There are several ways we can define elasticity E. Each indicates how the quantity demanded changes as the price is changed. In the examples below, we’ll utilize elasticity defined as
$latex \displaystyle \text{E}\approx \frac{P}{Q}\,\frac{dQ}{dP}$
With this definition, the revenue is maximized when E = -1.
Example 1 Suppose the demand function is defined by
$latex \displaystyle Q=30-\frac{P}{5}$
where Q units are demanded at a price of P dollars each.
a. Find an expression for the elasticity in terms of P.
b. Find the quantity at which the revenue is maximized.
Example 2 Suppose the demand function is defined by
$latex \displaystyle Q=40-\frac{P}{4}$
where Q units are demanded at a price of P dollars each.
a. Find an expression for the elasticity in terms of P.
b. Find the quantity at which the revenue is maximized.
Example 3 Suppose the demand function is defined by
$latex \displaystyle Q=39300-7{{P}^{2}}$
where Q units are demanded at a price of P dollars each.
a. Find an expression for the elasticity in terms of P.
b. Find the quantity at which the revenue is maximized.
