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Estimating Maximum Willingness to Pay
Jagmohan S. RajuJoseph J. Aresty Professor
The Wharton School
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Using Conjoint Analysisto Estimate Reservation Prices
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MP3 Player Survey Sample Profiles
Brand AppleStorage 5000 songs
Battery 18 hrs
Display Color
Warranty No
Price $249
Brand Generic
Storage 5000 songs
Battery 18 hrs
Display Color
Warranty 1 yr
Price $249
Brand Apple
Storage 50 songs
Battery 2 hrs
Display Monochrome
Warranty No
Price $249
Brand Generic
Storage 50 songs
Battery 2 hrs
Display Color
Warranty No
Price $99
A) B)
C) D)
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Coding the Profiles
Each player attribute in survey has two levels
Use 0 for lower level and 1 for higher level
Attribute Value Coded as
Brand Apple 1
Storage 5000 songs 1Battery 18 hrs 1
Display Color 1
Warranty No 0
Price $249 1
Example: Profile - a
AttributesBrand Capacity
(songs)Battery Life Display Warranty Price
Levels AppleGeneric
500050
18hrs2 hrs
Color Mono
1 yr None
$249$99
Attribute Value Coded as
Brand Generic 0
Storage 50 songs 0Battery 2 hrs 0
Display Mono 0
Warranty No 0
Price $99 0
Example: Profile - h
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Survey Data
Ratings collected from one respondent# Brand Price Capacity
Battery Warranty Display Rating
1 1 1
1 1 0 1 732 1 1 0 1 1 0 423 1 0 1 0 1 0 874 1 0 0 0 0 1 805 0 1
1 1 0 0 386 0 1 0 1 1 1 287 0 0 1 0 1 1 808 0 0 0 0 0 0 59 1 1 0 1
0 1 5110 1 0 1 1 1 0 95
11 1 1 0 0 1 0 3212 1 1 1 0 0 1 4713 0 0 0 1 0 0 6414 0 0 1 1 1
1 7515 0 1 0 0 1 1 2716 0 1 1 0 0 0 18
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Estimating Willingness to Pay
What is the utility-to-$ exchange rate?Exchange rate = ($249
$99) / 33.6 = 4. 45 $/utilWhen price changes from $99 to $249,
utility reduces byPrice
What is willingness to pay for a given product? Attribute Value
Dummy Level Utils
Brand Apple 1 25.7
Storage 5000 songs 1 18.8
Battery Life 10 hrs 0.5 7.75
Display Type Color 1 14.2
Warranty 1yr 1 7.0Intercept - -
Total Utils = 73.45
73.45 utils = 73.45 x $4.45 = $326.85
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ANNEXURES
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Conjoint Utility Model
Linear compensatory modelUtility = + BrandBrand
+CapacityCapacity
+ BatteryBattery +DisplayDisplay
+ WarrantyWarranty +PricePrice is utility from other (invariant)
attributess are known as the (attribute) partworths
Attributes can be represented using dummy variables Attribute
Brand Capacity Battery Display Warranty Price
Dummy = 0 Generic 50 2 hrs Mono- None $99
Dummy = 1 Apple 5000 18 hrs Color 1 yr $249
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Designing a Conjoint Survey
How many product attributes do we include?Include only those
that influence customer decision and (can) vary acrossproducts
MP3 Playback quality: little room for differentiationMP3 Player
size: Determined by battery life, storage, display
How many profiles should we use?Balance reliability with design
cost and task complexityIn the MP3 player example full factorial
design is too large
2 levels for 6 attributes => 26 = 64 possible profilesMay
cause respondent fatigueMay include dominated or meaningless
options
We used a fractional factorial design (16 profiles) A subset of
all profiles is sufficient to estimate our model
Assumption: Effect of one attribute is independent of another7
parameters (including intercept) => minimum of 7 profiles
Profiles can be determined using standard statistical
packages
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Variations and Extensions
Choice data instead of preference dataUse logistic regression to
calculate attribute partworthsHeterogeneity in consumer
preferences
Cluster analysis, Latent class or Bayesian models
Non-linear pricing plans (e.g. cell phone plans)Structural
models
