Here are several problems classes have worked out to calculate the elasticity *E*,

$latex \displaystyle E=\frac{P}{Q} \frac{dQ}{dP}$

In this formula, $latex \displaystyle \frac{dQ}{dP}$ is the derivative of the demand function when it is given as a function of *P*. Here are two examples the class worked.

**Problem 1** Suppose the quantity demanded by consumers in units is given by $latex Q=5000-5P$ where *P* is the unit price in dollars.

- Find the elasticity of demand with respect to price when
*P*= 200. - Find the quantity at which revenue is maximized.

This means that a 1% increase in price results in a 0.25% drop in the quantity demanded. The demand is inelastic and the price increase results in an increase in revenue.

**Problem 2** Suppose the quantity demanded by consumers in units is given by $latex Q=100-\frac{P}{2}$ where *P* is the unit price in dollars.

- Find the elasticity of demand with respect to price when
*P*= 110. - Find the quantity at which revenue is maximized.

This means that a price increase of 1% will lead to a 1.22% drop in demand, demand is elastic and the price increase results in a drop in revenue.

**Problem 3** Suppose the quantity demanded by consumers in units is given by $latex Q=500-0.1{{P}^{2}}$ where *P* is the unit price in dollars.

- Find the elasticity of demand with respect to price when
*P*= 100. - Find the quantity at which revenue is maximized.

An increase of 1% in price results in a drop in demand of 0.041%…demand is inelastic so the increase will result in an increase in revenue.