## Total Revenue and the Price Elasticity op Demand

When studying changes in supply or demand in a market, one variable we often want to study is total revenue, the amount paid by buyers and received by sellers of the good. In any market, total revenue b P x q, the price of the good limes Ihe quantity of the good sold. Wc can show total revenue graphically, as in Figure 2. The height of the box under the demand curve is P, and the width b Q. The area of tlus box, P X Q, equals Ihe total revenue in thb market. In Figure 2, where P = and Q - 100. total revenue is \$« x 100, or \$400.

How docs total revenue change as one moves along »he demand curvc? The answer depends on the price elasticity of demand. If demand b inelastic, as in panel (a) of Figure 3, then an increase in Ihe price causes an increase in total revenue. Here an increase in price from \$1 hi \$3 causes the quantity demanded to fall from 100 to 80, so total revenue rises from \$100 to S240. An increase in price raises P X Q because the fall in Q is proportk>nately smaller than the rise in P

We obtain the opposite result if demand is elastic. An increase in the price causes a decrease in total revenue. In panel (b) of Figure 3, for instance, when the price rises from \$4 to \$?, the quantity demanded falls from 50 to 20, so total revenue falls from S2C0 to \$100. Because demand b elastic, Ihe reduction in Ihe quantity demanded is so great that it more than offsets the increase in the price. That is, an increase in price reduces P X Q because the fall in Q is proportionately greater than the rise in P.

Although the examples in thb figure are extreme, they illustrate some general rules:

• When demand b inelastic (a price elasticity less than 1), price and total revenue move in the same direction.

• When demand is elastic (a price elasticity greater than 1), price and total revenue move in opposite directions.

total revenue the amount pa>d by buyers and received by «11-ei ol a geed, computed a« the price of the good time» the quantity sold

• If demand is unit elastic (a price elasticity exactly equal to 1), total revenue remains constant when the price changes-

elasticity and total revenue along 