Diffusion model basics

A typical discrete-choice survey asks respondents to choose among a set of hypothetical products on a simulated shelf.  Results are then used to produce estimates of potential market demand for these products in a competitive setting.  However, these estimates suffer from two shortcomings that arise from the survey itself.  First, during a typical questionnaire we introduce respondents to all products we want to test, so awareness is by definition 100%.  Second, the products are often imaginary, so we assume away any distribution problems that bedevil the real world.

In our real world, however, awareness is rarely 100%, nor are products available everywhere.  For these reasons we say that model forecasts apply to potential market demand rather than actual market demand.  In order to convert forecasts for potential demand to actual demand, the Simulator Wizard constructs a diffusion model  and places it in a worksheet with the same name.  A diffusion model attempts to replicate the temporal adoption of a new product as word of mouth travels through the target population and external communications attempt to influence demand.  A sample diffusion model worksheet with a graph of projected adoption appears below.  Click on sections of the image to link to explanations of its contents.

A diffusion model projects how a new idea or product will become adopted by a social system over time as awareness flows through communication channels.  Frequently, adoption paths take the form of S-shaped curves in which adoption proceeds at a slow rate in the beginning, accelerates to an inflection point, begins to decelerate, then tapers off to saturation.  Many researchers have attempted to model this process.  The most notable of these, Frank Bass, developed a number of models, one of which the Simulator Wizard employs.

Bass's model assumes that the traditional S shape of adoption curves comes from a mixture of internal and external influences.  Internal influences are those that arise from interactions within the social system, such as word of mouth.  External influences come from change agents such as advertising messages that lie outside the social system.  The combination of these two effects describes the adoption path for a new product.

Coefficients of external and internal influence

Two coefficients measure the degree to which external and internal influences affect adoption for a particular product.  The coefficient of innovation, sometimes called the coefficient of external influence, appears in cell C6 in the figure above and represents the impact that mass media, government agencies, promotional efforts and the like have on adoption.  The coefficient of imitation, also called the coefficient of internal influence, appears in cell C11 and represents the influence of social interaction, such as non-adopters talking to adopters.  This latter influence is stronger where populations are more dense; and the product concept, more compelling.

Estimates for these two parameters come from historical observations for typical products.  Bass Economics has compiled a number of estimates on its web site, http:// www.basseconomics.com .  The default values supplied by the Simulator Wizard are consistent with Bass' suggestions and have been applied successfully to many real-world products.  However, if you believe the default values don't suit your situation, you are encouraged to substitute your own.  Page down to find a section with a variety of estimates for p and q from a number of industries and sectors.  

If you happen to possess adoption data for a closely related product, you can estimate your own values for the two coefficients using Excel's Solver tool.

Estimate for potential market

In addition to the above parameters, the final requirement for the Bass model is an estimate of potential demand.  For this purpose the Simulator Wizard uses the potential market estimate for the left-hand product in the Main sheet.  In the example below, this value is located in cell H21.

Substituting another diffusion model

Though the Bass model is frequently used in adoption problems, a wide variety of other diffusion models exist.  These include dynamic diffusion models,  space-time diffusion models, multi-innovation, multi-stage and  multi-adoption diffusion models, and many more.  No one approach applies to all situations,but because the simulator exists in Excel, you are free to alter or customize the model however you choose.

Diffusion factor

The diffusion factor is the cumulative percentage of total saturation achieved by the product in a given year.  It is the direct product of the diffusion model, which by default is the most commonly used version of the Bass model.  The formula for the Bass model resides in cell D25 of the Diffusion model sheet.  "Alpha" and "Beta" in that formula refer to cells C6 and C11, the coefficients of external and internal influence. You can see the model in the formula window below.

To substitute your own model, overwrite the contents of cell D26, then copy it to the remaining cells in the row.

Starting adoption

In some cases, adoption for the product being modeled is already under way.  If this is so, place the number of products already adopted in cell C26.  The graph and other formulas in the sheet will reflect the change.

Cumulative adoption

The diffusion factors in row 25 are translated into cumulative product adoption in row 27. These are the cumulative number of units that are projected to be sold at various points in time.  The accompanying chart displays the values in this row.

Unit sales

This number represents the incremental sales in a given time period.  It is the change in cumulative adoption from one period to the next.

Unit revenues

Unit revenues, or revenue per period, equal unit sales times the price of Your prod. from the Main sheet.  The specific price used has a range name of APrice.

Extensions and modifications

In addition to the modifications to the diffusion formula, discussed above, you are free to make other modifications to this sheet.  For example, you may want to add a row that shows each year's unit sales, calculated as the annual difference in row 27's cumulative adoption.  Depending on the product under study, you might want to change the period from years to some other measure.  Other modifications are possible as well, limited only by your requirements and Excel's capabilities.