Price Elasticity of Demand - Effect On Total Revenue

Effect On Total Revenue

A firm considering a price change must know what effect the change in price will have on total revenue. Revenue is simply the product of unit price times quantity:

Generally any change in price will have two effects:

• the price effect : For inelastic goods, an increase in unit price will tend to increase revenue, while a decrease in price will tend to decrease revenue. (The effect is reversed for elastic goods.)
• the quantity effect : an increase in unit price will tend to lead to fewer units sold, while a decrease in unit price will tend to lead to more units sold.

For inelastic goods, because of the inverse nature of the relationship between price and quantity demanded (i.e., the law of demand), the two effects affect total revenue in opposite directions. But in determining whether to increase or decrease prices, a firm needs to know what the net effect will be. Elasticity provides the answer: The percentage change in total revenue is approximately equal to the percentage change in quantity demanded plus the percentage change in price. (One change will be positive, the other negative.) The percentage change in quantity is related to the percentage change in price by elasticity: hence the percentage change in revenue can be calculated by knowing the elasticity and the percentage change in price alone.

As a result, the relationship between PED and total revenue can be described for any good:

• When the price elasticity of demand for a good is perfectly inelastic (E_d = 0), changes in the price do not affect the quantity demanded for the good; raising prices will cause total revenue to increase.
• When the price elasticity of demand for a good is relatively inelastic (-1 < E_d < 0), the percentage change in quantity demanded is smaller than that in price. Hence, when the price is raised, the total revenue rises, and vice versa.
• When the price elasticity of demand for a good is unit (or unitary) elastic (E_d = -1), the percentage change in quantity is equal to that in price, so a change in price will not affect total revenue.
• When the price elasticity of demand for a good is relatively elastic ( -∞ < E_d < -1), the percentage change in quantity demanded is greater than that in price. Hence, when the price is raised, the total revenue falls, and vice versa.
• When the price elasticity of demand for a good is perfectly elastic (E_d is − ∞), any increase in the price, no matter how small, will cause demand for the good to drop to zero. Hence, when the price is raised, the total revenue falls to zero.

Hence, as the accompanying diagram shows, total revenue is maximized at the combination of price and quantity demanded where the elasticity of demand is unitary.

It is important to realize that price-elasticity of demand is not necessarily constant over all price ranges. The linear demand curve in the accompanying diagram illustrates that changes in price also change the elasticity: the price elasticity is different at every point on the curve.