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Recognizing that Two Can Be Less Than One with Economies of Scope
Chapter 7: Innovation and Technological Change: The Future Is Now
The expected net revenue, R n, from your research and development project equals
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where R n represents net revenue in millions of dollars and t is time measured in years.
Your time-cost trade-off function is
where C is development cost in millions of dollars and t is again time.
In order to determine the optimal time frame for the project’s completion, take the following steps:
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1. Note that the expected profit, π, from the project equals net revenue
minus the development cost represented by the time-cost trade-off function.
Thus,
2. In order to maximize profit, take the derivative of profit, π, with
respect to time, t.
This derivative equals
3. Set the derivative equal to zero and solve for t.
Thus, the project’s optimal time frame is four years. Substituting t equals 4 into the expected profit equation indicates that the expected profit is $4 million.
Evaluating projects
Ongoing review of research and development projects requires that you have criteria for project selection. These criteria vary from firm to firm and situation to situation; however, an evaluation process must include a precise specification of assumptions.
Keep two items in mind when evaluating research and development projects. First, research and development expenditures essentially represent a method of obtaining information. Therefore, even “unsuccessful” projects may provide valuable information for the firm. Second, because project managers have a self-interest in the project’s continuation, their forecasts and assumptions may be overly optimistic.
Spreading Diffusion
The diffusion of new technology introduces a crucial time element into managerial decision-making. You may be interested in how an innovation is going to affect your firm’s production costs over time. Or you may be interested in determining how diffusion occurs within your firm’s industry. Learning curve and diffusion models examine the relationship between time and technological change and provide you perspective on how technological change evolves.
Getting better with the learning-by-doing concept
Adopting an innovation doesn’t necessarily result in an immediate reduction in production costs. Often on-the-job experience is necessary before you can take full advantage of the innovation. Learning-by-doing results in decreasing production cost per unit as the cumulative output produced increases, and firms use the innovation more efficiently. The relationship between cumulative output and production cost per unit is described by a learning curve.
It’s easy to mistakenly believe the new innovation’s adoption immediately leads to impressive gains in productivity and output. The day before the innovation, workers are using the old, inferior production method. The next day, the new production method leads to dramatic increases in productivity and lower production costs. But many productivity gains are only realized
Chapter 7: Innovation and Technological Change: The Future Is Now
after an extended period of time. With the passage of time, further improvements in production techniques occur as greater experience is gained. This accumulated learning leads to additional refinements in both production and organization that support additional productivity gains that further reduce production costs.
Given the learning curve, you may want to accept short-term losses in order to gain experience in producing a product. Setting a lower price encourages greater demand for the firm’s product, resulting in increased production. The learning-by-doing associated with the increased production results in lower per-unit cost on subsequent units produced, ultimately resulting in greater profits. By accepting an initial loss through low prices and high production, you can take advantage of the learning curve in a shorter period of time, ultimately resulting in greater profits overall.
Watching developments by modeling diffusion
The speed with which an innovation is adopted by firms in an industry is influenced by a number of factors. The most profitable innovations are adopted first. In addition, innovations requiring a small investment are typically adopted more readily than innovations requiring a substantial investment. Also, innovations that have already been adopted by a large number of firms are more likely to be adopted by other firms due to increased information and competition.
The relationship between diffusion, as measured by the percent of firms using an innovation, and time is often described by an S-shaped diffusion curve. Edwin Mansfield’s logistic curve often is used to describe this diffusion process. The formula for Mansfield’s logistic curve is
where P(t) represents the percentage of firms using the innovation at time t. The symbol e (Euler’s number) approximates to 2.718. The parameters α and β describe the diffusion process, and they vary among innovations. The function described by the logistic curve is illustrated in Figure 7-2.
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Figure 7-2:
Diffusion (logistic) curve.
After you obtain data on the adoption of an innovation for previous years, you can estimate the logistic curve. After you estimate the curve, use it to predict the future diffusion path of the innovation. Firms have found that this technique has generated useful forecasts for the diffusion of a variety of innovations.
Mansfield’s logistic curve
In his early research on diffusion using the logistic curve, Edwin Mansfield examined several innovations, including continuous mining machines and railroad locomotives. Based upon this research, Mansfield concluded that several factors lead some firms to adopt innovations more quickly than other firms. For example, innovations tend to be adopted more rapidly by larger firms than smaller firms. However, Mansfield also concluded that technical leadership and a firm’s financial health aren’t important factors influencing how they adopt innovations. In other words, the same firms don’t consistently lead in the adoption of innovations. Finally, and not surprisingly, firms that find an innovation is more profitable tend to adopt it more quickly.
