Overview
Demand is typically modeled as a function of price, that is
{% demand = q(p) %}
For most products, increasing the price of the product will decrease demand, hence
demand is often represented as a downward sloping curve.
The sensitivity of demand to price is defined to be slope of the demand curve. That is, it specifies the amount of the change in demand for a product given a change in the price.
{% sensitivity = \frac{\Delta q}{ \Delta p} %}
Using
calculus
the sensitivity is simply the
derivative
of the demand function.
{% sensitivity = \frac{d q(p)}{d p} %}
Elasticity
Price sensitivity, as defined above, is useful when doing calculations, however, the number in itself is not very useful in communicating information about the demand curve. This is because, it is dependent on the units of measure used.
In order to remedy this situation, economists define the elasticity as the ratio of change in the percentage of quantity demanded to the change in percentage of price.
{% \frac{\Delta q(p)}{q} \times \frac{p}{\Delta p} %}
which in the
limit
becomes
{% \frac{d q}{d p} \times \frac{p}{q} %}
(Notice that units cancel out in this equation)
Measuring
Measuring and forecasting the demand curve is usually a responsibility of a firm's Marketing department. (see The Demand Curve and Pricing)
Understanding the dynamics of the curve is essential to optimizing the firms profit.