PRICE SKIMMING STRATEGY FOR NEW PRODUCT
DEVELOPMENT
Hassan Shavandi and Ata G. Zare
Industrial Engineering Dept., Sharif University of Technology, Tehran, Iran
P.O.Box: 11155-9414
Keywords: Skimming pricing, Non-linear programming, New product development.
Abstract: This article presents a new model for pricing a new product considering skimming pricing strategy in the
presence of the competition. We consider two periods for price setting including skimming and economy
period. The problem is deciding on a skimming price as well as an economy price in order to maximize the
total profit. The derived model is a non-linear programming model and we analyzed the structure and
properties of optimal solution to develop a solution method. Analytical results as well as managerial insights
are presented by mathematical analysis and numerical analysis.
1 INTRODUCTION
Pricing is a main step in the marketing planning that
generates revenue. Besides the other factors such as
product quality and performance, brand image,
distribution channels, and promotion plans, price
plays a main role to encourage the customers to buy
the product. So the companies have to consider
many factors and analyze them to set the price.
Hence, developing pricing models to get some
managerial insights are of interest to the marketing
managers. A company can consider any of five
major objectives for its pricing as survival,
maximum current profit, maximum market share,
maximum market skimming, or product-quality
leadership (Kotler, P., Armstrong, G., 2008).
The objective of price skimming involves a
relatively high price for a short time where a new,
innovative, or much-improved product is lunched to
the market. The objective is to skim off consumers
who are willing to pay more to have the product
sooner. Prices are lowered later when demand from
the early customers falls or competitors introduce
the same product with lower price. A company may
decide to be the product-quality leader in the market.
Price skimming is used by many companies
especially in the automobile, mobile phones, TV,
laptop, and many other luxury industries. For
example Sony Company is a frequent practitioner of
skimming pricing, where prices start high and are
lowered over time (Kotler, P., Armstrong, G., 2008).
The Apple inc., introduced its new mobile phone
named “iphone”, in June 2007 at a top price of $599
in the united states. Despite its high price,
consumers across the country stood in a long line to
buy the iphone on the first day of sales. After two
months later, Apple cut the price from $599 to $399
(D. Sliwinska, and et al., 2007-2008).
For the first time Nancy L. Stokey (1979),
develop a model to consider the price discrimination
policy to enter a new product to the market. It is
assumed a monopolist and the customer’s
reservation price to buy the product is considered as
a probability function. There is no competition and
the monopolist wants to maximize the present value
of profit over the time. D. Besanko and W L.
Winston (1990), consider rational customers and
analyze the optimal skimming price. The price
discrimination is considered over the time. The
objective of seller is to maximize its profit over the
time. L. Popescu and Y. Wu (2007), consider the
reference price and analyze the pricing strategy
using dynamic pricing. The consumers at each time
decide to buy the product based on their reference
prices. The reference price is shaped by the past
prices. So in a long run the monopolist can decide to
have a constant steady state price or skimming price
strategy. They investigate these situations using
dynamic programming method and show the optimal
policy.
108
Shavandi H. and G. Zare A..
PRICE SKIMMING STRATEGY FOR NEW PRODUCT DEVELOPMENT.
DOI: 10.5220/0003705301080113
In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems (ICORES-2012), pages 108-113
ISBN: 978-989-8425-97-3
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
Xuanming Su (2008), develops a model of
dynamic pricing with endogenous inter-temporal
demand. He assumes the finite inventory over a
finite time horizon. A. Haji and M. Asadi (2009),
develops a fuzzy expert system to new product
pricing. This fuzzy expert system includes practical
rule bases to analyze the appropriate price of new
product in fuzzy environment. A. Dolgui and J.
Proth (2010), discuses the pricing strategies and
models. They discuss the benefits price skimming
strategy for a company in the monopolistic market
and they recommend that the high price cannot be
maintained for a long time. A good review of pricing
models and their coordination with inventory
decisions can be found in Chan, L., et al. (2004).
In this paper, we develop a new model
considering price skimming and economy pricing in
the presence of competitor’s effects and customers
demand elasticity. The objective of the model is to
maximize the total profit of company at both
skimming and economy phases. In this article we try
to analyze the structure of the problem as well as
optimal solution properties to derive a solution
approach as well as managerial insights.
2 PROBLEM FORMULATION
Consider a market which can be segmented to two
segments: A and B. Segment A, contains the
customers who are willing to purchase the product
sooner with a higher price. Conversely in segment B,
the customers will purchase the product when the
market price is lower than their reservation price.
We set skimming price for segment A and economy
price for segment B. But at the first time that a new
product is introduced to the market, the skimming
phase is considered and the company set a higher
price to skim the segment A to achieve more profit.
The length of the skimming phase depends on
competitor’s ability and the profit margin of the
skimming price. The skimming phase will end when
the demand falls or a competitor joined the market
with a lower price. At this time, the economy phase
starts and the company has to decrease its price
based on its skimming price, the competitor’s price
and customer’s elasticity.
We assume that it is possible to estimate the
maximum volume of demand for each market
segment and the penetration rate of company to
capture the demand depends on its price. The
problem objective is to determine the best price for
skimming and economy phase in order to maximize
its overall profit and market share. At first two
definitions that are considered to model the problem
are presented in the following.
Definition 1. Maximum Reservation Price (MRP), is
the price above which none of the customers will
buy the product. In other words it is the lowest price
at which demand is equal to zero. Maximum Willing
to Buy (MWB), is the lowest price which all of the
customers will buy the product (Philips, Robert L.,
2005).
Definition 2. A myopic customer is one who makes
a purchase immediately if the price is below her
reservation price without considering the future
prices. Conversely, a strategic (or rational) customer
takes into account the future estimated prices when
making purchasing decisions (Philips, Robert L.,
2005).
In this article we assume the myopic behavior for
customers. The parameters and variables needed to
formulate the problem are defined as follows.
2.1 Notations
Parameters:
FC: The finished cost of product.
: Maximum reservation price.
: The maximum estimated of total market demand
volume.
: The maximum estimated of market demand
volume for skimming phase.
: The penetration rate function at skimming
phase.
: The penetration rate function at economy
phase.
Variables:
(
) : The skimming (economy) price for
product.
2.2 Analysis of Penetration Rate
Functions
The penetration rate at the skimming phase depends
on the price of product. If the skimming price is
high, then the penetration rate is low. In the real
situation the relationship between penetration rate
and price is non-linear and the negative exponential
function is more consistent and was applied more
than other functions in the literature. So we apply
the negative exponential function to model the
penetration rate at the skimming and economy
phases. We propose the penetration rate at skimming
phase as:
=
(
)
(1)
PRICE SKIMMING STRATEGY FOR NEW PRODUCT DEVELOPMENT
109
It can be simplified by substituting the
parameters as:
=
(
)
(2)
Where, =
and ≥1. The parameter is
the shape parameter which is estimated by historical
data from market for previous product that presents
the behavior of customers.
The penetration rate at economy phase depends
on the skimming price, competitor’s price and also
the economy price. We assume that the competitor
will join the market with a lower price. So the
competitor will set its price smaller than skimming
price and larger than finished cost of product. We
assume that the cost function of production for
competitor is the same as company. We also assume
that there is just one opportunity to set the price and
the company cannot estimate the exact price of the
competitor. A high skimming price increases the
penetration rate of competitor and the company will
lose its market share for economy phase and we
apply this concept by defining the coefficient .
Therefore deciding the best skimming price to gain
more profit at skimming phase as well as more
market share and profit at economy phase is the aim
of this model. Customers who buy the product at the
skimming phase are removed from the market and
the penetration rate at economy phase is calculated
for remained market volume. When the skimming
price is equal to MRP then the competitor will have
a big chance to increase its penetration rate but we
assume that it cannot capture the whole market
because of the originality of company brand and we
apply this concept in defining coefficient and
formulate the penetration rate of company at
economy phase as:
=
(
)
(3)
It can be also simplified as:
=
(
)
(
)
(4)
Where, ≥0 and ≥1 are the shape parameters
for economy phase and are estimated based on the
market situation. So by considering these penetration
rate functions at skimming and economy phase, we
can write the model of the problem which is
appeared in the next sub-section.
2.3 The Model
The problem can be formulated as a non-linear
programming (NLP) model as follows:
=.
〖
〗
^(^−)+(
−.
〖
〗
^)
〖
〗
^(^−)
(5)
s.t.
≤ (6)
≤
(7)
≥0,
≥0
The objective function (5), attempts to maximize the
company’s profit over the skimming and economy
phases. By substituting the penetration rate functions
from relations (2) and (4) in the objective function
we see that it has the non-linear. All the constraints
are in the form of linear and constraint (6) states that
the price cannot be larger than maximum reservation
price and the economy price also cannot be larger
than skimming price (7).
3 STRUCTURAL ANALYSES
3.1 Optimal Solution Analysis
In this section we are going to do some structural
analysis on the model to find the properties of
optimal solution. By replacing the penetration
functions the objective function is as the form of:
(
,
)
=
(
)
(
−
)
+−
(
)
(
)
(
(
)
)(
−)
Theorem 1. The optimal economy price is derived
based on the optimal skimming price by the
following equation:
∗
=
+
−
(8)
Proof: By taking the first derivative condition of
objective function with respect to
we have:
=−
1
−
−
(
)
)
(
)
(
)
(
−
)
+−
(
)
(
)
(
(
)
)
=−
(
)
(
)
(
)
1
−
(
−
)
−
=0
∗
=
+
−
ICORES 2012 - 1st International Conference on Operations Research and Enterprise Systems
110
The second derivative of Z with respect to
ensures that the maximum value of Z can reach at
∗
and hence it is the optimal economy price.
=
1
(
−)
−
(
)
)
(
)
(
)
(
−
)
−
1
−
2
−
(
)
)
(
)
(
)
=
−
(
)
(
)
(
)
−
×(
(
−
)
−
−2)
=
−
(
)
(
)
(
)
−
(
1−2
)
<0
Proposition 1: The economy price is increasing in
skimming price and the skimming strategy is
reasonable for >1. Considering the constraint,
≤
, if ≤1 then the skimming and economy
prices are equal and it means that obtaining a single
price is optimal and the skimming strategy is not
acceptable. Therefore the economy price is always
equal or less than skimming price and hence the
constraint
≤
is surplace in the model and can
be eliminated.
Observation 1: Based on proposition 1, the
company can estimate the parameter using the
historical information about the price and demand of
previous products and decide to apply the skimming
strategy according to parameter . If ≤1 then the
price skimming strategy is not reasonable. The
historical data show the behaviour of customers
regarding to different values of price and if the value
of parameter is equal or less than 1 it means the
customers prefers to buy the product in one and
lower price.
Observation 2: The economy price is the average of
finished cost and skimming price in case of =2:
=
+
2
The model can be modified by replacing the
equation of optimal economy price in the objective
function and transforming it to a function of single
variable
. Therefore the model becomes:
=(
−)
(
)
+
(
(
)
−
()
(
)
s.t.
≤
≥0
By replacing, =
−, the objective function
can be transformed as:
=
+
(
−
(
)
(9)
In order to analyze the objective function and
optimal solution, it can be simplified as:
=
+
−
(
)
(10)
Parameters
and
are positive and,
=,
=
The parameters
,
and
are as follows:
=,
=
,
=
Since, ≥1 and TV>V, therefore we have
>
and
>
.
Now by first derivative condition on equation
(10) the optimal value of x can be determined as:
∗
=
+
−
(
)
+
−
(
+
)
(11)
The above equation can be solved numerically
by Mayple software. If equation (11) has one unique
solution then it is the optimal solution.
Now we are going to show the uniqueness of
optimal skimming price. Recalling the equation (11),
it can be transformed as equation (12). If we show
that the equation (12) has just one solution therefore
we can develop a procedure to obtain the optimal
solution.
(
)
=
(
1−
)
+
(
1−
)
−
(
)
(
1
−
(
+
)
)
=0
(12)
To show the uniqueness of solution for equation
(12), we solved 560 example problems which the
summary of their parameters are shown in table 1. In
all sample problems there was just one solution for
PRICE SKIMMING STRATEGY FOR NEW PRODUCT DEVELOPMENT
111
equation (12). The behaviour of equation (12) with
respect to x is shown in figure 1.
Table 1: The summary of example problems parameters.
FC TV V MRP
10 1660 744
15 1 1 1
20 1.5 1.5 1.5
50 2 3 2
100 3 5 2.5
5 3
5
10
Number of values 4 5 4 7
Based on this observation we can propose a solution
algorithm to solve the model which is presented in
the next sub-section.
Figure 1: The behaviour of relation (18) respect to x.
3.2 Solution Algorithm
Step 1: compute the value of
∗
by Mayple software
using the equation:
∗
=
+
−
(
)
+
−
(
+
)
(
)
Step 2: The optimal solution is:
∗
=
∗
+
∗
=
∗
4 EXPERIMENTAL RESULTS
By solving the 560 example problems we analyzed
the sensitivity of each parameter on solution. We
considered the distance between economy price and
skimming price as a criteria to analyze the effects of
each parameter to this criteria. The distance between
economy and skimming price gives an insight to
management about the importance of skimming
strategy. The more distance between economy and
skimming price, the more interest to apply the price
skimming strategy. Our observations are as follows:
1. The distance between skimming and economy
price (
−
) is increasing in . Figure 2, presents
the relation between skimming price and economy
price in . Skimming and economy prices are the
same in =0. By increasing , the economy price
decreases to finished cost and its distance from
skimming price increases.
Figure 2: The behavior of skimming and economy price in
.
2. For parameters and we observed that
−
is decreasing in both parameters and .
Figure 3 shows the behavior of skimming as well as
economy price respect to and . Decreasing in
skimming price is sharper than economy price in
both and . The most distance between skimming
and economy price is where and are equal to
one and by increasing theses parameters the distance
between skimming and economy price decreases.
Figure 3: The behavior of skimming and economy price in
().
5 CONCLUSIONS
In this article a new pricing model was developed
considering skimming pricing strategy for
introducing new product. We considered two periods
for price setting: first the skimming period and the
second one is economy period. In the skimming
period the company faces a monopolistic market but
in the economy period there is at least one
competitor. We formulate the effect of competitor in
ICORES 2012 - 1st International Conference on Operations Research and Enterprise Systems
112
the economy phase by penetration function. The
penetration rates at skimming and economy phases
were formulated as an exponential function and the
effect of competitor’s price was formulated as loss
of the market share in economy phase penetration
rate. The optimal economy price is calculated
considering the skimming price. An algorithm was
developed to solve the model based on the lower and
upper bound derived in structural analysis. Many
example problems were solved and some managerial
insights presented by numerical analysis. As an
extension, this problem can be analyzed by game
theory to realize the competition in dynamic
environment considering the reaction of competitor
and company. The other functions to formulate the
penetration rates and other solution methods can be
of interest for future research.
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