Estimating Maximum Willingness to Pay
Jagmohan S. Raju
Joseph J. Aresty Professor
The Wharton School
Using Conjoint Analysis
to Estimate Reservation Prices
MP3 Player Survey – Sample Profiles
A) Brand Apple B) Brand Apple
Storage 5000 songs Storage 50 songs
Battery 18 hrs Battery 2 hrs
Display Color Display Monochrome
Warranty No Warranty No
Price $249 Price $249
C) Brand Generic D) Brand Generic
Storage 5000 songs Storage 50 songs
Battery 18 hrs Battery 2 hrs
Display Color Display Color
Warranty 1 yr Warranty No
Price $249 Price $99
3
Coding the Profiles
Each player attribute in survey has two levels
Brand Capacity Battery Life Display Warranty Price
Attributes
(songs)
Apple 5000 18hrs Color 1 yr $249
Levels Generic Mono
50 2 hrs None $99
Use 0 for lower level and 1 for higher level
Example: Profile - a Example: Profile - h
Attribute Value Coded as Attribute Value Coded as
Brand Apple 1 Brand Generic 0
Storage 5000 songs 1 Storage 50 songs 0
Battery 18 hrs 1 Battery 2 hrs 0
Display Color 1 Display Mono 0
Warranty No 0 Warranty No 0
Price $249 1 Price $99 0
4
Survey Data
Ratings collected from one respondent
# Brand Price Capacity Battery Warranty Display Rating
1 1 1 1 1 0 1 73
2 1 1 0 1 1 0 42
3 1 0 1 0 1 0 87
4 1 0 0 0 0 1 80
5 0 1 1 1 0 0 38
6 0 1 0 1 1 1 28
7 0 0 1 0 1 1 80
8 0 0 0 0 0 0 5
9 1 1 0 1 0 1 51
10 1 0 1 1 1 0 95
11 1 1 0 0 1 0 32
12 1 1 1 0 0 1 47
13 0 0 0 1 0 0 64
14 0 0 1 1 1 1 75
15 0 1 0 0 1 1 27
16 0 1 1 0 0 0 18
5
Analyzing the Data
Estimate consumer preference weights using regression
Utility (Rating) = α + βBrand Brand + βCapacity Capacity
+ βBattery Battery + βDisplay Display
+ βWarranty Warranty + βPrice Price
Regression results
Attribute Coefficient Value
Intercept a 30.9
Brand bBrand 25.7
Price bPrice -33.6 R2 = 0.85
Capacity bCapacity 18.8
Battery bBattery 15.5
Warranty bWarranty 7.0
Display bDisplay 14.2
6
Estimating Willingness to Pay
What is the utility-to-$ “exchange rate”?
Exchange rate = ($249 – $99) / 33.6 = 4. 45 $/util
When price changes from $99 to $249, utility reduces by βPrice
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 7.0
Intercept - -
Total Utils = 73.45
73.45 utils = 73.45 x $4.45 = $326.85
7
Other Methods
Economic Value to the Customer
Estimation from Secondary Data
Postulate a choice model that includes a reservation price
Allow it to vary across buyers.
Estimate is as a parameter (individual level)
8
ANNEXURES
Conjoint Utility Model
Linear compensatory model
Utility = α + βBrand Brand + βCapacity Capacity
+ βBattery Battery + βDisplay Display
+ βWarranty Warranty + βPrice Price
α is utility from other (invariant) attributes
βs 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
10
Designing a Conjoint Survey
How many product attributes do we include?
Include only those that influence customer decision and (can) vary across
products
MP3 Playback quality: little room for differentiation
MP3 Player size: Determined by battery life, storage, display
How many profiles should we use?
Balance reliability with design cost and task complexity
In the MP3 player example full factorial design is too large
2 levels for 6 attributes => 26 = 64 possible profiles
May cause respondent fatigue
May 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 another
7 parameters (including intercept) => minimum of 7 profiles
Profiles can be determined using standard statistical packages
11
Variations and Extensions
Choice data instead of preference data
Use logistic regression to calculate attribute partworths
Heterogeneity in consumer preferences
Cluster analysis, Latent class or Bayesian models
Non-linear pricing plans (e.g. cell phone plans)
Structural models
12
