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Because of the law of demand, an increase in price is associated with a decrease in the number of units demanded of some good or service. But what can we say about the total expenditure on that good? That is, what happens to price times quantity when price falls? Recall that elasticity is defined as the ratio of the percentage change in quantity demanded to the percentage change in price. So if demand is elastic, a decrease in price is associated with a larger percentage rise in quantity demanded. For example, if elasticity were equal to negative two, then the percentage change in quantity demanded would be twice as large as the percentage change in price. It follows that a 10 percent fall in price would bring about a rise in quantity of greater magnitude, in this case 20 percent. True, each unit of the good has a lower price, but a sufficiently greater number of units are purchased so that total expenditure (price times quantity) would rise as price falls when demand is elastic.
If demand is inelastic, however, a 10 percent fall in price brings about a rise in quantity less than 10 percent in magnitude. Consequently, when demand is inelastic, a fall in price brings about a fall in total expenditure. If elasticity were equal to negative one, (unitary elasticity) the percentage decrease in price is just offset by an equal and opposite percentage increase in quantity demanded, so total expenditure does not change at all.
In summary, when demand is elastic, price and total expenditure move in opposite directions. When demand is inelastic, price and total expenditure move in the same direction. When demand is unitary elastic, changes in price are associated with no change in total expenditure. This relationship is easy to identify in the case of a linear demand curve. Recall from Exhibit 20 that above the midpoint, demand is elastic; and below the midpoint, demand is inelastic. In the upper section of Exhibit 22, total expenditure (P× Q) is measured as the area of a rectangle whose base is Q and height is P. Notice that as price falls, the inscribed rectangles at first grow in size but then become their largest at the midpoint of the demand curve. Thereafter, as price continues to fall, total expenditure falls toward zero. In the lower section of Exhibit 22, total expenditure is shown for each quantity purchased. Note that it reaches a maximum at the quantity that defines the midpoint, or unit-elastic, point on the demand curve.Exhibit 22. Elasticity and Total Expenditure
It should be noted that the relationships just described hold for any demand curve, so it does not matter whether we are dealing with the demand curve of an individual consumer, the demand curve of the market, or the demand curve facing any given seller. For a market, the total expenditure by buyers becomes the total revenue to sellers in that market. It follows, then, that if market demand is elastic, a fall in price will result in an increase in total revenue to sellers as a whole, and if demand is inelastic, a fall in price will result in a decrease in total revenue to sellers. Clearly, if the demand faced by any given seller were inelastic at the current price, that seller could increase revenue by increasing its price. Moreover, because demand is negatively sloped, the increase in price would decrease total units sold, which would almost certainly decrease total cost. So no one-product seller would ever knowingly choose to set price in the inelastic range of its demand.