Diffusion Theory in Marketing: A Historical Perspective Frank M. Bass, 1999

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Diffusion Theory in Marketing: A Historical Perspective

Frank M. Bass, 1999

• Before Bass (BB): Tarde: 1903 New Ideas • Epidemiology: Disease

• Rogers (1962): Bell-Shaped Curve-Innovators and Imitators

• “Discussion largely literary”

• 1999-is 30th Anniversary of Publication of

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The Bass Model

• Diffusion of Innovations

• Mark Twain and the Price of a Lecture • “Bass Model”: Urban and Hauser (1980) • More than 250 Papers: Applications,

Refinements, and Extensions

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Empirical Generalization: Always (Almost) Looks Like a Bass Curve

Adoption of VCR’s

Actual and Fitted Adoption VCR's 1980-1989 0 2000 4000 6000 8000 10000 12000 80 81 82 83 84 85 86 87 88 89 Year A dop ti o n i n T h o u sa nd s

Actual Adopt ion Fitt ed Adopt ion

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History

Published in

Management

Science

in1969, “A New Product

Growth Model For Consumer

Durables”

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Color TV Forecast 1966

Color TV 0 1000 2000 3000 4000 5000 6000 7000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Ye ar S a le s ( x 10 00) Sales Predic ted Peak in 1968 Industry Built Capacity For 14 million units

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Empirical Generalizations and

Science

• Philosophy of Science-Nagel (1961): “Science Seeks to Provide Generalized

Explanatory Statements About Phenomena” • Marketing Science (1995) Special Issue on • Empirical Generalizations in Marketing

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Bass Model:100’s of

Applications-An Empirical

Generalization

Widely Cited

Numerous Extensions

Published in Several Languages

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How to become famous

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The Model

• f(t)/[1-F(t)]=p+qF(t) Hazard Model

• m=ultimate market potential • p=coefficient of innovation • q=coefficient of imitation

• S(t)=mf(t)=m[p+qF(t)][1-F(t)]

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A Differential Equation

• Solution: S(t) =

• m[(p+q)2/p]e-(p+q)t/(1+(q/p)e-(p+q)t)2

• t*=1/(p+q)Ln(q/p)

• Beautiful !

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Special Cases When p=0 and q=0

• Fourt and Woodlock q=0, Exponential Distribution, (1960) Grocery Products

Journal of Marketing

• Mansfield, p=0, Logistic Distribution,

(1961) Industrial Products (Locomotives)

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Why it Works--Saturation

• S(t)=m[p+qF(t)][(1-F(t)] Gets Bigger and Bigger Gets Smaller and Smaller

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An Empirical Generalization

Adoption of Answering Machines 1982-1993t 0 2000 4000 6000 8000 10000 12000 14000 82 83 84 85 86 87 88 89 90 91 92 93 Year

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Another Example 35 mm

Projectors

Actual and Fitted Adoption of 35 mm Projectors, 1965-1986, m=3.37 million, p=.009,q=.173 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 Un it s

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Actual and Fitted Adoption of OverHead Projectors,1960-1970, m=.961 million,p=.028,q=.311 0 20000 40000 60000 80000 100000 120000 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 Year Un it s _{Overhead Proj} Fitted

Another Example: Overhead

Projectors

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Some Extensions

• Successive

Generations of Technologies:

• Norton & Bass (87,92) • Generalized Bass Model: Includes 0 20 40 60 80 100 120 140 160 180 Stocks

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Successive Generations of Technology

The Law of Capture-Migration&Growth

• The Equations: Three Generations

• S_1,t=F(t₁)m₁[1-F(t₂)]

• S_2,t=F(t₂)[m₂+F(t₁)m₁][1-F(t₃)]

• S_3,t=F(t₃){m₃+F(t₂)[m₂+F(t₁)m₁]}

• m_i=incremental market potential for gen.i

• t_i=time since introduction of ith generation

and F(t_i) is Bass Model cumulative function

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Capture Law- DRAMS

Norton and Bass: Management Science (1987)

Sloan Management Review (1992)

Four Generationsof DRAMS: 4K, 16K, 64K, 256K, 1sr Quarter 1974-4th Quarter 1985, Actual and Fitted Shipments, p=.0037, q=.3369

0 50 100 150 200 250 300 Thous a n d s

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Capture Law-Mainframes-Beautiful!

Generations of Mainframe Computers (Performance Units) 1974-1992

0 20000 40000 60000 80000 100000 120000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Year Sa le s

Gen1 Actual Gen1 Fit and Forecast Gen2 Actual Gen2 Fit and Forecast Gen3 Actual Gen3 Fit and Forecast Gen4 Actual Gen4 Fit and Forecast

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World Wide Sales of Generations of Desktop PC's 0 2 4 6 8 10 12 14 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 Year U n it S a le s in M illio n s Generations of PC’s

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What About Prices ?

What About Prices?

❚ The Generalized Bass Model

❚ With Prices, Advertising, and other

Marketing variables the curve is shifted with different policies but the shape stays the same.

❚ Explain Why Adoption Curves Always

Looks The Same Even Though Policies

❚ Vary Greatly: Model Must Reduce to Bass

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Generalized Bass Model: Bass, Krishnan, and

Jain (1994) Marketing Science

• A Higher Level Theory

• Must Reduce as

Special Case to Bass Model

• Prices Fall Exponentially

Prices of VCR's Based on Sales Data and HH Adoption Data 1978-1989 100 200 300 400 500 600 700 800 900

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The Bass Model (BM) and GBM

• BM: f(t)/[1-F(t)]=[p+qF(t)]

• GBM: f(t)/[1-F(t)]=x(t)[p+qF(t)]

• where x(t) is a function of percentage change in price and other variables

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Effects of Different Prices

GBM -Diffusion Under Two Different Pricing Schemes

0 200 400 600 800 1000 1200 1400 1600 1800 2000 S a le s ( A do pt io n)

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Impulse Response of 20% Percent Price Reduction in Period 4 for GBM Compared with a "Current Effects" Model-Curve Shifts to the Left for GBM,

But Returns to Baseline for Current Effects Model

0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 Year M illio n s o f U n it s

Impulse at t=4, GBM Adoption Impulse Response at t=4, "Current Effects" Model Baseline Adoption without Impulse at t=4

Impulse Response Comparison:

GBM and “Current Effects” Model “Carry-Through” Effects for GBM

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Some Applications

• Guessing Without Data: • Satellite Television

• Satellite Telephone (Iridium) • New LCD Projector

• Wireless Telephone Adoption Around World and Pricing Effects

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Satellite TV Forecast-1993-”Guessing By Analogy” and Purchase Intentions

• Use of “Adjusting Stated Intention

Measures to Predict Trial Purchase of New

Products: A Comparison …” Journal of

Marketing Research (1989), Jamieson and Bass

• “Guessing By Analogy”: Cable TV vs.Color TV

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1993 Bass Model Forecast of Satellite TV Subscriptions Under Scenario Chosen By Management Compared With Actual, 1994-1999 (99 Projected from February)

0 2 4 6 8 10 12 94-95 95-96 96-97 97-98 98-99* Year M illio ns

Rapid Diffusion Like Cable in 80's and Lower Potential 16% of TV Homes Actual through February, Projected through June =9.989 Million

Forecast 1999 =9..4 Million

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Projection of World-Wide PC Demand,

1999-2010-Data From Bill Gates, Newsweek

Actual Worldwide PC Shipments, 1981-1999 and Fitted and Projected Shipments, 1981-2010, m=3.384 Billion, p= .001, q= .195 0 20 40 60 80 100 120 140 160 180 81 83 85 87 89 91 93 95 97 99 ₁₀₁ ₁₀₃ ₁₀₅ ₁₀₇ ₁₀₉ Year Mi ll ions of U n it s

World Wide PC Shipments Fitted World Wide PC Shipments

Peak 2008

697 Million Units Shipments through 1999

Shipments Includes Replacements (Upgrades)

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Bottom Line and Quotation

“In Forecasting the Time of Peak It is Helpful to Know that a Peak Exists”