Product Differentiation

Introduction

We wish to develop a model to explain the common tendency for products to differentiate themselves from each other. Our model is a simple one - it assumes that we are dealing with a set of products that each have several attributes; each attribute may be changed without affecting the subsequent cost to the manufacturer or to the consumer. This sort of model, therefore, would better describe the different types (color, flavor, etc.) of toothpaste that are on the market than the different types of computers available, since the feature set of a computer is largely price determined.

We assume that each consumer has a certain set of preferences in "feature space", and that the consumer will buy the product that is closest to him in this space. If we assume that everyone places equal weights on each feature, the distance between consumer and product is simply the sum of the squares of the difference between each individual feature. On the other hand, we may wish to allow individuals to disagree on the importance of each feature; the program allows the user to specify such an option. In this case, the distance will be a weighted sum of squares, where the weights placed on each feature will differ from person to person.

The behavior of the consumers, then, has been greatly simplified. There is no "inertia", no product loyalty, on the part of the consumer. Furthermore, each consumer acts alone - the popularity of a product does not influence the behavior of any consumer. In fact, we fix consumer preferences over time.

On the other hand, we will allow the manufacturers of the products in question to play a more active role. We assume that each manufacturer is influenced by two factors:

  1. The desire to secure one's own market niche, to better satisfy existing customers.
  2. The desire to follow the trends of other manufacturers, in particular the market leaders.
To persue such a strategy, each manufacturer is allowed to send to his current customers a survey form that reads as follows:
Dear Valued Customer,

In order to better meet your needs and improve the quality of our product, we have developed a NEW, IMPROVED version of .

(Describe how great (new product) is here)

Enclosed is a free sample of (new product). Please let us know what you think about (new product) by sending the included questionaire back to us.

(blah blah blah)

The manufacturer will, on the basis of this survey, decide whether or not to actually improve his product in the proposed fashion. The "improvements" are actually derived by modifiying each feature of the product in a small random increment. Note that the manufacturer in this case is attempting to maximize the combined utility function of his current customers. He has no knowledge of whether or not his proposed change will actually change the *number* of customers he has.

If the proposed change turns out to have negative appeal, the manufacturer, with nothing better to do, will turn to the second strategy - that is, trying to follow the market leader(s). The user may set the following parameters:

  1. How *many* market leaders the system has. The manufacturer will choose a competing manufacturer to follow by choosing randomly among the top manufacturers. Manufacturers are ranked by market share at each iteration; who the market leaders are at each step is therefore highly variable.
  2. How far in the market leader's direction the manufacturer will go at each step.
  3. The magnitude of a "random drift" factor - companies can't be expected to copy each other perfectly.
To summarize, then, each manufacturer first tries to improve his product in a way that will better satisfy his own customers; if this fails, he will attempt to follow those who have clearly succeeded - the market leaders.

The degree of product differentiation that results is highly dependent on the above parameters. As expected, for example, "market leader following" works strongly against product differentiation. However, there is one last factor that is even more critically affects product differentiation - the distribution of consumers in feature space.

Does everyone want roughly the same set of features? Or do people deliberately want features at the extremes of feature space? (No one drinks *warm* coffee, for instance.) Or is everyone generally indifferent to what features are present? (Who cares about toothpaste flavor?) Four consumer distributions are available: 1. The uniform distribution. 2. The distribution of extremes - everything spread out to the edges of feature space. 3. The central distribution - everyone wants roughly the same set of features. 4. The "spread around a cube distribution" - everyone has *one* feature that they prefer to be extreme on. And that's all there is to the model.

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