Managers of firms, as well as industry analysts, government policymakers, and academic researchers, are frequently interested in how total revenue changes when there is a movement along the demand curve. Total revenue (TR), which also equals the total expenditure by consumers on the commodity, is simply the price of the commodity times quantity demanded, or
TR 5 P 3 Q
As we have emphasized, price and quantity demanded move in opposite direc- tions along a demand curve: If price rises, quantity falls; if price falls, quantity rises. The change in price and the change in quantity have opposite effects on total revenue. The relative strengths of these two effects will determine the overall ef- fect on TR. We will now examine these two effects, called the price effect and the quantity effect, along with the price elasticity of demand to establish the relation between changes in price and total revenue.
Price Elasticity and Changes in Total Revenue
When a manager raises the price of a product, the increase in price, by itself, would increase total revenue if the quantity sold remained constant. Conversely, when a manager lowers price, the decrease in price would decrease total revenue if the quantity sold remained constant. This effect on total revenue of changing price, for a given level of output, is called the price effect. When price changes, the quantity sold does not remain constant; it moves in the opposite direction of price. When quantity increases in response to a decrease in price, the increase in quantity, by itself, would increase total revenue if the price of the product remained constant.
Alternatively, when quantity falls after a price increase, the reduction in quantity, by itself, would decrease total revenue if product price remained constant. The ef- fect on total revenue of changing the quantity sold, for a given price level, is called the quantity effect. The price and quantity effects always push total revenue in opposite directions. Total revenue moves in the direction of the stronger of the two effects. If the two effects are equally strong, no change in total revenue can occur.
Suppose a manager increases price, causing quantity to decrease. The price ef- fect, represented below by an upward arrow above P, and the quantity effect, rep- resented by a downward arrow above Q, show how the change in TR is affected by opposing forces
TR 5 P 3 Q
To determine the direction of movement in TR, information about the relative strengths of the price effect and output effect must be known. The elasticity of demand tells a manager which effect, if either, is dominant.
If demand is elastic, |E| is greater than 1, the percentage change in Q (in abso- lute value) is greater than the percentage change in P (in absolute value), and the quantity effect dominates the price effect. To better see how the dominance of the
total revenue (TR) The total amount paid to producers for a good or service (TR 5 P 3 Q).
price effect The effect on total revenue of changing price, holding output constant.
quantity effect The effect on total revenue of changing output, holding price constant.
quantity effect determines the direction in which TR moves, you can represent the dominance of the quantity effect by drawing the arrow above Q longer than the arrow above P. The direction of the dominant effect—the quantity effect here—
tells a manager that TR will fall when price rises and demand is elastic:
TR 5 P 3 Q
If a manager decreases price when demand is elastic, the arrows in this diagram reverse directions. The arrow above Q is still the longer arrow because the quan- tity effect always dominates the price effect when demand is elastic.
Now consider a price increase when demand is inelastic. When demand is in- elastic, |E| is less than 1, the percentage change in Q (in absolute value) is less than the percentage change in P (in absolute value), and the price effect dominates the quantity effect. The dominant price effect can be represented by an upward arrow above P that is longer than the downward arrow above Q. The direction of the dominant effect tells the manager that TR will rise when price rises and demand is inelastic
TR 5 P 3 Q
When a manager decreases price and demand is inelastic, the arrows in this diagram would reverse directions. A downward arrow above P would be a long arrow because the price effect always dominates the quantity effect when demand is inelastic.
When demand is unitary elastic, |E| is equal to 1, and neither the price effect nor the quantity effect dominates. The two effects exactly offset each other, so price changes have no effect on total revenue when demand is unitary elastic.
Relation The effect of a change in price on total revenue (TR 5 P 3 Q) is determined by the price elasticity of demand. When demand is elastic (inelastic), the quantity (price) effect dominates. Total revenue always moves in the same direction as the variable (P or Q) having the dominant effect. When demand is unitary elastic, neither effect dominates, and changes in price leave total revenue unchanged.
Table 6.2 summarizes the relation between price changes and revenue changes under the three price elasticity conditions.
Elastic Unitary elastic Inelastic
|%DQ| . |%DP | |%DQ| 5 |%DP | |%DQ| , |%DP | Q-effect dominates No dominant effect P-effect dominates Price rises TR falls No change in TR TR rises
Price falls TR rises No change in TR TR falls T A B L E 6.2
Relations between Price Elasticity and Total Revenue (TR )
Changing Price at Borderline Video Emporium: A Numerical Example
The manager at Borderline Video Emporium faces the demand curve for Blu-ray DVD discs shown in Figure 6.1. At the current price of $18 per DVD Borderline can sell 600 DVDs each week. The manager can lower price to $16 per DVD and increase sales to 800 DVDs per week. In Panel A of Figure 6.1, over the interval a to b on demand curve D the price elasticity is equal to 22.43. (You will learn how to make this calculation in Section 6.4.) Because the demand for Blu-ray DVDs is elastic over this range of prices (|22.43| . 1), the manager knows the quantity effect dominates the price effect. Lowering price from $18 to $16 results in an in- crease in the quantity of DVDs sold, so the manager knows that total revenue, which always moves in the direction of the dominant effect, must increase.
To verify that revenue indeed rises when the manager at Borderline lowers the price over an elastic region of demand, you can calculate total revenue at the two prices, $18 and $16
Point a: TR 5 $18 3 600 5 $10,800 Point b: TR 5 $16 3 800 5 $12,800
F I G U R E 6.1
Changes in Total Revenue of Borderline Video Emporium
Price per DVD (dollars)
E = 22.43
D a
b f
g
600 18
16 13 11
Quantity of DVDs per week Panel A — An elastic region of demand
Quantity effect dominates
800 1,1001,300 2,400
24
0 2,400
Price per DVD (dollars)
D a
b
600 18
16
9 7 24
0
Quantity of DVDs per week Panel B — An inelastic region of demand
Price effect dominates
800 1,500 1,700 E = 20.50 c
d
Total revenue rises by $2,000 (5 12,800 2 10,800) when price is reduced over this elastic region of demand. Although Borderline earns less revenue on each DVD sold, the number of DVDs sold each week rises enough to more than offset the downward price effect, causing total revenue to rise.
Now suppose the manager at Borderline is charging just $9 per compact disc and sells 1,500 DVDs per week (see Panel B). The manager can lower price to $7 per disc and increase sales to 1,700 DVDs per week. Over the interval c to d on demand curve D, the elasticity of demand equals 20.50. Over this range of prices for DVDs, the demand is inelastic (|20.50| , 1), and Borderline’s manager knows the price ef- fect dominates the quantity effect. If the manager lowers price from $9 to $7, total revenue, which always moves in the direction of the dominant effect, must decrease.
To verify that revenue falls when the manager at Borderline lowers price over an inelastic region of demand, you can calculate total revenue at the two prices,
$9 and $7
Point c: TR 5 $9 3 1,500 5 $13,500 Point d: TR 5 $7 3 1,700 5 $11,900
Total revenue falls by $1,600 (DTR 5 $11,900 2 $13,500 5 2$1,600). Total revenue always falls when price is reduced over an inelastic region of demand. Borderline again earns less revenue on each DVD sold, but the number of DVDs sold each week does not increase enough to offset the downward price effect and total revenue falls.
If the manager decreases (or increases) the price of Blu-ray DVDs over a unitary-elastic region of demand, total revenue does not change. You should ver- ify that demand is unitary elastic over the interval f to g in Panel A of Figure 6.1.
Note in Figure 6.1 that demand is elastic over the $16 to $18 price range but in- elastic over the $7 to $9 price range. In general, the elasticity of demand varies along any particular demand curve, even one that is linear. It is usually incorrect to say a demand curve is either elastic or inelastic. You can say only that a demand curve is elastic or inelastic over a particular price range. For example, it is correct to say that demand curve D in Figure 6.1 is elastic over the $16 to $18 price range and inelastic over the $7 to $9 price range.
Now try Technical Problems 3–5.
I L L U S T R AT I O N 6 . 1 P 3 Q Measures More Than Just Business’
Total Revenue
As you know from our explanation in Section 6.2, demand elasticity provides the essential piece of in- formation needed to predict how total revenue changes—
increases, decreases, or stays the same—when the price of a good or service changes. We mention in that dis- cussion that price multiplied by quantity can also mea-
sure the amount spent by consumers who buy Q units of the good at price P. In other words, total revenue for a business is exactly equal to the total expenditure by consumers.
While business owners and managers focus on P 3 Q as measuring their revenue for the purpose of computing their business profit, politicians and gov- ernment policymakers frequently view P 3 Q as mea- suring the “burden” on consumers buying the good