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

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 Bass Model, Management Science (1969) Copyright, (c) Frank M. Bass, 1999

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 Central Themes of this Historical Perspective: Empirical Generalization and Science

Empirical Generalization: Always (Almost) Looks Like a Bass Curve Adoption of VCR s Actual and Fitted Adoption VCR's 1980-1989 1200 0 1000 0 Adoption in Thousands 8000 6000 4000 2000 Actual Adopt ion Fitted Adopt ion 0 80 81 82 83 84 85 86 87 88 89 Year

History Published in Management Science in1969, A New Product Growth Model For Consumer Durables Working Paper 1966

Color TV Forecast 1966 Color TV 7000 6000 5000 Sales (x 1000) 4000 3000 2000 1000 0 Peak in 1968 Industry Built Capacity For 14 million units 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Sales Predic ted Ye ar

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 ETET vs TETE - Ehrenberg Higher Level Theories - Bass

Bass Model:100 s of Applications-An Empirical Generalization Widely Cited Numerous Extensions Published in Several Languages Growing Software Applications

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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)] =pm+(q-p)y(t)-(q/m)[y(t)] 2

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) t*=time of Peak Sales Beautiful!

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) Econometrica

Why it Works--Saturation S(t)=m[p+qF(t)][(1-F(t)] Gets Bigger and Bigger Gets Smaller and Smaller

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

Another Example 35 mm Projectors Actual and Fitted Adoption of 35 mm Projectors, 1965-1986, m=3.37 million, p=.009,q=.173 Units 180000 160000 140000 120000 100000 80000 60000 40000 20000 0 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 Year 35mm Proj Fitted

Another Example: Overhead Projectors Actual and Fitted Adoption of OverHead Projectors,1960-1970, m=.961 million,p=.028,q=.311 120000 100000 80000 Units 60000 40000 Overhead Proj Fitted 20000 0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 Year

Some Extensions Successive Generations of Technologies: Norton & Bass (87,92) 180 160 140 120 100 Stocks 80 Stock by Generations, Wireless Phones, 1986-2025 Generalized Bass Model: Includes Decision Variables: Prices, Advertising 60 40 20 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Year Stock G1 Stock G2 Stock G3

Successive Generations of Technology The Law of Capture-Migration&Growth The Equations: Three Generations S 1,t =F(t 1 )m 1 [1-F(t 2 )] S 2,t =F(t 2 )[m 2 +F(t 1 )m 1 ][1-F(t 3 )] S 3,t =F(t 3 ){m 3 +F(t 2 )[m 2 +F(t 1 )m 1 ]} 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 and p and q are the same for each generation

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 300 250 Thousands 200 150 100 50 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 Quarter 4K-A 4K-F 16K-A 16K-F 64K-A '64K-F 256K-A 256K-F

Capture Law-Mainframes-Beautiful! Generations of Mainframe Computers (Performance Units) 1974-1992 120000 100000 80000 Sales 60000 40000 20000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Year Gen1 Actual Gen1 Fit and Forecast Gen2 Actual Gen2 Fit and Forecast Gen3 Actual Gen3 Fit and Forecast Gen4 Actual Gen4 Fit and Forecast

Generations of PC s World Wide Sales of Generations of Desktop PC's 14 12 Unit Sales in Millions 10 8 6 4 2 0 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 Year 8 Bit 16 Bit 32 Bit

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 Model

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 900 800 700 600 500 400 300 200 100 0 Prices of VCR's Based on Sales Data and HH Adoption Data 1978-1989 78 79 80 81 82 83 84 85 86 87 88 89 Price Based on VCR Sales Data Price Based on Household Adoption Data

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

Effects of Different Prices GBM-Diffusion Under Two Different Pricing Schemes 2000 1800 1600 Sales (Adoption) 1400 1200 1000 800 600 400 200 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Time 10% Below Baseline Prices Baseline Price

Impulse Response Comparison: GBM and Current Effects Model Carry-Through Effects for GBM 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 Millions of Units 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Year Impulse at t=4, GBM Adoption Baseline Adoption without Impulse at t=4 Impulse Response at t=4, "Current Effects" Model

Some Applications Guessing Without Data: Satellite Television Satellite Telephone (Iridium) New LCD Projector Wireless Telephone Adoption Around World and Pricing Effects Projecting Worldwide PC Growth

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

1993 Forecast of Satellite TV Penetration in 1999 1993 Bass Model Forecast of Satellite TV Subscriptions Under Scenario Chosen By Management Compared With Actual, 1994-1999 (99 Projected from February) 12 10 8 Actual through February, Projected through June =9.989 Million Forecast 1999 =9..4 Million Millions 6 4 2 0 94-95 95-96 96-97 97-98 98-99* Year Rapid Diffusion Like Cable in 80's and Lower Potential 16% of TV Homes Measured Actual Number of Television Homes

Projection of World-Wide PC Demand, 1999-2010-Data From Bill Gates, Newsweek 5-31-99 Millions of Units 180 160 140 120 100 80 60 40 20 Actual Worldwide PC Shipments, 1981-1999 and Fitted and Projected Shipments, 1981-2010, m=3.384 Billion, p=.001, q=.195 Shipments Includes Replacements (Upgrades) 697 Million Units Shipments through 1999 Peak 2008 0 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 Year World Wide PC Shipments Fitted World Wide PC Shipments

Bottom Line and Quotation In Forecasting the Time of Peak It is Helpful to Know that a Peak Exists By Frank Bass