product life cycle · introductory stage to the growth stage of the product life cycle (for most...
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Product Life Cycle
Penetration of Color TV to the US
0
1000
2000
3000
4000
5000
6000
7000
1950 1955 1960 1965 1970 1975
Year
Un
its
VCR penetration to the US
0
2000000
4000000
6000000
8000000
10000000
12000000
14000000
1975 1980 1985 1990 1995
year
un
its
Fax Machines - Do not forget the Take off
Fax
0
500000
1000000
1500000
2000000
2500000
1960 1965 1970 1975 1980 1985 1990 1995
Will It Ever Fly ? Modeling the Takeoff
of Really New Consumer Durables
Presented by Javier Pozas
Peter N., Golder and Gerard J. Tellis (1997),
Marketing Sciences, Vol.16, No.3 p.256-270
Au
tom
ob
ile
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60
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80
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10
00
12
00
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00
18
00
20
00
1898
1900
1902
1904
1906
1908
1910
Ye
ar
Un it sa les ( in th ousands)
Automobile
0
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1200
1400
1600
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200018
98
19
00
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04
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06
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12
19
14
Automobile
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2000
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98
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00
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Automobile
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18
98
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00
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02
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06
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08
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19
16
Takeoff Definitions
Conceptual definition: the point of transition from the
introductory stage to the growth stage of the product life cycle (for most new products, the start of the
growth stage is dramatic and clear).
Operational definition: the first year in which an
individual category’s growth rate relative to base sales crosses a threshold
Threshold for takeoff: the plot of percentage sales
growth relative to a base level of sales, common
across all categories.
Product’s Relative growth rate: the plot of its annual growth in sales relative to its base sales for that year.
Electric Shaver
0
200
400
600
800
1000
1200
1400
1600
1800
1931 1932 1933 1934 1935 1936 1937
0
200
400
600
800
1000
1200
1400
1600
1947 1948 1949 1950 1951 1952 1953 1954 1955
Clothes Dryer
Color Television
0
1000
2000
3000
4000
5000
6000
1954 1956 1958 1960 1962 1964 1966
CD Player
0
500
1000
1500
2000
2500
3000
3500
4000
1983 1984 1985 1986 1987 1988 1989
0
500
1000
1500
2000
2500
3000
3500
1985 1986 1987 1988 1989 1990 1991 1992 1993
CD-ROM
Threshold for Takeoff
0
50
100
150
200
250
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
B ase Sa les in Un its (000)
Pe
rc
en
t In
cre
as
e
The Interpretation of a Concept Test’s Results
• Definitely will buy 15%
• Probably will buy 45%
• Might/might not buy 20%
• Probably not buy 10%
• Definitely not buy 9%
To go or not to go?
Relationships Between Intent and Actual Purchase (Tauber, 1981)
Definitely buy 71 31 52
Probably 60 16 43
Might/might not 54 17 56
Probably not 52 8 50
Definitely not 38 10 40
Stated intention Became aware of
the product
Tried given aware Repeat given trial
Newness Maps(Goldenberg, Lehmann and Mazursky, 2001)
Newness to the World = Firm Newness + Market Newness
Market Newness
Firm Newness
Low
Low
Mod
Mod High
High
Cannibalization or
Incremental sales
Product Company fit
issues
Product Market fit issues
Bass Model
The Bass diffusion model developed by Professor Frank Bass in 1969, is one of the
fundamental models to describe, and sometimes predict, first purchases for consumer
durable products.
This model is particularly useful for modeling the evolution of demand for “Really
New Products”, whose sales curves over time follow a familiar product life cycle - an
S shaped growth curve followed by stabilization and then decline.
The Bass Model (1969)
( )( ) ( )( ) ( )( )n t p M N t qN t
MM N t p q
N t
MM N t( ) (
( ) ( )= − + − = +
−
Where: n(t) = numbers of adopters at time t, M = market potential, N(t) =
cumulative number of adopters, p = coefficient of innovation , q = coefficient
of imitation (word of mouth effect)
innovation effect imitation effect
d N
d tn t= ( )
The Solution of the Differential Equation -
The properties of the Diffusion
( )
( )
+
−=
+−
+−
tqp
tqp
ep
q
eMtN
1
1)(
N(t) - Cumulative sales by time t after introduction (or “take off”)
M - Ultimate Market Potential (in units)
p - Coefficient of innovation
q - Coefficient of imitation (WOM effect)
Other important properties can be obtained easily:
)(')( tNtn =•The sales rate:
•The timing of the peak t*:
+
=q
p
qpt ln
1*
•The peak sales rate: ( )2
4*)( qp
q
Mtn +=
•The peak cumulative sales:
−=
q
pMtN
25.0*)(
Estimating the Bass Model
The Bass model can be estimated by using a simple regression.
Use the approximation: )1()()(')( −−≈= tNtNtNtn
Thus, the model can be rewritten: ( ) [ ]2)1()1()( −−−−+= tNM
qtNpqpMtn
Or: [ ]2)1()1()( −−−+= tNctbNatn
a, b, and c can be estimated by running ordinary least squares regression, using the
cumulative sales as dependent variables, the lagged sales and the squared lagged
sales as the independent variables.
After estimating a, b, c the bass parameters can be derived:
bpq
c
acbbM
M
ap
+=
−±−=
=
2
42
Caution: In order to produce reasonably accurate data one needs to have at least 10-12
years of data.
Fit
Adoption of VCR’s
Actual and Fi tted Adoption VCR's
1980-1989
0
2000
4000
6000
8000
10000
12000
80 81 82 83 84 85 86 87 88 89
Year
Ado
ptio
n in T
hou
sand
s
Actual Adopt ion
Fitted Adopt ion
Exercise in Bass Model
Use the data below on the cumulative sales of cellular subscribes (source:
CTIA, 1996 - estimated numbers) to estimate the growth of cellular
subscribers to year 2000, use the Bass diffusion model. According to your
estimations: What is the market potential? When do you expect the peak
to occur?
Repeat your calculation but this time use data only up to 1993. Compare p
and q and your estimation to the former estimations. What are your
conclusions?
Year Cumulative Number of Cellular
Subscribers (millions)
1983 0.01
1984 0.13
1985 0.33
1986 0.68
1987 1.23
1988 2.07
1989 3.51
1990 5.28
1991 7.56
1992 11.03
1993 16.01
1994 24.13
1995 33.79
1996 45.41
The question:
How can we tie individual level behavior to the
aggregate level data managers often face ?
Diffusion of Innovation - First steps with CA
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 0 0 0 0
1 0 0 0 0 0 0
0 0 0 0 0 1 0
0 0 1 0 0 1 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
1 1 1 1 0 0 1
1 1 1 1 1 1 1
1 0 1 1 0 1 1
1 1 1 1 1 1 1
0 0 1 1 0 1 1
1 1 1 1 1 1 0
0 - a potential buyer
1 - an adopter
p - probability to adopt due to external effects
q - probability to adopt due to an interaction
with one adopter
Individual Probability of Adoption = PA =1- (1-p)(1-q)k
Saddle’s Ubiquity
0
2000
4000
6000
8000
10000
12000
14000
1975 1980 1985 1990 1995 2000
Saddle in Personal Computers
0
5000
10000
15000
20000
25000
30000
35000
1975 1980 1985 1990 1995 2000
Saddle in Cordless Phones
Different types of adopters
The Chasm
Saddle’s explication
Dual Market - the saddle case
Time
Sa
les Innovators
Majority
Total Market
Saddle’s Criticality
Dual Market - the non-saddle case
Time
Sale
s Innovators
Majority
Total Market
Fax Machines
Fax Machines
0
500
1000
1500
2000
2500
3000
3500
4000
1986 1988 1990 1992 1994 1996 1998 2000
?
Evaluation of Sales Formations
Use existing products
Become aware of a new product
New product is available
Buy new product
aw
av
bc
P a a bw v cc
N
==∑
1
P a a t rw v c cc
N
==∑
1
Where: tc - trial probability, given awareness and availability
rc - long run share of purchases per period for new brand by customer c,
given that he tried the product
Test Market Analysis
Hierarchy of effects model:Awareness
Intent
Search
Trial
Repeat
Recursive methods - TRACKER (Blattberg and Golanty, 1978)
)()( 112121 −−−− −+−+= tttttt TAAATT βαWhere:
•T - the trial at time t
•A - awareness at time t
•The coefficients are estimated by a regression.
Sales Forces
Maximize Z PQ X C Q C X= − −( ) ( ) ( )1 2
Where: Z = profit, P = selling price, Q(X) = number of units sold as a function of selling
effort, C1(Q) = total cost of producing and merchandising Q units, C2(X) = total cost of
selling effort of level X
Sales force sizing
Allocation of selling resources across products
32 4
N NDN
DN
Dc h q= + +
Each salesperson contacts N customers and promotes three products on each contact. The
total effort is 3N. Dc is the number of product receiving complete coverage, Dh is the
number of products receiving half coverage and Dq are receiving quarter coverage.
The effect of Promotions
•Couponing
•Price-off
•Sampling
Where:
s - percentage of target group sampled.
Np - number of consumers purchases in the product category per period
Rs - long run share of purchases for new product among those who have even
made a trial purchase
Us - Proportion of samples sent that are used by members of target group
P s N a a TR N a U Rp w v p v s s= − +( )1
Awareness, Trials and GRPs (PDMA Handbook)
Cumulative Gross Rating Points0 500 1000 1500 2000 2500 3000 3500 4000 4500
90
80
70
60
50
40
30
20
10
0
Ad
just
ed a
war
enes
s
am
on
g u
sers
Brand-awareness among users0 10 20 30 40 50 60 70 80 90 100
80
70
60
50
40
30
20
10
0
Tri
al a
mo
ng u
sers