Purchase Response
Overview
Purchase response is a function which describes the quantity of product purchased by customers over a period of time in response
to a set of underlying factors, such as product price and marketing expenditures.
{% Purchases_t = f(price_t, marketing\_expenditures_t, ...) %}
Purchase Response Elasticity
The Elasticity (or sensitivity) of the purchase response function is the change that occurs to the function at a given point, when
one of the inputs is changed by a single unit.
Here, we demonstrate the sensitivity to the purchase response function to a change in price.
{% \Delta Purchases_t = f(price_t + 1, expenditures_t, ...) - f(price_t + 1, expenditures_t, ...) %}
From a calculus perspective, this can be stated as a
partial derivative.
The sensitivities allow one to optimize the price charged for a product, as well as the marketing spend allocated to it.
Fitting the Purchase Response Function
Fitting the purchase response function to data typically means choosing a functional form of the function
(i.e. linear, polynomial, exponential ....) and then finding the parameters that minimize the error between projected values and
the dataset.
The simplest method assumes the purchase response function is linear and to use
OLS Regression
to fit the function to the data.
