Editing Price elasticity of demand (section)

==Effect on entire revenue==
{{See also|Total revenue test}}

[[File:Price elasticity of demand and revenue.svg|right|thumb|A set of graphs shows the relationship between demand and revenue (PQ)   for the specific case of a linear demand curve. As price decreases in the elastic range, the revenue increases, but in the inelastic range, revenue falls. Revenue is highest at the quantity where the elasticity equals 1.]]
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:

:<math> \text{Revenue} = PQ_d</math>

Generally, any change in price will have two effects:<ref>Krugman, Wells (2009). p. 151.</ref>
===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.)<ref>Goodwin, Nelson, Ackerman & Weisskopf (2009). p. 122.</ref> 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 elasticity and revenue can be described for any good:<ref>Gillespie, Andrew (2002). p. 51.</ref><ref name="Arnold2008">Arnold, Roger (2008). p. 385.</ref>
* When the price elasticity of demand for a [[Good (economics and accounting)|good]] is ''perfectly inelastic'' (''E''<sub>''d''</sub> = 0), changes in the price do not affect the quantity demanded for the good; raising prices will always cause total revenue to increase. Goods necessary to survival can be classified here; a rational person will be willing to pay anything for a good if the alternative is death. For example, a person in the desert weak and dying of thirst would easily give all the money in his wallet, no matter how much, for a bottle of water if he would otherwise die. His demand is not contingent on the price.
* When the price elasticity of demand is ''relatively inelastic'' (−1 < ''E''<sub>''d''</sub> < 0), the percentage change in quantity demanded is smaller than that in price. Hence, when the price is raised, the total revenue increases, and vice versa.
* When the price elasticity of demand is ''unit (or unitary) elastic'' (''E''<sub>''d''</sub> = −1), the percentage change in quantity demanded is equal to that in price, so a change in price will not affect total revenue.
* When the price elasticity of demand is ''relatively elastic'' (−∞ < ''E''<sub>''d''</sub> < −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 is ''perfectly elastic'' (''E''<sub>''d''</sub> is − '''[[Infinity (mathematics)|∞]]'''), any increase in the price, no matter how small, will cause the quantity demanded for the good to drop to zero. Hence, when the price is raised, the total revenue falls to zero. This situation is typical for goods that have their value defined by law (such as [[fiat currency]]); if a five-dollar bill were sold for anything more than five dollars, nobody would buy it [unless there is demand for economical jokes], so demand is zero (assuming that the bill does not have a misprint or something else which would cause it to have its own inherent value).

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.<ref name="Arnold2008"/>

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.