Reservation Price Estimation
by Adaptive Conjoint Analysis
Christoph Breidert1, Michael Hahsler1, and Lars Schmidt-Thieme2
1 Department of Information Business,
Vienna University of Economics and Business Administration,
1090 Vienna, Austria
2 Computer-based New Media group,
Institute for Computer Science,
University of Freiburg, 79110 Freiburg, Germany
Abstract. Though reservation prices are needed for many business decision pro-
cesses, e.g., pricing new products, it often turns out to be difficult to measure them.
Many researchers reuse conjoint analysis data with price as an attribute for this
task (e.g., Kohli and Mahajan (1991)). In this setting the information if a consumer
buys a product at all is not elicited which makes reservation price estimation impos-
sible. We propose an additional interview scene at the end of the adaptive conjoint
analysis (Johnson (1987)) to estimate reservation prices for all product configura-
tions. This will be achieved by the usage of product stimuli as well as price scales
that are adapted for each proband to reflect individual choice behavior. We present
preliminary results from an ongoing large-sample conjoint interview of customers
of a major mobile phone retailer in Germany.
1 Introduction
Pricing products is a difficult task for every business. Thorough knowledge of
the demand in the market is necessary to predict the different effects that arise
from the pricing strategy as well as from the set price for a product: Customer
switching effects, cannibalization effects, and market expansion or contraction
effects. Many of these effects can be analyzed for different strategies using
the reservation prices of the participants in the market (Jedidi and Zhang
(2002)). Varian (p. 4, 2003) defines the reservation price as follows:
The reservation price is the highest price that a given person will
accept and still purchase the good. In other words, a person’s reser-
vation price is the price at which he or she is just indifferent between
purchasing or not purchasing the good.
However, this definition is different from the definition of reservation price
used by other authors. For example, Kohli and Mahajan (1991) define the
reservation price for their study as the price for a product such that an in-
dividual switches away from her most preferred product. To our knowledge

2 Breidert et al.
Jedidi and Zhang (2002) are the only researchers who have applied the eco-
nomic definition of reservation price in combination with a conjoint study on
product pricing.
In this paper we present a novel approach to estimate the economic reser-
vation price using the popular conjoint analysis. We do not incorporate price
as an attribute in the conjoint analysis but we introduce price by an addi-
tional choice-based scene after the conjoint analysis. The paper is organized
as follows: In section 2 we identify shortcomings of the estimation of reserva-
tion prices using only data from conjoint analysis. In section 3 we present our
novel approach and its foundation in economic theory. In section 4 we outline
an application of the method for a mobile phone retailer. We conclude with
a short discussion of further research.
2 Conjoint Analysis for Reservation Price Estimation
Conjoint analysis and especially adaptive conjoint analysis (ACA) (Johnson
(1987)) is a popular tool in marketing research to survey consumers’ pref-
erences for products that are seen as the combination of several attributes
which have different levels. With conjoint analysis utility-scores for the at-
tribute levels are estimated that reflect the respondents valuations of the
inclusion, exclusion or degree of the levels.
The major approach in pricing studies by conjoint analysis is incorporat-
ing the price as an additional attribute (e.g., Green and Srinivasan (1990),
Orme (2001)). The attribute price is then assigned a part-worth utility as the
other attributes and some interpolation heuristics are applied. To estimate
reservation prices several studies using conjoint data are found in the cur-
rent literature (e.g., Kohli and Mahajan (1991), Jedidi and Zhang (2002)).
In these studies authors try to estimate reservation prices from previously
acquired conjoint data which include price as an attribute. However, these
approaches have the following shortcomings:
1. Conjoint analysis only measures the preference structure for the analyzed
product configurations. If the individual would really purchase at a given
price is not elicited. Therefore, reservation price in an economic sense
cannot be measured.
2. The number-of-levels and the range effect are well-known in conjoint anal-
ysis (Verlegh et al. (2002)). If the number of attribute levels or the range
covered by the attribute levels is increased by the researcher, the per-
ceived importance of that attribute also increases. These effects are es-
pecially problematic for pricing studies in which often a large number of
different prices is surveyed.
In the following we address these issues by excluding the price from the
conjoint analysis and estimate the reservation price with an additional inter-
view scene which also allows for non-purchases.

Reservation Price Estimation by Adaptive Conjoint Analysis 3
3 Reservation Price Estimation based on Economic
Theory
Following Varian (2003, p. 63) a utility function for two products X and Γ
can be formulated as
U(x, γ) = uX(x) + uΓ (γ). (1)
Hereby x is the amount of product X, for which the reservation price of
one specific individual is to be estimated, and γ denotes the amount of the
so-called composite product Γ . Varian (2003, p. 21) defines the composite
good as everything that the consumer might want to buy other than good X.
By definition the amount of money not spent on good X is spent on good Γ .
Note, that the composite good is arbitrarily divisible and also includes the
possibility to save money for later consumption.
The reservation price for a good X is defined as ”the price at which the
consumer is just indifferent between consuming good X or not consuming it”
(Varian (2003, pp.108-109)). Therefore, the reservation price p∗X for one unit
of product X is found, when the customer is indifferent between purchasing
or not purchasing the product. Formally, indifference can be expressed by the
following condition
U(1, γ) = U(0, γ′) where γ′ > γ. (2)
On the left hand side of this equation the utility is given for an individual
who consumes one unit of product X and consumes some amount of the
composite good. On the right hand side of the equation the individual does
not consume product X and therefore consumes a greater amount of the
composite good denoted by γ′.
When consuming the goods X and Γ at the unit prices pX and pΓ each
consumer is confronted with an individual budget constraint which can be
defined as m = pXx + pΓ γ. Since the composite good is defined to be arbi-
trarily divisible, we can set the price for one unit of Γ to 1 (Varian (2003,
p. 21)). For the consumption and non consumption of one unit of product X
the following equations derived from the budget constraint hold
γ = m− pX (3)
γ′ = m. (4)
We only consider the case of buying one or zero units of X. For zero units
no utility is derived from X (uX(0) = 0). For the sake of formal simplicity
let uX denote the utility of consuming one unit of product X, that is uX :=
uX(1). Using the utility function in equation 1 the condition for indifference
in equation 2 can be rewritten as
uX + uΓ (γ) = uΓ (γ
′). (5)

4 Breidert et al.
Fig. 1. Estimation of a high and a low reservation price point in the PE scene from
observed upper- or a lower bounds of the price (denoted by the arrows).
When consuming the composite good, an individual will certainly always
choose a combination that gives her the highest utility for her budget. Since
the composite good is arbitrarily divisible and constructed from all possible
goods (except good X), the consumer will face a large number of different
combinations which equally have the same highest utility per price ratio k.
Therefore, for uΓ (γ) a linear function with slope k and an intercept uΓ (0) = 0
can be used (compare Jedidi and Zhang (2002)).
uX + k · γ = k · γ
′ (6)
Applying the budget constraint from equations 3 and 4 the following
condition for the consumption of one unit of product X at the reservation
price p∗X can be formulated
uX + k · (m− p
∗
X) = k ·m. (7)
Applying some simple arithmetics to the equation m can be eliminated.
Then, if the utility and the reservation price for one unit of product X is
known, the slope k of the utility function of the composite product Γ can be
calculated by
k =
uX
p∗X
. (8)
Economically, the factor k represents the exchange rate between utility
and money. With the factor k the reservation price for any product con-
figuration for which the utility is known can be calculated. Note, that this
calculation is based on ratio-scaled absolute utility but the conjoint analysis
only produces interval-scaled utility-scores for products.

Reservation Price Estimation by Adaptive Conjoint Analysis 5
find-reservationprice-point(u, p,∆u,∆p,∆pstop, smax, i) :
b+ := (u+, p+) := ∅, b− := (u−, p−) := ∅, j := 1
while b+ = ∅ or b− = ∅ do
if purchase(product(u), p)
b− := (u, p)
(u, p) := (u + ∆u, p + j∆p)
else
b+ := (u, p)
(u, p) := (u−∆u, p− j∆p)
fi
j := j + i
od
while p+ − p− > ∆pstop and smax-- > 0 do
(u, p) := ( 12 (u
− + u+), 12 (p
− + p+))
if purchase(product(u), p)
b− := (u, p)
else
b+ := (u, p)
fi
od
return ( 12 (u
− + u+), 12 (p
− + p+))
Fig. 2. Search algorithm for a reservation price point.
However, in the following we will show how to transform the interval-
scaled utility-scores to ratio-scaled absolute utility while estimating the factor
k. For this transformation we append the new Price Estimation scene (PE
scene) at the end of the adaptive conjoint analysis. At this point all part-worth
utilities are already estimated by the conjoint analysis and the utility-scores
for all attribute combinations can be calculated. The PE scene is a choice-
based scene where we offer the proband several times a different product at
a dynamically set price and he or she has the option to accept the offer or
leave it. With these questions we iteratively search for two reservation price
points in the utility × price space. As shown in figure 1 with every question
we find an upper or lower bound for price at a certain utility. Once we have
found the reservation prices for two different products a straight line through
the two points gives us an estimate for the factor k. At the same time we
get an intercept with the utility axis which represents the conjoint analysis
utility-score for the price 0 which by economic theory must correspond to an
absolute utility of 0. Therefore, as shown in figure 1, we can assign an origin
to the utility axis and utility is now ratio-scaled as necessary for reservation
price estimation.
The algorithm for the estimation of the reservation price of one product
combination is presented in figure 2. The function product(u) chooses the
product configuration closest to a desired utility u from the list of all possible

6 Breidert et al.
combinations. Function purchase(product(u), p) asks whether the user would
buy the product chosen by product(u) at a given price p.
The first while loop in figure 2 starts with an initial guess (u, p). The
algorithm tries to box the probands utility/price exchange ratio by locat-
ing an upper and a lower bound (b+, b−), i.e., a price point at which the
proband would purchase for a given utility and one at which the proband
would decline to purchase. In the second loop of the algorithm this interval
is gradually narrowed by a bisection search. The bisection search terminates
when the found interval, in which the reservation price lies, is narrowed to
a predefined accuracy ∆pstop. To limit the maximal number of purchasing
decisions a participant has to make, a second termination condition restricts
the algorithm to a predefined maximal number of search steps smax.
If only two reservation price points, (u1, p1) and (u2, p2), are used, the
utility/price exchange ratio can be easily found by k = (u2 − u1)/(p2 −
p1). When n > 2 reservation price points (ui, pi) are used the utility/price
exchange ratio can be found by least squares fitting.
The possibility that the procedure influences the respondent’s behavior
needs attention. To avoid this influence the respondent should be explicitly
asked to view each offer independently. Furthermore, the respondent can be
presented product combinations from the n reservation price estimations in
randomized or alternating order (e.g. alternating high utility with low utility
combinations), such that the influence is minimized.
4 Application of the Method
We implemented the PE scene in the modular framework of the Java Adaptive
Conjoint tool (jAC version 1.1, Schmidt-Thieme (2004)) and incorporated it
in a study designed for the NOKIA online-shop in the German market for
mobile phones and accessories. In this shop customers are offered suitable
telephone enhancements at discounted price on the purchase of a telephone.
In terms of Pigou (1920) this strategy can be described as price discrimination
of the third degree, because the shown telephone enhancements are only
offered to a certain group of people at a lower price. The strategy can also
be viewed as a mixed-bundling strategy as described by Adams and Yellen
(1976). The telephone is offered together with enhancement at a discount,
but the products can also be purchased individually without a discount. At
the moment the marketing experts of the online-shop set the discounts for
the telephone enhancements manually in view of the cost structure and sales
information of the different products.
To enable the online-shop to optimize the pricing strategy we estimate
the reservation prices of customers at the individual level. First, we use the
adaptive conjoint analysis to estimate the part-worth utilities of all attribute
levels excluding the price information. And then, we use the Price Estimation
scene to estimate the reservation prices.

Reservation Price Estimation by Adaptive Conjoint Analysis 7
Utility Reservation Price Extra Charger Car Accessory Headset Leather Case
17,64 171,46 EUR ACP-12E LCH-12 HDW-2 CNT-327
17,26 168,59 EUR DCV-14 LCH-12 HDW-2 CNT-327
17,05 167,01 EUR ACP-12E - HDW-2 CNT-327
16,67 164,14 EUR DCV-14 - HDW-2 CNT-327
16,60 163,63 EUR ACP-12E MBC-15S HDW-2 CNT-327
16,22 160,77 EUR DCV-14 MBC-15S HDW-2 CNT-327
15,99 159,05 EUR ACP-12E LCH-12 HS-3 CNT-327
15,97 158,93 EUR ACP-12E LCH-12 HDW-2 -
15,61 156,19 EUR DCV-14 LCH-12 HS-3 CNT-327
15,59 156,06 EUR DCV-14 LCH-12 HDW-2 -
15,43 154,87 EUR - LCH-12 HDW-2 CNT-327
15,40 154,60 EUR ACP-12E - HS-3 CNT-327
Table 1. Estimated reservation prices for a sample proband.
A large-sample online study will be carried out with the newsletter recip-
ients of the NOKIA online-shop later this year. Here we only show how the
procedure works by presenting results from a single sample participant. We
searched for two reservation price points (with utilities around the 0.25 and
0.75 quantiles). Utility increments ∆u were chosen to allow 20 steps in the
search procedure. ∆pstop was set to 2,- EUR. Initial guesses for prices, price
increments, and increase in step length were set by domain experts. Table 1
contains a subset of the results for the sample proband. The exchange rate
between utility (measured by the conjoint analysis) and reservation price was
estimated to utility = 0.13 · price− 5.22 (rounded values). The stimuli of the
conjoint analysis consisted of a fixed telephone and contract with different
additionally bundled components.
¿From a single interview we can estimate reservation prices for all product
combinations at the individual level. However, we can also aggregate the data
to estimate reservation prices at market-level. To avoid the problem of pref-
erence heterogeneity we can segment the customers by self-selection, i.e., the
preference for a certain phone type (business, fun, etc.), demographic vari-
ables, or characteristics of the self-explicated task of the adaptive conjoint
analysis (Moore et al. (1998)). For these, more homogeneous groups distri-
butions of reservation prices can be estimated. By applying an appropriate
choice rule market reaction at different prices can be predicted.
5 Conclusion and Further Research
The approach presented in this paper addresses shortcomings of traditional
pricing studies with conjoint analysis that arise from including price as an at-
tribute in the study. We exclude price from the conjoint analysis and estimate
it in an additional interview scene. With this procedure the number-of-levels
effect and the range effect do not occur for price. Furthermore, by the use of

8 Breidert et al.
a no-purchase option we can also measure the reservation price as defined in
economic theory.
The new approach needs to be tested in a real setting which will be done
in a large-sample reservation price survey together with the NOKIA online-
shop. Further research is also necessary to compare this approach to tradi-
tional pricing studies and other techniques of reservation price estimation as
described by Sattler and Nitschke (2003).
Finally, it has to be noted that the presented approach is not bound to
conjoint analysis. Any estimation method that delivers preference information
for products and product combinations relatively scaled at the individual level
can be combined with our new estimation scene.
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