Firm Revenue
Overview
Revenue is the money that a company earns from selling its products or services. Sometimes called the top line, it represents
money coming into the firm over a given period (a quarter or a year) prior to any expenses being removed. A simple
equation for revenue is
{% Revenue = price \times quantity %}
Price is often abbreviated as p, and quantity as q.
Of course, most firms have more than one product, so that total revenue becomes the sum of the revenues of all these
individual products and services.
Pricing Effects on Revenue
To understand pricing effects on revenue, we start with the basic revenue equation, which expresses revenue as a function of price
{% Revenue(p, q) = p \times q %}
then, by a simple application of the
chain rule, we have
{% \frac{\partial Revenue(p, q) }{\partial p} = q + p \times \frac{\partial q}{\partial p} %}
Focusing on the first term, one can see that the increase to profitability that results from a $1 increase in
price is equal to the amount of product currently being sold. That is, if one sells 10 widgets, but then increases
the price by $1, one will earn an additional $10 (10 x 1).
Of course, this assumes that the amount of product being sold does not change with the change in price.
Certainly, this cant be true, otherwise a firm would be incented to increase the price arbitrarily.
Elasticity
The second term in the profitability equation reflects the effects of the change in the amount of product sold
when the price changes. The term :
{% \partial{q}/\partial{p} \approx \Delta q / \Delta p %}
is the change in the amount sold divided by the change in the price. This is usually referred to as the
elasticity.
