ulrich and Eppinger (2008) combine an analysis of a $1 increase in the price of a product with a
$1 decrease in the marginal cost of a product, stating that �each results in a $1 increase in the unit
pro�t margins.� In a recent study, Kim and Netessine (2009) investigate how the supply chain
members�incentives to collaborate during the product design stage are impacted when there is an
opportunity to reduce production cost together but there is information asymmetry regarding it.
While this work is closely related to ours, we focus on other aspects that they do not consider, i.e.,
strategic consumer behavior and comparison of cost reduction with quality improvement.
The third and �nal pertinent area is the operations literature on strategic (or forward-looking)
consumer behavior. Su and Zhang (2008) analyze the impact of strategic consumer behavior on
�rm inventory and pricing decisions, as well as supply chain performance. Liu and van Ryzin (2008)
determine when it is optimal for a �rm to intentionally ration capacity (that is, purposely price
such that demand exceeds supply) when selling to rational consumers. Aviv and Pazgal (2008)
analyze multiperiod pricing schemes in the presence of forward-looking consumers. Cachon and
Swinney (2009a) and Swinney (2009) both examine the value of quick response inventory systems
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when consumers are strategic, the former with consumers whose valuations for the product decline
over time and the latter with consumers who have uncertain valuations. Other related papers that
consider the impact of operational or marketing levers on consumer purchasing behavior include
Yin et al. (2009), Debo and van Ryzin (2009), Su (2009), Su and Zhang (2009), Liu and Xiao
(2008), and Lai et al. (2009); none of these papers, however, considers the impact of product design
decisions on strategic consumer purchasing.
The most relevant papers to our own in this stream are Balachander and Srinivasan (1998),
Cachon and Swinney (2009b), Krishnan and Ramachandran (2008), and Agrawal et al. (2009).
Balachander and Srinivasan (1998) explore how �rms can optimally price when consumers expect
future price reductions due to internal �rm process learning. In Balachander and Srinivasan
(1998), unlike our paper, the pursuit of cost reduction is not a decision of the �rm, but rather
inevitably occurs as a result of the �rm�s learning curve. Moreover, the possibility of quality
improvement is not considered by Balachander and Srinivasan (1998). Cachon and Swinney
(2009b) consider the value of so-called �fast fashion�production systems when selling to forward-
looking consumers. These systems combine reduced production leadtimes (or quick response
capabilities) with enhanced product design e¤orts that increase consumer value, much like our
notion of quality improvement. However, the focus in Cachon and Swinney (2009b) is on the
interaction (and complementarity) of rapid production and enhanced design�cost reduction as a
development decision is not considered. Krishnan and Ramachandran (2008) also consider product
design decisions when selling to strategic consumers, focusing on whether the �rm should pursue
modular, upgradeable designs when consumers anticipate future generations of a product (e.g.,
with technology goods that deterministically improve over time). Agrawal et al. (2009) considers
product design decisions when consumers value exclusivity. However, neither of these papers
consider the trade-o¤ between quality and cost as part of the design process.
To summarize, our model is, to the best of our knowledge, the �rst to consider the value of
optional cost reduction activities when selling to strategic consumers, as well as the �rst to analyze
�rm preferences between cost reduction and quality improvement in this setting.
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3 Model
In this section we introduce the basic characteristics of our model and discuss a special case that
serves as a benchmark: deterministic demand. We begin by describing the modeling assumptions
that are common to both the cost reduction and quality improvement models.
A single �rm sells a single product. Due to long production leadtimes or inherent uncertainties
in consumer demand for the product, the market is of unknown size; thus, the total number of
consumers in the market is D, a non-negative random variable with cdf F and pdf f . Let F denote
the complement of F . We assume that F exhibits the increasing generalized failure rate (IGFR)
property. Consumers are homogeneous and have equal valuations for the product. Before market
size is known, the �rm chooses an inventory level q and a selling price p. At the end of the season
all unsold inventory is salvaged at a discounted price.
Prior to production, the �rm invests in a single product enhancement strategy: either cost
reduction or quality improvement, but not both. We assume that the �rm pursues these activities
before it chooses an inventory level and selling price, a reasonable assumption since both cost
reduction and quality improvement involve such activities as product redesign, sourcing partner
selection, and market research, all of which require signi�cant up-front investment and advanced
planning that precede production. Without these measures, the unit production cost is equal to
c, the consumer valuation of the product is v, and the clearance price is s, with s < c < v. We
assume that the clearance market is in�nite and exogenous (i.e., there is no limit to the number of
units that may be disposed of at price s), both standard assumptions in the newsvendor model.
Cost reduction requires a �xed investment of Kcr and reduces the unit cost from c to c � �cr.
Quality improvement requires a �xed investment of Kqi and increases the consumer valuation from
v to v + �qi. We refer to �cr as the amount of cost reduction and �qi as the amount of value
increase resulting from quality improvement. Much of our analysis treats �cr and �qi as �xed
and exogenous, though we also discuss the values of these parameters that maximize �rm pro�t;
thus, our model captures situations in which the �rm does not have control over the extent of its
enhancement e¤orts as well as scenarios when the �rm can optimally adjust quality and production
cost. Observe that both categories of enhancement e¤orts (cost reduction and quality improvement)
lead to predictable outcomes, i.e., they bring higher pro�tability to the �rm, and are characterized
9
by positive �xed costs and zero variable costs.3
In addition to increasing consumer value for the product, quality improvement also results in an
increase of the salvage price from s to s+ �qi. The parameter represents the fractional residual
value of �qi retained in the markdown stage and assumes any value between 0 and 1: if = 0, the
added value �qi completely disappears during clearance, whereas if = 1, the entire added value
is retained. Both are extreme situations, however, and in reality, 0 < < 1 is expected (i.e., some
fraction of the improvement in product quality carries through to the markdown price); for this
reason, we assume that is de�ned in the open interval (0; 1) and treat = 0 and = 1 as the
limiting cases.
We assume 0 � �cr < c � s and 0 � �qi < (c � s)= to ensure that the �rm does not have an
incentive to produce an in�nite quantity of the product (i.e., we do not consider the case where the
overage cost is negative). We consider the entire range of �cr and �qi in order to identify situations
where cost reduction or value increase due to quality improvement are bene�cial for the �rm. In
other words, we aim to answer a general question: does the cost savings of �cr dollars justify the
investment of Kcr dollars, and does the value increase of �qi dollars justify the investment of Kqi
dollars? In addition, in order to conduct fair comparisons and to facilitate the generation of clear
insights, in a number of places we focus on the symmetric case �cr = �qi and Kcr = Kqi, i.e., when
the costs and bene�ts of cost reduction and quality improvement are identical. Note that, when
we consider the symmetric case, we restrict �qi to be less than c � s instead of (c � s)= since
�qi = �cr < c� s.
Summarizing, the sequence of events is as follows:
1. The �rm chooses whether to invest in cost reduction or quality improvement.
2. The �rm chooses a selling price and an inventory level.
3. Consumers arrive to the market and choose whether to buy given the selling price.
3Cost reduction and quality improvement activities resulting from the R&D e¤orts of a �xed sta¤ are frequentlycharacterized primarily by �xed costs; for example, see Spence (1984). The lack of variable costs (e.g., an e¤ortcost e (�cr) for each dollar of production cost reduction) is without loss of generality when �cr and �qi are exogenous.When these quantities are endogenous, variable e¤ort costs signi�cantly complicate the analysis and make the modelintractable. Moreover, while the lack of variable costs with endogenous �cr and �qi would lead one to believe thatthe �rm will simply reduce product costs or increase quality as much as possible, we �nd surprisingly in §5 that thisis not the case when customers behave strategically.
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4. All remaining inventory cleared at the salvage price.
For Step 3, we consider two separate cases: consumers who are myopic (i.e., they do not wait
for markdown pricing; in §4) and consumers who are strategic (forward-looking; in §5).
Now we present our �rst result, which establishes the equivalence between cost reduction and
value increase due to quality improvement for the symmetric case when the demand is deterministic.
Proposition 1 Suppose that �cr = �qi and Kcr = Kqi. With deterministic demand, cost reduction
and value increase are equivalent and yield the �rm the same expected pro�t.
Proof. All proofs appear in the appendix.
As others have noted, there may be additional bene�ts to quality improvement (speci�cally,
product innovation) relative to cost reduction (speci�cally, process innovation) �for example, an
increase in the market size (e.g., Levin and Reiss 1988) �but absent these mechanisms, as expected,
in a deterministic world a �rm is indi¤erent as to the source of an increase in its pro�t margin,
ceteris paribus. Thus, in this setting, one may think of cost reduction and quality improvement
as equivalent practices, which supports the line of research modeling R&D and innovation as cost
reducing activities (e.g., Spence 1984, Reinganum 1983). However, demand is rarely known with
absolute certainty, and so it is important to consider how this result is a¤ected if the �rm has
imperfect information about the total market demand for the product; consequently, in the following
pages we contrast the result derived in Proposition 1 with a similar analysis derived under the
condition of stochastic demand.
4 Myopic Consumers
In this section, we will consider the case of myopic consumers �that is, consumers who purchase
if their valuation weakly exceeds the selling price, without consideration of future purchasing op-
portunities (speci�cally, without considering the possibility of purchasing the product during the
clearance sale). We use the superscript m to denote prices, quantities, and pro�ts with myopic
consumers.
We �rst consider a baseline model in which the �rm does not invest in either cost reduction
or quality improvement. Because consumers are myopic, they purchase at the full price if p � v.
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Consequently, if the �rm does not invest in either strategy, the �rm�s expected pro�t as a function
of price and inventory is
�mb (p; q) = (p� s)S (q)� (c� s) q;
where S (q) = E[minfq;Dg] is the expected sales and the subscript b stands for �base� model
and the superscript m stands for myopic customers. Because consumers are myopic, the �rm can
extract all surplus and still induce consumers to purchase at the full price, i.e., pmb = v. Expected
pro�t is thus
�mb (q) = (v � s)S (q)� (c� s) q;
which is concave in q and has optimal inventory level qmb = F�1�1� c�s
v�s
�. Observe that, substi-
tuting qmb in, we get
�mb (qmb ) = (v � s)
Z qmb
0xf (x) dx+ (v � s)
Z 1
qmb
qmb f (x) dx� (c� s) qmb
= (v � s)Z qmb
0xf (x) dx+ (v � s) qmb F (qmb )� (c� s) qmb
= (v � s)Z qmb
0xf (x) dx+ (v � s) qmb
�1� 1 + c� s
v � s
�� (c� s) qmb ;
implying that that the �rm�s expected pro�t with optimal price and quantity is
�mb = (v � s)Z qmb
0xf (x) dx: (1)
We now describe our models of the two potential �rm strategies of cost reduction and quality
improvement, beginning with the former. Under the assumptions outlined in §3, the expected
pro�t as a function of inventory and price is
�mcr (p; q) = (p� s)S (q)� (c� �cr � s) q �Kcr:
It can be shown in a manner similar to the above argument that the �rm chooses optimal price
and inventory as pmcr = v and qmcr = F�1�1� c��cr�s
v�s
�, with the resulting optimal expected pro�t
being
�mcr = (v � s)Z qmcr
0xf (x) dx�Kcr: (2)
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It is clear from the expressions above that qmcr � qmb .
Next, we consider the case of �rm investment into quality improvement. The expected pro�t
is
�mqi (p; q) = (p� (s+ �qi))S (q)� (c� (s+ �qi)) q �Kqi:
As a result of quality improvement, the consumers purchase the product during the initial sales if
and only if p � v+ �qi. Again, similarly to the argument for the base model, it can be shown that
the �rm chooses optimal price and inventory as pmqi = v + �qi and qmqi = F�1�1� c�s� �qi
v�s+(1� )�qi
�,
with the resulting optimal expected pro�t being
�mqi = (v � s+ (1� ) �qi)Z qmqi
0xf (x) dx�Kqi: (3)
Moreover, it is also easy to see that qmqi � qmb . The following proposition characterizes situations
in which these two strategies are pro�table to the �rm.
Proposition 2 With myopic consumers, cost reduction is pro�table to the �rm for su¢ ciently
small Kcr and su¢ ciently large �cr. Similarly, quality improvement is pro�table for su¢ ciently
small Kqi and su¢ ciently large �qi. Moreover, �rm pro�t increases in both �cr and �qi.
In other words, the �rm prefers investing in cost reduction or quality improvement if the changes
in the unit cost or the product value (�cr or �qi) are large enough that the generated pro�t increase
is greater than the associated �xed cost (Kcr or Kqi). It is intuitive that the larger the changes,
the more pro�table the product is, i.e., the �rm�s expected pro�t increases in either �cr or �qi.
We are now in a position to compare the value of cost reduction and quality improvement.
Recall from Proposition 1 that these two strategies are equivalent with deterministic demand when
the costs and bene�ts of implementing them are symmetric. However, as the following proposition
shows, the same result no longer holds when demand uncertainty is introduced.
Proposition 3 Suppose that �cr = �qi and Kcr = Kqi. With myopic consumers, cost reduction
yields a greater expected pro�t than quality improvement.
In other words, if demand is uncertain, the �rm always prefers a cost reduction of size � to
a quality improvement of the same amount. The reason that the �rm prefers cost reduction to
13
quality improvement is quite simple: cost reduction is equally enjoyed on every unit produced, while
the full bene�t of quality improvement is only enjoyed on every unit sold. If demand is stochastic,
then in expectation, more units are always produced than are sold. Therefore, the �rm enjoys a
greater bene�t by pursuing cost reduction than quality improvement. More speci�cally, while the
underage cost is the same in both cases (i.e., v� (c� �) = (v+ �)� c), the overage cost under cost
reduction is smaller than that under quality improvement (i.e., (c � �) � s < c � ( � + s)), hence
the mismatch cost is greater under quality improvement.4 Recall from Proposition 1 that, with
deterministic demand, no such discrepancy exists since every unit produced is sold. Therefore,
the equivalence between cost reduction and quality improvement breaks down when demand is
stochastic, and the �rm prefers cost reduction to quality improvement. These results, however, are
for myopic, non-strategic customers; in the next section, we investigate how this insight changes if
the �rm faces strategic consumers who decide whether to purchase immediately or wait until the
clearance discount.
5 Strategic Consumers
We now consider the impact of having strategic (or forward-looking) consumers, beginning with
the base case in which neither cost reduction nor quality improvement are present. Our model
of strategic purchasing by consumers and inventory-pricing decisions by the �rm follows those of
Su and Zhang (2008) and Cachon and Swinney (2009b). In those papers and in ours, the entire
population of full-price consumers (as represented by the random variable D) is �strategic�in the
sense that every consumer considers the �rm�s actions (i.e., price and inventory) and the actions of
other consumers (i.e., when and whether they attempt to purchase the product) when making her
own purchase decision.
More speci�cally, the D full-price consumers arrive at the start of the selling season (when the
product is for sale at price p) and recognize that at the end of the season, a clearance sale will occur
in which all remaining inventory is sold for s. Each consumer then independently considers buying
the product immediately (at the full price) or delaying her purchase until the clearance sale. An
4 It is observed from these expressions that the two strategies are again equivalent in the limiting case ! 1 asthe overage costs become identical as well. As we motivated in §3, however, < 1 is a reasonable assumption sincethe discount re�ected in the ratio of valuations across the initial and clearance markets, s=v < 1, is likely to apply tothe added value �qi, at least partially.
14
immediate purchase yields surplus v � p, i.e., the consumer valuation minus the purchase price.
A delayed purchase at price s yields a greater potential surplus (v� s > v� p, since p > s) but
runs the risk of being unsuccessful: the retailer may run out of inventory. We assume that at the
start of the selling season, consumers believe a delayed purchase will be successful with probability �
and that an unsuccessful delayed purchase (i.e., an intentional delay only to experience a stock-out)
yields a consumer zero surplus. Hence, the expected surplus of a delayed purchase is � (v � s).5
We assume that consumers purchase the product at the full price if and only if their surplus
from doing so is at least as great as their surplus from waiting for the clearance sale. In other
words, strategic consumers pay p and purchase the product in the initial selling season if
v � p � � (v � s) : (4)
The consumer population and the �rm thus play a game in which the �rm chooses the inventory
level (q) and the selling price (p), and consumers choose when to purchase the product (at the full
price or the clearance price) based on the observed selling price (p), the clearance price (s), and
their beliefs concerning the availability of the product during the clearance sale (�). In order to
derive the equilibrium to this game, we must specify the consumer belief �. Our assumption is
that consumer beliefs are rational (Besanko and Winston 1990, Su and Zhang 2008, and Cachon
and Swinney 2009a and 2009b). This implies that � is the actual equilibrium product availability
in the clearance sale for a consumer who delays a purchase.
Because consumer beliefs are rational, all consumers must possess the same belief � of clearance
period inventory availability. Because consumers have the same valuations and beliefs, it follows
then that all consumers will attempt to purchase at the same time: either at the full price or during
the clearance sale. All consumers delaying until the clearance sale is clearly not supportable as an
equilibrium with non-zero production (since all sales would occur at s < c, the product would be
unpro�table in this case), hence we restrict our attention to the candidate equilibrium in which all
consumers purchase at the full price.
If all consumers purchase at the full price in equilibrium, then it must be true that (4) holds
5Observe that customers do not discount future consumption, i.e., if there is no stock-out risk a consumer valuesa purchase tomorrow and a purchase today equally. Discounting can be incorporated into the model, resultingin signi�cantly more complicated equilibrium price and inventory expressions but qualitatively similar customerbehavior; see Cachon and Swinney (2009b).
15
for all consumers. Moreover, it must also be true that � is the probability that a single strategic
consumer who unilaterally deviates from equilibrium successfully obtains the product at the clear-
ance sale. Recall our assumption of an in�nite clearance market from the myopic consumer case
(§4). We interpret that assumption here as an in�nite population of �bargain hunting�consumers
�distinct from the population of D strategic consumers �who arrive during the clearance sale and
purchase any remaining units at price s. We further assume that these consumers purchase after
any strategic consumer who delayed has a chance to purchase at the clearance price.6 Hence, a
strategic consumer unilaterally deviating from the equilibrium in which all D consumers attempt to
purchase early will obtain a unit in the clearance sale if and only if the �rm has su¢ cient inventory
to cover all D consumers, i.e., if q � D. The equilibrium probability that this occurs is F (q), the
in-stock probability, where q is the �rm�s equilibrium inventory level. Thus, rational consumer
expectations of clearance sale inventory availability imply � = F (q).
Consequently, any equilibrium must satisfy four conditions (where we employ the superscript s
to denote equilibrium prices, quantities, and pro�ts with strategic consumers):
1. Consumers must have incentive to purchase early: v � ps � � (v � s).
2. The �rm must price optimally: ps = argmaxp ((p� s)S (qs)� (c� s) qs).
3. The �rm must set inventory optimally: qs = argmaxq ((ps � s)S (q)� (c� s) q).
4. Consumer beliefs must be rational: � = F (qs).
It is easy to see from conditions (1) and (2) that the �rm�s optimal selling price is ps =
v � � (v � s), the greatest price which will induce early purchasing. From conditions (3) and (4),
in the base model (with neither cost reduction nor quality improvement), the in-stock probability
is � = F (q) = p�cp�s . Substituting this expression for � and solving for p yields the equilibrium
selling price and inventory
psb = s+p(c� s) (v � s); qsb = F�1
�1�
rc� sv � s
�:
6 In other words, customers who strategically wait have priority during the clearance sale, as assumed in Su andZhang (2008) and Cachon and Swinney (2009b). This might be the case if, e.g., strategic customers who purposelydelay a purchase carefully monitor the �rm for the announcement of a clearance sale, and quickly act to buy oncesuch a sale occurs.
16
The resulting optimal expected pro�t is
�sb =p(c� s) (v � s)
Z qsb
0xf (x) dx: (5)
5.1 Cost Reduction with Strategic Consumers
If the �rm pursues cost reduction, a similar analysis as above shows that the optimal selling price
is pscr = s +p(c� �cr � s) (v � s) and the optimal inventory is qscr = F�1
�1�
qc��cr�sv�s
�. The
resulting optimal expected pro�t is
�scr =p(c� �cr � s) (v � s)
Z qscr
0xf (x) dx�Kcr: (6)
Observe that pscr � psb and qscr � qsb . That is, the equilibrium price is lower and the equilibrium
order quantity is higher if the �rm pursues cost reduction than if it does not. To understand this
result, let us consider how a strategic consumer�s incentive to wait is a¤ected by cost reduction.
Recall that a consumer purchases the product at the full price if and only if v�p � � (v � s), where
� is equal to the in-stock probability in equilibrium. Reducing the unit cost by an amount of �cr
does not directly a¤ect the consumer�s utility, as neither the initial surplus v � p or the clearance
period surplus v � s is changed. Instead, cost reduction impacts the consumer�s expectation �
about the in-stock probability set by the �rm; the �rm�s underage cost is increased from p � c to
p � (c � �cr) while the overage cost is reduced from c � s to (c � �cr) � s, thereby increasing the
newsvendor critical fractile and requiring a higher level of inventory. As the consumer anticipates
that there will be more leftover units available during the clearance sale, she is more willing to wait.
Consequently, the �rm must reduce the selling price to discourage the consumers from waiting and
to induce them to purchase early at the high price. This is in contrast to the myopic consumers
case, where cost reduction activities did not impact the equilibrium selling price.
Now let us study how �rm�s expected pro�t varies with �cr. First, observe that
d�scrd�cr
=� (v � s)
2p(c� �cr � s) (v � s)
Z qscr
0xf (x) dx+
p(c� �cr � s) (v � s)qscrf (qscr)
dqscrd�cr
:
The �rst term is negative, while the second term is positive. The �rst is due to price reduction
17
(i.e., as costs decrease the equilibrium price also decreases, which reduces revenue on each unit
sold) and the second is due to volume increase (i.e., as costs decrease the equilibrium inventory
increases, which increases expected sales). This suggests that the value of cost reduction is not
monotonically increasing in �cr when the �rm faces strategic consumers. This stands in contrast
to the myopic consumers case, where we found in Proposition 2 that the �rms�s expected pro�t
is always increasing in �cr. The following proposition formalizes this observation by providing
conditions that dictate the behavior of equilibrium pro�t as a function of �cr when the �rm sells
to strategic consumers. In what follows, we say that cost reduction is pro�table to the �rm if it
yields greater expected pro�t than that of the base model, accounting for �xed costs.
Proposition 4 The Value of Cost Reduction with Strategic Consumers. Let bqcr be theunique solution of
�(q) � qF (q)�Z q
0xf(x)dx = 0
and b�cr � (c � s) � (v � s)F (bqcr)2. Firm pro�t with cost reduction is a quasi-concave function of
�cr and is maximized at b�cr. Two cases then arise:(i) If b�cr � 0, cost reduction is never pro�table for the �rm facing strategic consumers.
(ii) If b�cr > 0 and Kcr is su¢ ciently small, then there exists an interval of �cr around b�cr in whichcost reduction is pro�table for the �rm. The upper bound of this interval is strictly less than
c� s.
Intriguingly, �rm pro�t is not monotonically increasing in the degree of cost reduction (�cr)
when consumers are strategic. Moreover, the last part of Proposition 4 indicates that there is
an upper bound of �cr for which cost reduction is pro�table, even if the �xed and variable costs
associated with cost reduction are zero. In other words, cost reduction is not valuable to the �rm
if the extent of cost reduction is large. While this result may seem counterintuitive, it is in fact
a natural consequence of strategic purchasing behavior. Suppose that the �rm�s production cost is
extremely low. Then the pro�t margin is big while the loss incurred during clearance sale is limited,
so the �rm produces in large quantities, and as a result, the in-stock probability is high. Thus,
consumers have a very large incentive to delay purchasing until the clearance sale, which means
the �rm must o¤er heavy discounts in the full price period in order to induce early purchasing. If
18
0.5 1.0 1.5 2.0 cr
50
50
100
150
200
Figure 2. The incremental value of cost reduction with myopic consumers (upper line) and strategicconsumers (lower line) as a function of �cr, when demand is normally distributed with � = 100 and � = 20,
v = 5, c = 3, s = 1, and Kcr = 10.
�cr is too large (i.e., if the unit cost is lowered too much), the price discount e¤ect dominates the
bene�t the �rm receives from lower production costs, making cost reduction undesirable. Hence,
not only is �rm pro�t not monotonically increasing in �cr (as it was in the myopic consumer case), it
actually becomes better not to invest in cost reduction if the amount of reduction �cr is su¢ ciently
large; see Figure 2.
In fact, the proposition suggests that cost reduction may never be pro�table to the �rm (regard-
less of the �xed cost) if consumers�incentives to wait were already very high even before cost reduc-
tion. This happens if the overage cost c�s is too small such that b�cr = (c�s)�(v�s)F (bqcr)2 � 0.If c � s is su¢ ciently large, on the other hand, �rm pro�t is maximized at an intermediate valueb�cr that lies between the boundary of feasible costs. The last result suggests that, if the �rm does
have the capability to choose the extent of cost reduction to implement (i.e., choosing �cr), the
�rm will not generally desire to reduce the unit cost as much as possible when selling to strategic
consumers. (This is true even if cost reduction has zero marginal costs and only �xed costs, as we
assume in this model.) This is in stark contrast to the case with myopic consumers, in which the
�rm always prefers the greatest degree of cost reduction possible. Consequently, we conclude that
strategic behavior can have an enormous impact on how much a �rm values cost reduction and
how much cost reduction is optimal to pursue.
19
5.2 Quality Improvement with Strategic Consumers
We next consider the impact of quality improvement in the presence of strategic consumers. In-
corporating the increase in consumer valuation (�qi) and the increase in the salvage price ( �qi)
resulting from quality improvement, we see that strategic consumers will purchase at the full price
if
v + �qi � p � � (v � s+ (1� )�qi) ; (7)
where � is the probability of obtaining a unit at the clearance price, i.e., � = F (q) = p�cp�s� �qi . Thus,
the �rm�s optimal selling price and inventory are psqi = s+ �qi+p(c� s� �qi) (v � s+ (1� ) �qi)
and qsqi = F�1�1�
qc�s� �qi
v�s+(1� )�qi
�, respectively. The resulting optimal expected pro�t is
�sqi =q(c� s� �qi) (v � s+ (1� ) �qi)
Z qsqi
0xf (x) dx�Kqi: (8)
The following proposition shows when quality improvement is pro�table to the �rm with a strategic
consumer population, paralleling Proposition 4 for cost reduction. As before, we say that quality
improvement is pro�table to the �rm if it yields greater expected pro�t than the base model,
accounting for �xed costs.
Proposition 5 The Value of Quality Improvement with Strategic Consumers. Let bqqibe the unique solution of
�(q) � �(q) + (1� )F (q)2S(q) = 0; (9)
where �(q) is de�ned in Proposition 4, and
b�qi � (c� s)� (v � s)F (bqqi)2 + (1� )F (bqqi)2 : (10)
Firm pro�t with quality improvement is a quasi-concave function of �qi and is maximized at b�qi.Two cases then arise:
(i) If b�qi � 0, quality improvement is never pro�table for the �rm facing strategic consumers.
(ii) If b�qi > 0 and Kqi is su¢ ciently small, then there exists an interval of � around b�qi in whichquality improvement is pro�table for the �rm. The upper bound of this interval is strictly
20
less than (c� s)= .
Proposition 5 demonstrates that strategic consumer behavior has a signi�cant impact on the
value of quality improvement e¤orts, just as it did on the value of cost reduction activities. As the
proposition shows, the �rm�s pro�t with quality improvement (and hence the pro�t increase over
the base model, �sqi � �sb) is quasi-concave in the amount of value increase (�qi), and is maximized
at �qi = b�qi speci�ed in (10). Thus, it may not be optimal to improve quality (increase consumervalue) as much as possible with strategic consumers even if variable costs to doing so are zero,
unlike the myopic consumer case.
Comparing Propositions 4 and 5, we see that the qualitative behavior of the �rm�s pro�t increase
as a function of �qi due to quality improvement activities is similar to that under cost reduction.
In particular, as was the case with cost reduction, quality improvement is not pro�table to the �rm
regardless of the �xed costKqi if the added value �qi is too large, i.e., if �qi is close to its upper bound
(c � s)= . This similarity, however, masks a major distinction between quality improvement and
cost reduction: the pro�tability of quality improvement is a function of , whereas the pro�tability
of cost reduction is independent of this parameter. Indeed, the incentive dynamics of the consumers
and the �rm critically depend on the value discount .
In order to understand this, let us investigate how the consumer incentives to wait are impacted
by quality improvement, as we did in the discussion above Proposition 4 for cost reduction. Con-
sumers purchase the product in the initial sales stage if and only if the condition in (7) is satis�ed.
As apparent from the expression, the added value �qi directly impacts the consumers�utility, by
increasing both the initial stage surplus (from v � p to v + �qi � p) and the second stage surplus
(from v � s to v � s+ (1� )�qi). Because < 1 and � < 1, holding all else equal (in particular,
�xing �), increasing consumer value by �qi increases the initial stage surplus more than second
stage surplus, thereby increasing consumer incentives to pay full price and allowing the �rm to
charge a greater initial price, p.
However, the �rm will choose a higher inventory level since the overage cost is reduced from
c�s to c�s� �qi while the underage cost p�c increases if p increases. As a result, the consumers�
expectation � for the in-stock probability increases. In sum, both sides of (7) increase as a result
of quality improvement, and it is a priori unclear which side dominates, i.e., whether the consumer
21
has more incentive to wait or not.
Inspecting the two limiting cases, ! 0 and ! 1, helps resolve this ambiguity. Consider
= 1 �rst. Comparing (6) and (8), we see that the optimal solution coincides with that of
Proposition 4 with �qi and Kqi replaced by �cr and Kcr; as approaches 1, cost reduction and
quality improvement become equivalent. (Note that the same observation was made in the myopic
consumers case; more on this later.) Then, from the discussion above Proposition 4, we infer that
consumers are more willing to wait under quality improvement when = 1, which leads to a lower
equilibrium full price.
Now suppose that = 0. Then the condition (7) becomes v + �qi � p � �(v + �qi � s) and
the overage cost becomes c � s. As both the underage and the overage costs are independent
of �qi, the �rm leaves the in-stock probability unchanged and hence the consumers�expectation �
remains constant. The net e¤ect is then that the added value �qi increases the left-hand side of
v + �qi � p � �(v + �qi � s) by a larger amount than the right-hand side, as � < 1. As a result,
consumers are less willing to wait and therefore the �rm can charge a high price for the initial sales,
thereby increasing its pro�tability with higher �qi. Notice that the consumers�incentive to wait
with = 0 is exactly the opposite of what we observed when = 1; indeed, the degree of value
discount plays a critical role in evaluating the e¤ect of quality improvement investment.
5.3 Cost Reduction or Quality Improvement?
Having derived equilibrium pro�ts under both the cost reduction and quality improvement ap-
proaches, we may now answer our central question: which product enhancement approach is more
valuable to the �rm when selling to strategic consumers? We begin with the following proposition,
which focuses on how the maximizer b�qi varies with .Proposition 6 Let �scr(�cr) and �
sqi(�qi) be �rm pro�t with cost reduction and quality improvement
evaluated at particular values of �cr and �qi, and let b�qi, the value of �qi which maximizes �rm pro�t,be as de�ned in (10). Then:
(i) @b�qi=@ < 0 with lim !0 b�qi =1 and lim !1 b�qi = b�cr.(ii) @�sqi(b�qi)=@ < 0 with lim !1 �sqi(b�qi) = �scr(
b�cr) +Kcr �Kqi.
22
Proposition 6 demonstrates two features of �rm pro�t with quality improvement. First, that the
pro�t-maximizing amount of valuation increase, b�qi, lies in the interval (b�cr;1) and is a decreasingfunction of (the residual valuation increase in the clearance period). Second, that �rm pro�t
at the optimal �qi is decreasing in . Though perhaps not obvious at �rst, this is a fascinating
result. Recall that the clearance price for the product is s + �qi. Greater implies a greater
salvage value (more precisely, a greater fraction of the initial value retained in the clearance sale)
�so Proposition 6 demonstrates that the �rm�s equilibrium pro�t is lower if the clearance price is
higher. This is precisely the opposite result that we would expect from traditional newsvendor
logic (i.e., that a greater salvage price lowers overage costs and increases �rm pro�t).
The reason for this result is that a greater salvage price, ceteris paribus, results in an increase in
the inventory level of the �rm, which increases consumer incentives to wait for the sale by increasing
inventory availability, thereby forcing the �rm to lower the full price to induce early purchasing.
It�s not immediately obvious that an increase in will always result in a decrease in pro�t, however,
since higher also implies strategic consumers who wait have to pay a higher price in the clearance
sale, which should decrease consumer incentives to delay purchasing. In addition, higher clearly
implies the �rm earns more on each unit in the clearance sale. Despite these counteracting forces,
Proposition 6 shows that, at least when �qi is chosen optimally, �rm pro�t is a decreasing function
of , implying the price discounting e¤ect dominates.
Moreover, Proposition 6 also shows that the pro�t with quality improvement converges to the
pro�t with cost reduction (accounting for di¤erences in �xed costs) as approaches 1, i.e., as the
residual valuation increase in the clearance period approaches the valuation increase in the full
price period. The combination of these results immediately leads to the following corollary:
Corollary 1 If Kcr = Kqi, b�cr < b�qi and �scr(b�cr) < �sqi(b�qi).
Corollary 1 shows that if �xed costs are equal and the �rm may optimally determine the degree
of cost reduction and quality improvement to pursue, then quality improvement always outperforms
cost reduction with strategic consumers. More precisely, the �rm�s expected pro�t increases in
a longer interval and up to a higher level as a function of �qi under quality improvement than as
a function of �cr under cost reduction. See Figure 3 for numerical examples that support this
observation.
23
0.1
0.4
0.7
0.85
1
0.5 1.0 1.5 2.0qi
10
10
20
30
40
Figure 3. The value of quality improvement with strategic customers as a function of �qi, when demand isnormally distributed with � = 100 and � = 20, v = 5, c = 3, s = 1, and Kqi = 10. The thick line also
represents the value of cost reduction.
It follows that in at least some instances, quality improvement is preferred to cost reduction
when the �rm faces strategic consumers. While Corollary 1 shows that this is true at the optimal
choices of �cr and �qi when �xed costs are identical, the following proposition demonstrates when
this result holds in the case in which cost reduction and quality improvement are not optimally
chosen, but rather have identical dollar amounts, �cr = �qi.
Proposition 7 Suppose that � = �cr = �qi and Kcr = Kqi. With strategic consumers, quality
improvement yields a higher expected pro�t than cost reduction if � is su¢ ciently large.
Thus, unlike the myopic consumer case (discussed in Proposition 3), the �rm does not necessarily
prefer a cost reduction of � to quality improvement resulting in a valuation increase of the same
amount. This result is in stark contrast to Proposition 3, where we found that, ceteris paribus,
the �rm always prefers cost reduction to quality improvement; with strategic consumers, we �nd
that, if � is su¢ ciently large or if �cr and �qi are set optimally, the �rm�s preference among the two
strategies is reversed.
Note that for small �, quality improvement may or may not yield a higher expected pro�t
than cost reduction does, depending on parameter values. Numerical experiments reveal that the
situations where cost reduction is preferred to quality improvement for small � are characterized
24
c 3
c 4
c 4.5
0.2 0.4 0.6 0.8 1.0 1.2 1.4qi
0.5
0.5
1.0
1.5
2.0
2.5
3.0
Figure 4. The di¤erence between the �rm�s pro�t under quality improvement and the pro�t under costreduction as a function of �, when demand is normally distributed with � = 100 and � = 20, v = 5, s = 1,
and Kqi = Kcr = 10. In this example, = s=v.
by small and large c, all else being equal. Figure 4 shows examples in which cost reduction is
preferred for small � while quality improvement is preferred for large �.
Overall, as we combine the results of Corollary 1 and Proposition 7, a picture emerges that
quality improvement is more robust to strategic behavior than cost reduction. The reason for
this insight is that quality improvement can actually increase consumer incentives to buy early and
allow the �rm to raise the equilibrium selling price (for su¢ ciently small , as argued above), unlike
the cost reduction case, which always results in decreased consumer incentives to pay full price and
hence requires heavy price concessions in order to induce early purchasing.
However, in order to arrive at this conclusion, we relied on the analyses of two special cases:
(a) a scenario in which �cr and �qi are exogenously given and are the same across the two strategies
(Propositions 3 and 7 for non-strategic and strategic consumers, respectively), and (b) a scenario
in which the �rm can choose �cr and �qi optimally (Corollary 1 for strategic consumers). These
assumptions are made to facilitate fair comparisons. Now we raise the following question that is of
great managerial importance: if the �rm knows that investing K dollars results in cost reduction
of �cr dollars per item or value increase of �qi dollars (but �cr 6= �qi), and also knows whether the
consumers are strategic or not, which strategy should the �rm choose? The answer is investigated
numerically and a graphical example is shown in Figure 5. As Figure 5(a) suggests, cost reduction
25
Figure 5. Firm preference as a function of the amount of cost reduction and value increase with (a)myopic customers and (b) strategic customers, with Kcr = Kqi. The dark rectangles represent the areasin which neither strategy is pro�table to the �rm. The dotted line represents the symmetric case, i.e.,
�cr = �qi.
is preferred over a wider range of (�qi; �cr) combinations when consumers are myopic. However, the
opposite is true if consumers are strategic, as Figure 5(b) shows. This provides another validation
of our assertion that quality improvement becomes a more attractive option than cost reduction
when the �rm faces strategic consumers.
The results above also suggest that, at least in some circumstances, cost reduction and qual-
ity improvement activities are not as valuable with strategic consumers as they are with myopic
consumers. As the following proposition demonstrates, a cost reduction of �cr or a quality im-
provement of �qi is always less valuable due to strategic behavior compared to the same changes
made in the presence of myopic consumers.
Proposition 8 The value of each strategy, i.e., cost reduction and quality improvement, is lower
with strategic consumers than with myopic consumers.
Interestingly, Proposition 8 implies that �rms will have a harder time justifying either type of
enhancement e¤ort when consumers are strategic, compared to when they are myopic. Figure 2
demonstrates this for the cost reduction strategy, and Figure 6 for the quality improvement strategy.
26
0.5 1.0 1.5 2.0q i
50
100
150
200
Figure 6. The incremental value of quality improvement with myopic consumers (upper line) andstrategic consumers (lower line) as a function of �qi, when demand is normally distributed with � = 100
and � = 20, v = 5, c = 3, s = 1, = 0:8, and Kqi = 10.
In other words, the proposition shows that while consumers behave strategically in an attempt to
maximize their own welfare, this behavior can �back�re�on consumers to some degree by reducing
�rm incentives to improve the product via process or product innovation. Consequently, we expect
that �rms serving markets characterized by a high degree of strategic consumer behavior are less
likely, overall, to pursue any product enhancement strategy; when it is pro�table to pursue one
of the strategies, as Proposition 7 and Figure 5 demonstrate, strategic behavior makes quality
improvement relatively more attractive to the �rm.
6 Conclusion
A frequent and important decision made by �rms is whether to focus �nite product development
resources on reducing production costs or increasing consumer value. Firms making such product
enhancement decisions must consider numerous factors in�uencing the pro�tability of each strategy,
such as the relative R&D costs, the degree of cost reduction or quality improvement possible, the
size of the market, and the marketing and branding implications of both approaches. In this paper,
we have shown that two additional critical considerations are demand uncertainty and the behavior
of the consumer population.
27
Myopic Consumers Strategic ConsumersCost Reduction �mcr > �scr
_ _^Quality Improvement �mqi > �sqi
Table 1. A summary of the results on the value of cost reduction and quality improvement when Kq = Kc
and �q = �c.
To summarize our main results, we found that when demand is deterministic, quality improve-
ment and cost reduction (of identical amounts) are equivalent. When demand is stochastic and
consumers are non-strategic, cost reduction is always preferred to quality improvement (of the same
amount). Furthermore, �rm pro�t is strictly increasing in the amount of cost reduction and value
increase, so it is optimal to reduce costs and increase consumer value (improve quality) as much
as possible, ceteris paribus. When demand is stochastic and consumers are strategic, both cost
reduction and quality improvement are less valuable than if consumers are non-strategic. Quality
improvement is more robust to strategic behavior, and in particular, the �rm may prefer quality
improvement to cost reduction (of the same amount); see Table 1 for a summary of when each
strategy is preferred. Lastly, �rm pro�t is quasi-concave and has an interior maximum in the
amount of cost reduction and value increase, meaning there is an optimal (interior) degree of both
cost reduction and quality improvement even absent variable costs to these strategies, and more-
over, quality improvement is always preferred to cost reduction when comparing the strategies at
their individual optima.
It is important to recognize that our model does not consider a variety of factors that may
in�uence �rm preferences between the two strategies. For example, quality improvement may
result in the addition of a feature to the product that leads to the arrival of additional consumers
to the market; for example, the addition of video playback capability to an MP3 player increases
the potential market from consumers in search of a music player to consumers searching for both
music and video players, possibly increasing total demand, D. Similarly, cost reduction may
allow a �rm to lower the price enough that low-value consumers are willing to buy at the full
price, which could also result in an increase in total market size. Our model does not incorporate
these e¤ects, showing instead that, ceteris paribus, the two product enhancement strategies have
di¤erent implications in how they in�uence strategic consumer purchasing behavior, leading the
�rm to value these practices di¤erently when selling to a forward-looking consumer population than
28
it would when selling to non-strategic consumers. If other factors are considered, e.g., if quality
improvement leads to substantial new sources of demand, then how a �rm values each strategy will
clearly change.
Our results show that product design and enhancement decisions are signi�cantly impacted by
both demand uncertainty and its interactions with consumer purchasing behavior. Both factors
lead to the result that $1 of cost reduction is not equivalent to a $1 increase in the valuation of
consumers (and hence the selling price); demand uncertainty causes the �rm to value $1 of cost
reduction more, while strategic consumer behavior can cause the �rm to value $1 of consumer
valuation increases more. This demonstrates the key interplay between operational decisions
(production decisions under demand uncertainty and investment into process innovation), design
decisions (investment into product innovation), and marketing decisions (pricing). More impor-
tantly, the insights generated from our analysis provide useful guidelines to the managers who face
product enhancement decisions.
Acknowledgements. The authors thank participants from the 2009 INFORMS Annual
Meeting in San Diego for helpful comments.
A Appendix: Proofs
Proof of Proposition 1. With deterministic demand, the �rm will always produce exactly Dunits, i.e., the �rm sets q = D. Since there are no leftover inventories, all consumers are myopicand purchase the product if and only if p � v. To maximize the pro�t, the �rm sets p = v. Thus,the �rm pro�t under cost reduction is vD � (c� �cr)q �Kcr = (v � c+ �cr)D �Kcr and the �rmpro�t under value increase is (v+ �qi)D� cq�Kqi = (v + �qi � c)D�Kqi. These two expressionsare identical with �cr = �qi and Kcr = Kqi.
Proof of Proposition 2. Comparing (1) and (2), we see that cost reduction is pro�table tothe �rm if
Kcr < (v � s)Z qmcr
qmb
xf (x) dx:
Notice that qmcr = F�1�1� c��cr�s
v�s
�increases from qmb = F�1
�1� c�s
v�s
�to 1 as �cr goes from
0 to its upper bound, c � s. As a result, the right-hand side of this inequality increases from 0to (v � s)
R1qmbxf (x) dx. Hence, for any Kcr < (v � s)
R1qmbxf (x) dx, there is exactly one value of
�cr over which cost reduction is pro�table. Similarly, comparing (1) and (3), we see that qualityimprovement is pro�table to the �rm if
Kqi < (v � s)Z qmqi
qmb
xf (x) dx+ (1� ) �qiZ qmqi
0xf (x) dx:
29
Di¤erentiating qmqi = F�1�1� c�s� �qi
v�s+(1� )�qi
�with respect to �v, we �nd that
@qmqi@�qi
=1
f(qmqi )
(v � s) + (1� ) (c� s)(v � s+ (1� ) �qi)2
> 0:
Therefore, qmqi increases from qmb = F�1�1� c�s
v�s
�to1 as �qi goes from 0 to its upper bound, (c�
s)= . As a result, the right-hand side of the inequality above increases from 0 to (v � s)R1qmbxf (x) dx+
1� (c� s)�. Hence, for any Kqi < (v � s)
R1qmbxf (x) dx+ 1�
(c� s)�, there is exactly one valueof �qi over which quality improvement is pro�table.
Proof of Proposition 3. Let � = �cr = �qi and K = Kcr = Kqi. Consider expected �rmpro�t as a function of q (i.e., not at the optimal q but at any arbitrary q). In the cost reductioncase, such pro�t is �mcr (q) = (v � s)S (q) � (c� � � s) q � K. In the quality improvement case,expected pro�t is �mqi (q) = (v + � � s� �)S (q) � (c� s� �) q � K. The di¤erence betweenthese pro�t functions is
�mcr (q)� �mqi (q) = � (1� ) (q � S (q)) :
Because, with stochastic demand, S(q) < q, it follows that �mcr (q) > �mqi (q) for any q, since0 < < 1. Since cost reduction dominates quality improvement for any quantity, it clearly doesso at the optimal quantities for each case.
Proof of Proposition 4. Let �scr(�cr) = �scr(�cr) � �sb be the increase in the expected pro�tdue to cost reduction. Then
�scr(�cr) =p(c� �cr � s)(v � s)
Z qscr(�cr)
0xf(x)dx�
p(c� s)(v � s)
Z qsb
0xf(x)dx�Kcr:
Di¤erentiating �scr(�cr),
d�scr(�cr)
d�cr= �1
2
rv � s
c� �cr � s
Z qscr(�cr)
0xf(x)dx
+p(c� �cr � s)(v � s)qscr(�cr)f (qscr(�cr))
1
2p(c� �cr � s)(v � s)f (qscr(�cr))
=1
2
qscr(�cr)�
rv � s
c� �cr � s
Z qscr(�cr)
0xf(x)dx
!:
Inverting qscr(�cr) = F�1�1�
qc��cr�sv�s
�, we can express the �rst-order condition d�scr(�cr)=d�cr =
0 as
�(q) = qF (q)�Z q
0xf(x)dx = S(q)� 2
Z q
0xf(x)dx = 0:
The lower and upper bounds �cr = 0 and �cr = c� s correspond to q = qsb = F�1�1�
qc�sv�s
�and
q =1. Note that �(0) = 0 and limq!1 �(q) = �� 2� = �� < 0. Di¤erentiating �(q),
�0(q) = F (q)� 2qf(q) = F (q) [1� 2g(q)] ;
where g(q) � qf(q)=F (q) is the generalized failure rate. Since g(q) is monotonically increasing, �0(q)decreases whenever q � g�1(1=2) and crosses zero at most once at q = g�1(1=2). Combined with�0(0) = 1 > 0, we conclude that �0(q) either (1) monotonically decreases or (2) decreases, crosses
30
zero at q = g�1(1=2) from positive to negative and stays negative afterwards. The �rst case ariseswhen g(q) < 1=2 in the entire domain of q. However, as pointed out in Lariviere (2006), �realisticproblems must have g(q) > 1 for all q > y for some �nite y�. Therefore, the second case is isadopted. Combined with the earlier results �(0) = 0 and limq!1 �(q) = ��, in this case, �(q) startsfrom zero and increases initially (with the slope �0(0) = 1), peaks at q = g�1(1=2), then decreasesafterwards, approaching �� < 0 as q ! 1. Therefore, there is exactly one bqcr > 0 satisfying
�(q) = 0. Transforming q 2 [0;1) back into � by inverting qscr(�cr) = F�1�1�
qc��cr�sv�s
�, we
conclude that �scr(�cr) is a quasi-concave function of �cr (that is, the slope has at most one changein sign, from positive to negative) and has a unique maximum at b�cr = (c � s) � (v � s)F (bqcr)2in the domain [�(v � c); c � s). If b�cr � 0, then �scr(�cr) is decreasing in [0; c � s) starting from�scr(0) = �Kcr, and therefore cost reduction is never pro�table. If 0 < b�cr < c � s, on theother hand, �scr(�cr) increases from �scr(0) = �Kcr, peaks at b�cr, then decreases until it approaches�scr(c� s) = �
p(c� s)(v � s)
R qsb0 xf(x)dx�Kcr. If
Kcr <
q(c� b�cr � s)(v � s)Z qscr(
b�cr)0
xf(x)dx� �sb;
i.e., �scr(b�cr) > 0, there exists an interval around b�cr in which �scr(�cr) > 0, i.e., cost reduction ispro�table. The upper bound of this interval is strictly less than c � s since �scr(0) = �Kcr >�scr(c� s), ensuring that lim�!c�s�scr(�cr) < 0 for all Kcr � 0.
Proof of Proposition 5. Let �sqi(�qi) = �sqi(�qi)� �sb be the increase in the expected pro�tdue to quality improvement. Then
�sqi(�qi) =q(c� s� �qi) (v � s+ (1� ) �qi)
Z qsqi(�qi)
0xf(x)dx�
p(c� s)(v � s)
Z qsb
0xf(x)dx�Kqi:
Di¤erentiating �sqi(�qi),
d�sqi(�qi)
d�qi=
� 2
sv � s+ (1� ) �qi
c� s� �qi+1� 2
sc� s� �qi
v � s+ (1� ) �qi
!Z qsqi(�qi)
0xf(x)dx
+1
2
� + (1� ) c� s� �qi
v � s+ (1� ) �qi
�qsqi(�qi): (11)
Inverting qsqi(�qi) = F�1�1�
qc�s� �qi
v�s+(1� )�qi
�, we can express the �rst-order condition d�sqi(�qi)=d�qi =
0 as
�(q) =
�qF (q)�
Z q
0xf(x)dx
�+ (1� )F (q)2
�qF (q) +
Z q
0xf(x)dx
�= �(q) + (1� )F (q)2S(q) = 0:
Note that �(0) = 0 and limq!1 �(q) = � � + (1 � ) � 0 = � � < 0, where we have usedlimq!1 �(q) = �� from the proof of Proposition 4. Di¤erentiating �(q) and using the result�0(q) = F (q) [1� 2g(q)] with g(q) = qf(q)=F (q) from the proof of Proposition 4,
�0(q) = F (q) [1� 2g(q)] + (1� )F (q)3[1� 2h(q)];
31
where h(q) � f(q)S(q)=F (q)2, which is increasing (see Lemma 1 of Cachon 2004). Observe that
h(q) =f(q)S(q)
F (q)2=
f(q)
F (q)2
�qF (q) +
Z q
0xf(x)dx
�= g(q) +
f(q)
F (q)2
Z q
0xf(x)dx > g(q);
which implies that �0(q) < [ F (q) + (1 � )F (q)3] [1� 2g(q)]. Hence, �0(q) < 0 for q > g�1(1=2).This, combined with �(q) � �(q) from (9) and that �(q) increases from zero until it peaks atq = g�1(1=2) and then decreases until it approaches �� (see the proof of Proposition 4), impliesthat �(q) is positive for 0 < q < g�1(1=2) and it decreases for q > g�1(1=2), crossing zero exactlyonce at some q greater than the root of �(q) to approach � � as q ! 1. Thus, the solutionof �(q) = 0, i.e., bqqi, is unique. Transforming q 2 [0;1) back into �qi by inverting qsqi(�qi) =F�1
�1�
qc�s� �qi
v�s+(1� )�qi
�, we conclude that �sqi(�qi) is a quasi-concave function of �qi (that is, the
slope has at most one change in sign, from positive to negative) and has a unique maximum at b�qispeci�ed in (10) in the domain [�(v � c); (c � s)= ). The rest of the proof is similar to that ofProposition 4.
Proof of Proposition 6. (i) Via implicit di¤erentiation of (9),
@bqqi@
= ��(bqqi)� F (bqqi)2S(bqqi)�0(bqqi) ; (12)
where �(q) and �(q) are de�ned in Propositions 4 and 5. It was shown in the proof of Proposition4 that bqqi is to the right of bqcr, i.e., the solution of �(q) = 0, and that �(q) < 0 for q � bqcr. Hence,�(bqqi) < 0, which implies that the numerator of the right hand-side of (12) is negative. In thesame proof, we also showed that that �0(bqqi) < 0, i.e., the denominator is also negative. Combiningthe two, we conclude from (12) that @bqqi=@ < 0. Now consider the denominator of the righthand-side of (10), + (1 � )F (bqqi)2. Di¤erentiating this expression with respect to , we obtain1�F (bqqi)2� 2(1� )f(bqqi)F (bqqi)@bqqi@ > 0, i.e., the denominator increases in . On the other hand,
the numerator of the same expression, (c� s)� (v� s)F (bqqi)2, decreases in . Combining the two,we conclude that b�qi decreases in . To show lim !0 b�qi = 1, substitute = 0 in (9) to obtainthe �rst-order condition F (q)2S(q) = 0, which has two solutions bqqi = 0 and bqqi = 1. Only thelatter remains since @bqqi=@ < 0 implies negative quantity for > 0 if the �rst solution were true.Then, from the expression in (10), it is clear that b�v approaches in�nity as ! 0. Similarly, toshow lim !1 b�qi = b�cr, substitute = 1 in (9) to obtain the �rst-order condition �(q) = 0, which isidentical to that of cost reduction. Hence, b�qi and b�cr coincide at = 1.
(ii) Note that
�scr(b�cr) =
q(c� b�cr � s)(v � s)Z qscr(
b�cr)0
xf(x)dx� �sb �Kcr;
�sqi(b�qi) =
r�c� s� b�qi��v � s+ (1� )b�qi�Z qsqi(
b�qi)0
xf(x)dx� �sb �Kqi;
where qscr(b�cr) = F�1�1�
qc�b�cr�sv�s
�and qsqi(
b�qi) = F�1�1�
rc�s� b�qi
v�s+(1� )b�qi�. From these
expressions, it is clear that lim !1�sqi(b�qi) = �scr(b�cr) +Kcr �Kqi since lim !1 b�qi = b�cr by part
32
(i). To show @�sqi(b�qi)=@ < 0, apply the envelope theorem to obtain
@�sqi(b�qi)
@ = �
b�qi2
0@vuutv � s+ (1� )b�qi
c� s� b�qi +
vuut c� s� b�qiv � s+ (1� )b�qi
1AZ qsqi(b�qi)
0xf(x)dx
+b�qi2
v � c+ b�qiv � s+ (1� )b�qi qsqi(b�qi): (13)
Note that b�qi satis�es the �rst-order condition (11) appearing in the proof of Proposition 5. Thecondition can be rewritten as
1
2
0@vuutv � s+ (1� )b�qi
c� s� b�qi +
vuut c� s� b�qiv � s+ (1� )b�qi
1AZ qsqi(b�qi)
0xf(x)dx
=1
2
vuut c� s� b�qiv � s+ (1� )b�qi
Z qsqi(b�qi)
0xf(x)dx+
1
2
1 +
�1
� 1�
c� s� b�qiv � s+ (1� )b�qi
!qsqi(b�qi):
Substituting this in (13) and collecting terms, we can show that
@�sqi(b�qi)
@ = �
b�qi2
vuut c� s� b�qiv � s+ (1� )b�qi
Z qsqi(b�qi)
0xf(x)dx�
b�qiqsqi(b�qi)2
c� s� b�qiv � s+ (1� )b�qi < 0:
Proof of Proposition 7. Let s(�) � �sqi(�) � �scr(�) be the increase in the �rm�s expectedpro�t when it employs quality improvement compared to when it employs cost reduction. Then
s(�) =p(c� s� �)(v � s+ (1� )�)
Z qsqi(�)
0xf(x)dx�
p(c� � � s)(v � s)
Z qscr(�)
0xf(x)dx:
Observe that lim�!0 s(�) = 0 and
lim�!c�s
s(�) =p(1� )(c� s)(v � s+ (1� )(c� s))
Z F�1�1�q
(1� )(c�s)v�s+(1� )(c�s)
�0
xf(x)dx > 0:
Since s(�) is continuous, there exists �s < c� s such that s(�) > 0 for all � > �s.Proof of Proposition 8. Let �mqi(�qi) = �mqi(�qi) � �mb and �sqi(�qi) = �sqi(�qi) � �sb be the
increases in the expected pro�t due to quality improvement for the myopic consumers case and thestrategic consumers case. Then
�mqi(�qi) = (v � s+ (1� )�qi)Z qmqi (�qi)
0xf(x)dx� (v � s)
Z qmb
0xf(x)dx�Kqi;
�sqi(�qi) =q(c� s� �qi)(v � s+ (1� )�qi)
Z qsqi(�qi)
0xf(x)dx�
p(c� s)(v � s)
Z qsb
0xf(x)dx�Kqi;
where qmqi (�qi) = F�1�1� c�s� �qi
v�s+(1� )�qi
�> F�1
�1�
qc�s� �qi
v�s+(1� )�qi
�= qsqi(�qi). Consider the
di¤erence �qi(�qi) � �mqi(�qi)��sqi(�qi). Observe that �qi(0) = 0 and, after di¤erentiating �qi(�qi)
33
and collecting terms,
d�qi(�qi)
d�qi=
2
sv � s+ (1� )�qic� s� �qi
Z qsqi(�qi)
0xf(x)dx
+(1� ) Z qmqi (�qi)
0xf(x)dx� 1
2
sc� s� �qi
v � s+ (1� )�qi
Z qsqi(�qi)
0xf(x)dx
!
+
�c� s+ (v � c)v � s+ (1� )�qi
��qmqi (�qi)�
1
2qsqi(�qi)
�> 0;
where we have usedq
c�s� �qiv�s+(1� )�qi < 1 and q
mqi (�qi) > qsqi(�qi). Hence, �qi(�qi) starts from zero at
�qi = 0 and increases afterwards. Therefore, �qi(�qi) > 0 for �qi > 0, i.e., pro�t increase in themyopic consumer case is greater than that in the strategic consumer case. The analogous resultfor cost reduction is obtained by letting = 1 and replacing �qi with �cr in the above proof, since�mcr(�cr) = �
mqi(�qi) and �
scr(�cr) = �
sqi(�qi) under such conditions.
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