Modeling the Customer
Overview
An alternative function that marketers define is the willingness to pay. Willingness to pay for a single customer
is defined as the maximum price that that customer is willing to pay for a product or service.
(also known as the
reservation price)
Willingness to Pay
Given the willingness to pay of a set of market participants, the marketer attempts to construct
a willlingness to pay density function
{% w(x) %}
such that, the fraction of the population that has a willingness to pay between price p1 and p2 is given by
{% \int_{p1}^{p2} w(x) dx %}
then, the demand function is given by
{% q(p) = D \int_p ^{\infty} w(x) dx %}
Where D is defined to be the demand when the price is zero. That is, if the product were free, how much would people demand of the product.
(Standard economics might assume that this number is infinity, although clearly it would have a finite limit.) This is the hypothetical maximum demand.
There are some caveats to this definition. The issues mainly concern a custmomers likelihood to buy multiple units of the product over time, in which case
there may be a different willigness to pay for each unit, for example. This does not stop us from defining a demand density as we did above, its
just that its correspondence to willingness to pay will only be approximate.
