# BASS, a Sales Growth Model

**Topics:**Marketing, Innovation, Bass diffusion model

**Pages:**9 (1453 words)

**Published:**December 26, 2012

The BASS model was first developed in 1969 by Frank Bass. It is a sales growth model that predicts future product class sales for a durable good, using historical product sales levels. Managerial estimates of initial probability of trial (the probability that a purchase will be made early in the introductory phase of the product life cycle) and of imitation or diffusion rate (reflecting the influence of positive word-of-mouth communication) are also required. Given these estimates, the sales of the product class at time t are estimated by the model as:

s(t) = p(0)m + [q-p(0)]Y(t) – (q/m) [Y(t)2],

where p and q are the initial trial probability and diffusion rate parameters, m is the number of potential buyers, and Y(t) is the total (cumulative) number of purchases by time t.

The Bass diffusion curve works on the principle that the growth rate of the market will follow a diffusion curve similar in shape to the product life cycle. Future sales can be predicted as a function of the sales histories of the products in the product class. The initial cumulative rate of diffusion (growth in cumulative sales) is based on the rate of acceptance of the product by innovators. Following the early purchases by innovators, the growth rate accelerates due to word-of-mouth influence and the increase in the number of products in use. As more members of the total potential market acquire the product (that is, cumulative sales approach market potential), the growth rate slows. The rate of diffusion is accelerated or retarded by the price evolution of the product.

INPUT

Market Size (000s)—This is the estimate of the total market potential in thousands of customers. This is the number of initial purchasers only and does not include repeat purchases. In other words, it is the number of potential buyers who might become users of your product over time regardless of how many times they purchase the product. This projection is based on the planned initial price of the product, not whether subsequent price increases or decreases are anticipated.

Innovation Rate—This is the estimate of the parameter that represents the initial probability of trial. It is the rate at which innovators will purchase the product in the early stage of product introduction. Innovators are usually first into the market and are the opinion leaders who influence adoption of the product by others. Innovation rate is a parameter between 0.00 and 1.00, and the closer to 1.00, the more quickly it is estimated that the innovators will adopt the product.

Imitation Rate—This is the estimate of the parameter that represents the rate of diffusion. It is the rate at which other adopters will try based on the early purchases by innovators and word-of-mouth influence. Imitation rate is a parameter between 0.00 and 1.00, and the closer to 1.00, the more rapid will be the diffusion of the product into the total potential market.

Initial Price—This is the introductory price of the product.

Final Price—This reflects the price evolution during the time of market growth. Price increases after introduction will slow the rate of diffusion and price increases will accelerate the rate of diffusion.

OUTPUT

Sales—This is the number of new customers who will purchase the product during each quarter based on the rate of diffusion. The magnitude of the increase, leveling-off, or decline from quarter to quarter allows an assessment of the rate at which the product is penetrating the potential market.

Cumulative Sales—This is the total number of customers in the potential market for the product who have made a purchase of the product. It is a measure of the extent to which the product has penetrated the total market. It is not total unit sales, but total number of first-time buyers.

BASS Exercise

You work for Titanic Products, a manufacturer of electric kitchen accessories, as an assistant in market research....

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