Growth

Although Bass model has been a great paradigm aiming to deal with growth stage in marketing field, there still existed some limitations had to be break. Following are extensions of Bass model and limitations of Bass model.

2.4.1 Redefinition of Bass model

In contrast to Bass’s explanation of coefficients p, q that p is related to innovator and q is related to imitator, Rogers’s definition that innovators are the first 2.5%

adopters of all potential adopters is quite different from Bass’. In other words, Bass

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defined innovators as buyers who are not influenced by others instead of buyers who adopt an innovation first. So how does Bass model associate with classic normal distribution proposed by Rogers?

Mahajan, Muller and Srivastava (1990) proposed a rewritten form of Bass’s basic assumption (equation2).

Where n(t) is equal to s(t) and N(t) is equal to Y(t) in Bass model.

They suggested that the term “innovator” in Bass model should not be called innovator because those buyers are necessarily not the first adopters in Rogers’s definition. Therefore, they cited Lekvall and Wahlbin’s opinion (1973) that the coefficients p, q in Bass model should be referred to as the coefficient of external influence and the coefficient of internal influence, respectively. They thought that the potential adopters of an innovation are influenced by two means of communication:

mass media (external influence) and word of mouth (internal influence). And innovators are influenced only by mass media communication while imitators are influenced only by word of mouth communication.

Lekvall and Wahlbin also proposed an explicit expression to estimate the total adopters affected by external influence.

Consequently, adopters influenced by internal influence are

This explanation helped connect Bass model with Rogers’s work. Next, how does Bass model compare with Rogers’s five categories? This answer is simple. Mahajan,

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Muller and Srivastava (1990) indicated that the point of inflection represents one standard deviation away from the mean of the normal distribution. Thus, finding the point of inflection of Bass’s equation can yield five categories of Bass model.

2.4.2 Limitation of lacking data

Bass model yields good prediction when adding sales data. However, managers want to know how consumers react to new products before launching instead of after launching. To solve this problem, Mahajan, Muller and Bass (1990) suggested that if no data are available, parameter estimates can be obtained by using either

management judgments or the diffusion history of analogous products.

2.4.3 Including Marketing Variables

Bass model do not contain marketing variables such as price and advertisement.

Managers would like to know how to improve sales through those variables.

Kamakura and Balasubramanian (1988) discovered that the decline of price only influences the adopted probability of products which have higher price.

Price seems to play different role among products. Horsky and Simon (1983) added the expenditure of advertisement of producers at given time T into Bass model. Bass, Krishnan and Jain (1994) created the Generalized Bass model, adding two factors, price and advertisement, into Bass model:

Where x(t) is present marketing investment, the expression is as following:

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is the change of price while is the change of expenditure on advertisement. They found that the fitness of Bass model is good enough as the percentage of change on decision variables remains constant while the fitness provided by Generalized Bass model is better than by Bass model as the percentage of change on decision variables alters remarkably.

2.4.4 Including Supply Restrictions

Some researchers discussed other restrictions in management. Jain, Mahajan, and Muller (1991) discussed supply side limitation such as limited production ability and limited logistics ability. They deemed that consumers transform into waiting applicants from potential adopters first, then transform into adopters in the end. Here is their model:

And

The term reflects the change of waiting applicants. This change consists of increases on waiting applicants A(t) and the number of adopters N(t) and decreases because waiting applicants A(t) becomes adopters. c(t) is the supply coefficient, meaning that a certain percentage of waiting applicants can really get the merchandise due to limitation on supply side. They produced the formula of increasing new

adopters as following:

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Ho, Savin and Terwiesch (2002) further discussed the real situation: In the presence of a supply constraint, potential customers who are not able to obtain the new product join the waiting queue, generating backorders and potentially reversing their adoption decision, resulting in lost sales.

2.4.5 Including Competitive Effects

Some researchers considered the influence on the diffusion of present brands resulted from the entry of new competitors. One new brand may result in two effects:

(1) A new brand will increase the market potential of the product category due to product diversity and raising promotion. (2) A new brand will reduce the diffusion of present brands due to competition. Mahajan, Sharma and Buzzell (1993) investigated camera market, indicating that the new brand entry, Kodak, got exceeding 30% sales of existing brand Polaroid’s potential buyers while bringing about the market

expansion. Krishnan, Bass and Kumar (2000) investigated cell phone market, finding that the diffusion effect created by new brands entry differs among different markets.

Some increase market potential while others obstruct the diffusion speed of their competitive brands. Although these articles discussed competitive impact, they didn’t explain the impetus behind the phenomenon.

2.4.6 Including Technological Generations

Norton and Bass (1987) assessed the market penetration of successful high-tech multi-generations products based on Bass model. They used 4k, 16k, 64k ,256k DRAM as samples, developing a model to deal with the substitution effect among

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multi-generation products. To facilitate our later discussion, we use the term

“Substitute Bass model” to represent their model. Following lists a formula of a simple situation between two generations:

τ2 is the launching time of second generation, Yi(t) is the cumulative sales at given time T of generation i, Ｆi(t) is the cumulative adopted rate and mi is market potential of generation i. This model captured the diffusion and substitution effect quite well.

Next, Norton and Bass (1992) continually applied this substitution model to other industry such as recording media and computer products and pharmaceuticals.

Mahajan and Muller (1996) explained a leapfrogging phenomenon: some consumer skip a generation, adopting the latest generation directly. Kim, Chang and Shocker (2000) tried to coordinate substitution effect and complementary effect in a new model.

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