CHAPTER 2 LITERATURE REVIEW
2.3 The Growth Curve
This section will talk about the growth curve, which is commonly used in interpreting the trend of a product, an industry or a service. First part will interpret the definition of growth curve. Then the representative form of growth curve will also be introduced. Finally, the adoption of life cycle which is similar to product life cycle will also be presented in this section.
2.3.1 The Definition of Growth Curve
Every product or service has its own growth curve, and every growth curve may roughly look similar but different in detail. These growth curves may appear in a wide variety, such as parabolic, power, exponential, sigmoid, and so on. Some researchers investigated these phenomena and demonstrated the growth may show not only sigmoid curve but also other forms (Rai and Kumar 2003, Porter et al 1991).
However, the most commonly growth curve is sigmoid curve (S-curve). The S-Curve is the well-known concept in the innovation management, and this concept is also applied in interpreting the trend of one technology. The technical progress or performance of products basically follows sigmoid shape of performance versus time, and the measurement can be a product life cycle, a technological life cycle, or some economic performance or technical parameters. Consequently, the S-curve plays an important role in technology forecasting, because it can roughly describes the trend of technology forecasting by a graph. There are many strong evidences that in many cases, the diffusion of technologies demonstrated that it follows the smooth growth pattern just like the S-shaped. For example, Palmer and Williams (1999) employed the Fisher-Pry model to fit the microprocessor clock speed. Hodges (1998) used Fisher-Pry and Gompertz model to fit the analog and digital cellular, and he found that the trend roughly obey the S-shaped curve.
The S-curve shows the revolution of technology and it can be divided into three phases of performance (Figure 2.4). In the first phase of introduction, the new technology may just be developed, and there are still a lot of problems such as financing, process of production, unfamiliar, imperfect and so on. Therefore, the growth of first stage rises slowly and gently. In the second phase of rapid adoption, the new technology has been achieved the economies of scale, and people learn more
about the new technology. Besides, the new technology improves and finds more applications. Therefore, the trend of this stage rises sharply in market share. Finally, the third phase of saturation seems to rise more gently than phase 2. The development of technology in this phase may meet the bottleneck, and some new technology may grow stronger and overtake the market share of old technology. In another word, this technology is mature.
Figure 2. 4 The S-Curve
Limit of Performance
Performance Parameter
Phase 1 Phase 2 Phase 3
Saturation
Introduction
Rapid Adoption
Time
Source: From “Development of a Methodological Framework for Examining Science and Technology in Flanders,” 2000.
The point of inflection is an important characteristic of growth curve (Figure 2.5). It happens when the rate of change reached the maximum value. The point of inflection can be used to judge the growth curve is symmetric or not. In general, the maximum rate of change symmetric curve (e.g. Logistic) is a constant that occurs when 50% of potential adopters have adopted the product. However, the nonsymmetrical curve, such as Gompertz, can also be calculated its point of inflection.
For example, the percentage which the point of inflection reached is about 37%. That means the point of inflection in Gompertz will happen before 50%. Flexible models, which have flexible point of inflection, will reach the maximum rate of change when equal or less than 50%.
Figure 2. 5 The point of inflection in S-curve.
dF (t)/dt
F(t)
t t
t* t*
2.3.2 The Representative of Growth Curve
Some different kinds of growth shape have been mentioned briefly in last section, and some representatives of growth curves will be introduced now. The growth curve is based on calculating the cumulative sales, penetrations, or key performance parameter. For example, calculating the proportion of cumulative adopters who have adopted a product can draw the shape of growth curve.
Consequently, here are some questions about the growth curve. What kind of curve may the growth of technology be? Is it an exponential, sigmoid, or other curve? The most commonly curves are exponential and sigmoid, and there are some comparisons of two curves in the underlying section.
The growth of population or technology may shows the exponential growth, but they wouldn’t always grow up rapidly (Equation 1). If a negative feedback term is added to this equation, some restrained effect will turn the exponential growth curve into sigmoid curve.
e
tt
p ( ) = β
α (1) The most widely used modification of exponential growth is logistic. Adding a negative term will make exponential growth transferring to logistic growth (Equation 2). The feedback term is near to zero when P (t) → k and near to 1 when P(t)<<k.Therefore, solving the differential equation can get the solution by integrating, and the solution will be similar to S-shaped curve (Equation 3).
⎟⎠ be revealed. The new equation belongs in the technology growth or other field such as population growth. Every technology can’t grow infinitely and show a development like the exponential curve. Consequently, it has its limitation in market share, just like the life cycle of technology. The half of life cycle can be divided into three phase;
Introduction, Rapid adoption, and Saturation. The logistic function can fit better than exponential function in technology forecasting (Figure 2.6).
Exponential
Logistic
Time Figure 2. 6 Comparison of exponential and logistic
2.3.3 Technology Adoption Life Cycle
When one new product is thrown into the market, it may success or fails in market. Same as one new technology is proposed. Therefore, the technology adoption life cycle can show what place the technology or product is in. It classifies the market and the reactions to a high-tech product. The technology adoption life cycle is the tool for determining the products, pricing and marketing strategies for high-tech products, and was defined as consisting of six phases, including innovation, chasm, tornado, Main Street, decline and obsolescence.
The phases and the trend of life cycle can be shown (Figure 2.7). The phase of chasm means that it goes down in phase 1. Consequently, some new technology may fall into this phase and can be judged that it may not go to the phase of Main Street.
(Meade, P.T., Rabelo, L., 2004)
The S-curve also can be divided roughly into three phase: growth, saturation,
and decline. In the first phase, the new technology has to compete with other technologies. In the saturation stage, all technologies have competed, and the growth of new technology faces the limit. In the last phase, no competition will be concerned.
Market
Share Main Street
Tornado Decline
Chasm
Obsolescence Innovators
Time
Figure 2. 7 Life cycle phases
Note. From “The technology adoption life cycle attractor: Understanding the dynamics of high-tech markets,” by Meade, P.T., Rabelo, L., 2004, Technology Forecasting & Social Change, 71, p.670.
2.3.4 Technological Obsolescence
Obsolescence can be thought simply as the assets loss in value when the market expectation is increasing, the utility of assets is still the same. For example, when the utility of notebook increase, such as wireless function and power saving, the consumer’s expectation will also increase. Then the old generation notebook will lose its value gradually in that the consumers’ need increases.
The technology S-curve was introduced in the last section. Consequently, technological obsolescence will happen following with the technology change, and
this phenomenon can be observed by using technological substitution analysis, such as Fisher-Pry model, which based on the adoption of potential adopters. The old technology has economics of scale, and it is well known and mature in the first stage.
Basically, the appearance of obsolescence is not very clear in old technology at early stage when a new technology entries in the market. However, when new technology grows up and achieves its economics of scale and has more improvements, the old technology can’t enhance its market share and start to follow a downward tendency.
In the final stage, the old technology will decline to zero and be displaced by new technology (Figure 2.8).
Market Share
Market Share of
Figure 2. 8 The typical obsolescence and S-curve chart
Time Old Technology
Market share of New Technology Saturation
Rapid Adoption
Introduction