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Total Revenue and Price Elasticity

25 April, 2016 - 09:12

A firm’s elasticity of demand with respect to price has important implications for assessing the impact of a price change on total revenue. Also, the price elasticity of demand can be different at different points on a firm’s demand curve. In this section, we shall see why a monopoly firm will always select a price in the elastic region of its demand curve.

Suppose the demand curve facing a monopoly firm is given by Equation 10.1, where Q is the quantity demanded per unit of time and P is the price per unit:

EQUATION 10.1

Q = 10 − P

This demand equation implies the demand schedule shown in Figure 10.3. Total revenue for each quantity equals the quantity times the price at which that quantity is demanded. The monopoly firm’s total revenue curve is given in Panel (b). Because a monopolist must cut the price of every unit in order to increase sales, total revenue does not always increase as output rises. In this case, total revenue reaches a maximum of $25 when 5 units are sold. Beyond 5 units, total revenue begins to decline.

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Figure 10.3 Demand, Elasticity, and Total Revenue
 

Suppose a monopolist faces the downward-sloping demand curve shown in Panel (a). In order to increase the quantity sold, it must cut the price. Total revenue is found by multiplying the price and quantity sold at each price. Total revenue, plotted in Panel (b), is maximized at $25, when the quantity sold is 5 units and the price is $5. At that point on the demand curve, the price elasticity of demand equals −1.

The demand curve in Panel (a) of Figure 10.3 shows ranges of values of the price elasticity of demand.We have learned that price elasticity varies along a linear demand curve in a special way: Demand is price elastic at points in the upper half of the demand curve and price inelastic in the lower half of the demand curve. If demand is price elastic, a price reduction increases total revenue. To sell an additional unit, a monopoly firm must lower its price. The sale of one more unit will increase revenue because the percentage increase in the quantity demanded exceeds the percentage decrease in the price. The elastic range of the demand curve corresponds to the range over which the total revenue curve is rising in Panel (b) of Figure 10.3.

If demand is price inelastic, a price reduction reduces total revenue because the percentage increase in the quantity demanded is less than the percentage decrease in the price. Total revenue falls as the firm sells additional units over the inelastic range of the demand curve. The downward-sloping portion of the total revenue curve in Panel (b) corresponds to the inelastic range of the demand curve.

Finally, recall that the midpoint of a linear demand curve is the point at which demand becomes unit price elastic. That point on the total revenue curve in Panel (b) corresponds to the point at which total revenue reaches a maximum.

The relationship among price elasticity, demand, and total revenue has an important implication for the selection of the profit-maximizing price and output: A monopoly firm will never choose a price and output in the inelastic range of the demand curve. Suppose, for example, that the monopoly firm represented in Figure 10.3 is charging $3 and selling 7 units. Its total revenue is thus $21. Because this combination is in the inelastic portion of the demand curve, the firm could increase its total revenue by raising its price. It could, at the same time, reduce its total cost. Raising price means reducing output; a reduction in output would reduce total cost. If the firm is operating in the inelastic range of its demand curve, then it is not maximizing profits. The firm could earn a higher profit by raising price and reducing output. It will continue to raise its price until it is in the elastic portion of its demand curve. A profit-maximizing monopoly firm will therefore select a price and output combination in the elastic range of its demand curve.

Of course, the firm could choose a point at which demand is unit price elastic. At that point, total revenue is maximized. But the firm seeks to maximize profit, not total revenue. A solution that maximizes total revenue will not maximize profit unless marginal cost is zero.