Procter & Gamble Co. (P&G) helps consumers clean up. Households around the world rely on “new and improved” Tide to clean their clothes, Ivory and Ariel detergents to wash dishes, and Pantene Pro-V to shampoo and condition hair. Other P&G products dominate a wide range of lucrative, but slow-growing, product lines, including disposable diapers (Pampers), feminine hygiene (Always), and facial moisturizers (Oil of Olay). P&G’s ongoing challenge is to figure out ways of continuing to grow aggressively outside the United States while it cultivates the profitability of dominant consumer franchises here at home. P&G’s challenge is made difficult by the fact that the company already enjoys a dominant market position in many of its slow-growing domestic markets.
Worse yet, most of its brand names are aging, albeit gracefully. Tide, for example, has been “new and improved” almost continuously over its 70-year history. Ivory virtually introduced the concept of bar soap nearly 100 years ago; Jif peanut butter and Pampers disposable diapers are more than 40 years old. How does P&G succeed in businesses where others routinely fail? Quite simply, P&G is a marketing juggernaut. Although P&G’s vigilant cost-cutting is legendary, its marketing expertise is without peer. Nobody does a better job at finding out what consumers want. At P&G, demand estimation is the lynchpin of its “getting close to the customer” operating philosophy.
Nothing is more important in business than the need to identify and effectively meet customer demand. This chapter examines the elasticity concept as a useful means for measuring the sensitivity of demand to changes in underlying conditions.
DEMAND SENSITIVITY ANALYSIS: ELASTICITY
Nothing is more important in business than the need to identify and effectively meet customer demand. This is the fundamental factor behind the success of today’s global companies: “to determine and meet costumers needs correctly and on time”.
For constructive managerial decision making, the firm must know the sensitivity or responsiveness of demand to the changes in factors that make up the underlying demand function.
One measure of responsiveness employed not only in demand analysis but throughout managerial decision making is “elasticity”.
The Elasticity Concept
One measure of responsiveness employed not only in demand analysis but throughout managerial decision making is elasticity, defined as the percentage change in a dependent variable, Y, resulting from a 1 percent change in the value of an independent variable, X. The equation for calculating elasticity is
The concept of elasticity simply involves the percentage change in one variable associated with a given percentage change in another variable. In addition to being used in demand analysis, the concept is used in finance, where the impact of changes in sales on earnings under different production levels (operating leverage) and different financial structures (financial leverage) are measured by an elasticity factor. Elasticities are also used in production and cost analysis to evaluate the effects of changes in input on output as well as the effects of output changes on costs.
Factors such as price and advertising that are within the control of the firm are called endogenous variables. It is important that management know the effects of altering these variables when making decisions. Other important factors outside the control of the firm, such as consumer incomes, competitor prices, and the weather, are called exogenous variables. The effects of changes in both types of influences must be understood if the firm is to respond effectively to changes in the economic environment. For example, a firm must understand the effects on demand of changes in both prices and consumer incomes to determine the price cut necessary to offset a decline in sales caused by a business recession (fall in income). Similarly, the sensitivity of demand to changes in advertising must be quantified if the firm is to respond appropriately with price or advertising changes to an increase in competitor advertising. Determining the effects of changes in both controllable and uncontrollable influences on demand is the focus of demand analysis.
Point Elasticity and Arc Elasticity
Elasticity can be measured in two different ways, point elasticity and arc elasticity. Point elasticity measures elasticity at a given point on a function. The point elasticity concept is used to measure the effect on a dependent variable Y of a very small or marginal change in an independent variable X.
Although the point elasticity concept can often give accurate estimates of the effect on Yof very small (less than 5 percent) changes in X, it is not used to measure the effect on Y of large-scale changes, because elasticity typically varies at different points along a function. To assess the effects of large-scale changes in X, the arc elasticity concept is employed. Arc elasticity measures the average elasticity over a given range of a function.
Using the lowercase epsilon as the symbol for point elasticity, the point elasticity formula is written
The ΔY/ΔX term in the point elasticity formula is the marginal relation between Y and X, and it shows the effect on Y of a one-unit change in X. Point elasticity is determined by multiplying this marginal relation by the relative size of X to Y, or the X/Y ratio at the point being analyzed. Point elasticity measures the percentage effect on Y of a percentage change in X at a given point on a function. If _X = 5, a 1 percent increase in X will lead to a 5 percent increase in Y, and a 1 percent decrease in X will lead to a 5 percent decrease in Y. Thus, when _X > 0, Y changes in the same positive or negative direction as X. Conversely, when _X < 0, Y changes in the opposite direction of changes in X. For example, if _X = –3, a 1 percent increase in X will lead to a 3 percent decrease in Y, and a 1 percent decrease in X will lead to a 3 percent increase in Y.
Advertising Elasticity Example
An example can be used to illustrate the calculation and use of a point elasticity estimate. Assume that management is interested in analyzing the responsiveness of movie ticket demand to changes in advertising for the Empire State Cinema, a regional chain of movie theaters. Also assume that analysis of monthly data for six outlets covering the past year suggests the following demand function:
where Q is the quantity of movie tickets, P is average ticket price (in dollars), PV is the 3-day movie rental price at video outlets in the area (in dollars), I is average disposable income per household (in thousands of dollars), and A is monthly advertising expenditures (in thousands of dollars). (Note that I and A are expressed in thousands of dollars in this demand function.) For a typical theater, P = $7, PV = $3, and income and advertising are $40,000 and $20,000, respectively. The demand for movie tickets at a typical theater can be estimated as
The numbers that appear before each variable in Equation 5.3 are called coefficients or parameter estimates. They indicate the expected change in movie ticket sales associated with a one-unit change in each relevant variable. For example, the number 5,000 indicates that the quantity of movie tickets demanded falls by 5,000 units with every $1 increase in the price of movie tickets, or ΔQ/ΔP = –5,000. Similarly, a $1 increase in the price of videocassette rentals causes a ,500-unit increase in movie ticket demand, or ΔQ/ΔPV = 3,500; a $1,000 (one-unit) increase in disposable income per household leads to a 150-unit increase in demand. In terms of advertising, the expected change in demand following a one-unit ($1,000) change in advertising, or ΔQ/ΔA, is 1,000. With advertising expenditures of $20,000, the point advertising elasticity at the 10,000-unit demand level is
Thus, a 1 percent change in advertising expenditures results in a 2 percent change in movie ticket demand. This elasticity is positive, indicating a direct relation between advertising outlays and movie ticket demand. An increase in advertising expenditures leads to higher demand; a decrease in advertising leads to lower demand.
For many business decisions, managers are concerned with the impact of substantial changes in a demand-determining factor, such as advertising, rather than with the impact of very small (marginal) changes. In these instances, the point elasticity concept suffers a conceptual shortcoming.
To see the nature of the problem, consider the calculation of the advertising elasticity of demand for movie tickets as advertising increases from $20,000 to $50,000. Assume that all other demand-influencing variables retain their previous values. With advertising at $20,000, demand is 10,000 units. Changing advertising to $50,000 (ΔA= 30) results in a 30,000-unit increase in movie ticket demand, so total demand at that level is 40,000 tickets. Using Equation 5.2 to calculate the advertising point elasticity for the change in advertising from $20,000 to $50,000 indicates that
The advertising point elasticity is _A = 2, just as that found previously. Consider, however, the indicated elasticity if one moves in the opposite direction—that is, if advertising is decreased from $50,000 to $20,000. The indicated elasticity point is
The indicated elasticity _A= 1.25 is now quite different. This problem occurs because elasticities are not typically constant but vary at different points along a given demand function. The advertising elasticity of 1.25 is the advertising point elasticity when advertising expenditures are $50,000 and the quantity demanded is 40,000 tickets.
To overcome the problem of changing elasticities along a demand function, the arc elasticity formula was developed to calculate an average elasticity for incremental as opposed to marginal changes. The arc elasticity formula is
The percentage change in quantity demanded is divided by the percentage change in a demand-determining variable, but the bases used to calculate percentage changes are averages of the two data endpoints rather than the initially observed value. The arc elasticity equation eliminates the problem of the elasticity measure depending on which end of the range is viewed as the initial point. This yields a more accurate measure of the relative relation between the two variables over the range indicated by the data. The advertising arc elasticity over the $20,000–$50,000 range of advertising expenditures can be calculated as
Thus, a 1 percent change in the level of advertising expenditures in the range of $20,000 to $50,000 results, on average, in a 1.4 percent change in movie ticket demand. To summarize, it is important to remember that point elasticity is a marginal concept. It measures the elasticity at a specific point on a function. Proper use of point elasticity is limited to analysis of very small changes, say 0 percent to 5 percent, in the relevant independent variable. Arc elasticity is a better concept for measuring the average elasticity over an extended range when the change in a relevant independent variable is 5 percent or more. It is the appropriate tool for incremental analysis.
PRICE ELASTICITY OF DEMAND
The most widely used elasticity measure is the price elasticity of demand, which measures the responsiveness of the quantity demanded to changes in the price of the product, holding constant the values of all other variables in the demand function.
Price Elasticity Formula
Using the formula for point elasticity, price elasticity of demand is found as
where ΔQ/ΔP is the marginal change in quantity following a one-unit change in price, and P and Q are price and quantity, respectively, at a given point on the demand curve.
The concept of point price elasticity can be illustrated by referring to Equation 5.3:
Q = 8,500 – 5,000P + 3,500PV + 150I + 1,000A
The coefficient for the price variable indicates the effect on quantity demanded of a one-unit change in price:
At the typical values of PV = $3, I = $40,000, and A = $20,000, the demand curve is calculated as
This demand curve relation can be used to calculate _P at two points: (1) where P1 = $7 and Q1 = 10,000 and (2) where P2 = $8 and Q2 = 5,000. This implies _P1 = –3.5 and _P2 = –8 because
Therefore, a 1 percent increase in price from the $7 movie ticket price level results in a 3.5 percent reduction in the quantity demanded. At the $8 price level, a 1 percent increase results in an 8 percent reduction in the quantity demanded. This indicates that movie ticket buyers, like most consumers, become increasingly price sensitive as average price increases. This example illustrates how price elasticity tends to vary along a linear demand curve, with _P increasing in absolute value at higher prices and lower quantities. Although price elasticity always varies along a linear demand curve, under certain conditions it can be constant along a curvilinear demand curve. This point will be illustrated in a later section.
When evaluating price elasticity estimates, recognize that price elasticities are uniformly negative. This is because the quantity demanded for all goods and services is inversely related to price. In the previous example, at a $7 price, a 1 percent increase in price leads to a 3.5 percent decrease in the quantity of movie tickets demanded. Conversely, a 1 percent decrease in price leads to a 3.5 percent increase in the quantity demanded. For expository convenience, the equation for price elasticity is sometimes multiplied by –1 to change price elasticities to positive numbers. Therefore, when price elasticities are reported as positive numbers, or in absolute value terms, it is important to remember the underlying inverse relation between price and quantity.
Using the arc elasticity concept, the equation for price elasticity is
This form is especially useful for analyzing the average sensitivity of demand to price changes over an extended range of prices. For example, the average price elasticity over the price range from $7 to $8 is
This means that, on average, a 1 percent change in price leads to a 5 percent change in quantity demanded when price is between $7 and $8 per ticket.
Price Elasticity and Total Revenue
One of the most important features of price elasticity is that it provides a useful summary measure of the effect of a price change on revenues. Depending on the degree of price elasticity, a reduction in price can increase, decrease, or leave total revenue unchanged. A good estimate of price elasticity makes it possible to accurately estimate the effect of price changes on total revenue.
For decision-making purposes, three specific ranges of price elasticity have been identified. Using |_P| to denote the absolute value of the price elasticity, three ranges for price elasticity are
1. |_P| > 1.0, defined as elastic demand
Example: _P = –3.2 and |_P| = 3.2
2. |_P| = 1.0, defined as unitary elasticity
Example: _P = –1.0 and |_P| = 1.0
3. |_P| < 1.0, defined as inelastic demand
Example: _P = –0.5 and |_P| = 0.5
With elastic demand, |_P| > 1 and the relative change in quantity is larger than the relative change in price. A given percentage increase in price causes quantity to decrease by a larger percentage. If demand is elastic, a price increase lowers total revenue and a decrease in price raises total revenue. Unitary elasticity is a situation in which the percentage change in quantity divided by the percentage change in price equals –1. Because price and quantity are inversely related, a price elasticity of –1 means that the effect of a price change is exactly offset by the effect of a change in quantity demanded. The result is that total revenue, the product of price times quantity, remains constant. With inelastic demand, a price increase produces less than a proportionate decline in the quantity demanded, so total revenues rise. Conversely, when demand is inelastic, a price decrease generates a less than proportionate increase in quantity demanded, so total revenues falls. These relations are summarized in Table.
Price elasticity can range from completely inelastic, where _P = 0, to perfectly elastic, where _P = –∞. To illustrate, consider first an extreme case in which the quantity demanded is independent of price so that some fixed amount, Q*, is demanded regardless of price. When the quantity demanded of a product is completely insensitive to price, ΔQ/ΔP = 0, and price elasticity will equal zero, irrespective of the value of P/Q. The demand curve for such a good or service is perfectly vertical, as shown in Figure.
The other limiting case, that of infinite price elasticity, describes a product that is completely sensitive to price. The demand curve for such a good or service is perfectly horizontal, as shown in Figure. Here the ratio ΔQ/ΔP = –∞ and _P = –∞, regardless of the value of P/Q.
The economic as well as mathematical properties of these limiting cases should be understood. Afirm faced with a vertical or perfectly inelastic demand curve could charge any price and still sell Q* units. Theoretically, such a firm could appropriate all of its customers’ income or wealth. Conversely, a firm facing a horizontal or perfectly elastic demand curve could sell an unlimited quantity of output at the price P*, but it would lose all sales if it raised prices by even a small amount. Such extreme cases are rare in the real world, but monopolies that sell necessities such as pharmaceuticals enjoy relatively inelastic demand, whereas firms in highly competitive industries such as grocery retailing face highly elastic demand curves.
Relationship Between Price Elasticity and Total Revenue
Completely Inelastic Demand Curve: εP = 0
Uses of Price Elasticity Information
Price elasticity information is useful for a number of purposes. Obviously, firms are required to be aware of the price elasticity of demand when they price their products. For example, a profitmaximizing firm would never choose to lower its prices in the inelastic range of the demand curve. Such a price decrease would decrease total revenue and at the same time increase costs, because the quantity demanded would rise. A dramatic decrease in profits would result. Even over the range in which demand is elastic, a firm will not necessarily find it profitable to cut price. The profitability of a price cut in the elastic range of the demand curve depends on whether the marginal revenues generated exceed the marginal cost of added production. Price elasticity information can be used to answer questions such as
What is the expected impact on sales of a 5 percent price increase?
How great a price reduction is necessary to increase sales by 10 percent?
Given marginal cost and price elasticity data, what is the profit-maximizing price?
The importance of price elasticity information was illustrated during 2000–2001 in California when electric utilities were forced to raise prices dramatically because of a rapid increase in fuel costs. The question immediately arose: How much of a cutback in quantity demanded and, hence, how much of a reduction in future capacity needs would these price increases cause? In other words, what was the price elasticity of electricity? In view of the long lead times required to build electricity-generating capacity and the major economic dislocations that arise from power outages, this was a critical question for both consumers and producers of electricity.
Price elasticity information has long played a major role in the debate over national energy policy. Some industry and government economists argue that the price elasticity of demand for energy is sufficiently large that an equilibrium of demand and supply will occur following only modest price changes. Others argue that energy price elasticities are so low that unconscionable price increases are necessary to reduce the quantity demanded to meet pending supply shortfalls. Meanwhile, bouts of falling oil prices raise fears among some that low oil prices may increase Western reliance on imported oil. These same issues have also become a focal point in controversies surrounding nuclear energy, natural gas price deregulation, and alternative renewable energy sources. In this debate on energy policy, the relation between price and quantity supplied—the price elasticity of supply—is also an important component. As with most economic issues, both demand and supply sides of the marketplace must be analyzed to arrive at a rational decision.
Completely Elastic Demand Curve: εP = –∞
Another example of the importance of price elasticity information relates to the widespread discounts or reduced rates offered different customer groups. The Wall Street Journal offers students bargain rates; airlines, restaurants, and most hotel chains offer discounts to vacation travelers and senior citizens; large corporate customers get discounts or rebates on desktop computers, auto leases, and many other items. Many such discounts are substantial, sometimes in the range of 30 percent to 40 percent off standard list prices. The question of whether reduced prices attract sufficient additional customers to offset lower revenues per unit is directly related to the price elasticity of demand.
Additional uses of price elasticity information are examined in later chapters. At this point, it becomes useful to consider some other important demand elasticities.
PRICE ELASTICITY AND MARGINAL REVENUE
There are simple, direct relations between price elasticity, marginal revenue, and total revenue. It is worth examining such relations in detail, given their importance for pricing policy.
Varying Elasticity at Different Points on a Demand Curve
All linear demand curves, except perfectly elastic or perfectly inelastic ones, are subject to varying elasticities at different points on the curve. In other words, any linear demand curve is price elastic at some output levels but inelastic at others. To see this, recall the definition of point price elasticity expressed in Equation 5.6:
The slope of a linear demand curve, ΔP/ΔQ, is constant; thus, its reciprocal, 1/(ΔP/ΔQ) = ΔQ/ΔP, is also constant. However, the ratio P/Q varies from 0 at the point where the demand curve intersects the horizontal axis and price = 0, to +∞at the vertical price axis intercept where quantity = 0. Because the price elasticity formula for a linear curve involves multiplying a negative constant by a ratio that varies between 0 and +∞, the price elasticity of a linear curve must range from 0 to –∞.
Figure illustrates this relation. As the demand curve approaches the vertical axis, the ratio P/Q approaches infinity and _P approaches minus infinity. As the demand curve approaches the horizontal axis, the ratio P/Q approaches 0, causing _P also to approach 0. At the midpoint of the demand curve (ΔQ/ΔP) _ (P/Q) = –1; this is the point of unitary elasticity.
Price Elasticity and Price Changes
The relation between price elasticity and total revenue can be further clarified by examining Figure and Table. Figure reproduces the demand curve shown in Figure along with the associated marginal revenue curve. The demand curve shown in Figure is of the general linear form
where a is the intercept and b is the slope coefficient. It follows that total revenue (TR) can be expressed as
By definition, marginal revenue (MR) is the change in revenue following a one-unit expansion in output, ΔTR/ΔQ, and can be written
Price Elasticity of Demand Varies Along a Linear Demand Curve
Relations Among Price Elasticity and Marginal, Average, and Total Revenue: (a) Demand (Average Revenue) and Marginal Revenue Curves; (b) Total Revenue
The relation between the demand (average revenue) and marginal revenue curves becomes clear when one compares Equations. Each equation has the same intercept a. This means that both curves begin at the same point along the vertical price axis. However, the marginal revenue curve has twice the negative slope of the demand curve. This means that the marginal revenue curve intersects the horizontal axis at 1/2QX, given that the demand curve intersects at QX. Figure shows that marginal revenue is positive in the range where demand is price elastic, zero where _P = –1, and negative in the inelastic range. Thus, there is an obvious relation between price elasticity and both average and marginal revenue.
As shown in Figure), price elasticity is also closely related to total revenue. Total revenue increases with price reductions in the elastic range (where MR> 0) because the increase in quantity demanded at the new lower price more than offsets the lower revenue per unit received at that reduced price. Total revenue peaks at the point of unitary elasticity (where MR= 0), because the increase in quantity associated with the price reduction exactly offsets the lower revenue received per unit. Finally, total revenue declines when price is reduced in the inelastic range (where MR < 0). Here the quantity demanded continues to increase with reductions in price, but the relative increase in quantity is less than the percentage decrease in price, and thus is not large enough to offset the reduction in revenue per unit sold. The numerical example in Table illustrates these relations. It shows that from 1 to 5 units of output, demand is elastic, |_P| > 1, and a reduction in price increases total revenue. For example, decreasing price from $80 to $70 increases the quantity demanded from 3 to 4 units. Marginal revenue is positive over this range, and total revenue increases from $240 to $280. For output above 6 units and prices below $50, demand is inelastic, |_P| < 1. Here price reductions result in lower total revenue, because the increase in quantity demanded is not large enough to offset the lower price per unit. With total revenue decreasing as output expands, marginal revenue must be negative. For example, reducing price from $30 to $20 results in revenue declining from $240 to $180 even though output increases from 8 to 9 units; marginal revenue in this case is –$60.
PRICE ELASTICITY AND OPTIMAL PRICING POLICY
Firms use price discounts, specials, coupons, and rebate programs to measure the price sensitivity of demand for their products. Armed with such knowledge, and detailed unit cost information, firms have all the tools necessary for setting optimal prices.
Price Elasticity and Revenue Relations: A Numerical Example
Optimal Price Formula
As a practical matter, firms devote enormous resources to obtain current and detailed information concerning the price elasticity of demand for their products. Price elasticity estimates represent vital information because these data, along with relevant unit cost information, are essential inputs for setting a pricing policy that is consistent with value maximization. This stems from the fact that there is a relatively simple mathematical relation between marginal revenue, price, and the point price elasticity of demand.
Given any point price elasticity estimate, relevant marginal revenues can be determined easily. When this marginal revenue information is combined with pertinent marginal cost data, the basis for an optimal pricing policy is created.
The relation between marginal revenue, price, and the point price elasticity of demand follows directly from the mathematical definition of a marginal relation.2 In equation form, the link between marginal revenue, price, and the point price elasticity of demand is
Because _P < 0, the number contained within brackets in Equation 5.10 is always less than one. This means that MR< P, and the gap between MRand P will fall as the price elasticity of demand increases (in absolute value terms). For example, when P = $8 and _P = –1.5, MR = $2.67. Thus, when price elasticity is relatively low, the optimal price is much greater than marginal revenue.
Conversely, when P = $8 and _P = –10, MR = $7.20. When the quantity demanded is highly elastic with respect to price, the optimal price is close to marginal revenue.
Optimal Pricing Policy Example
The simple relation between marginal revenue, price, and the point price elasticity is very useful in the setting of pricing policy. To see the usefulness of Equation in practical pricing policy, consider the pricing problem faced by a profit-maximizing firm. Recall that profit maximization requires operating at the activity level where marginal cost equals marginal revenue.
Most firms have extensive cost information and can estimate marginal cost reasonably well. By equating marginal costs with marginal revenue as identified by Equation, the profit-maximizing price level can be easily determined. Using Equation, set marginal cost equal to marginal revenue, where
MC = MR
which implies that the optimal or profit-maximizing price, P*, equals
This simple relation between price, marginal cost, and the point price elasticity of demand is the most useful pricing tool offered by managerial economics.
To illustrate the usefulness of Equation, suppose that manager George Stevens notes a 2 percent increase in weekly sales following a 1 percent price discount on The Kingfish fishing reels. The point price elasticity of demand for The Kingfish fishing reels is
What is the optimal retail price for The Kingfish fishing reels if the company’s wholesale cost per reel plus display and marketing expenses—or relevant marginal costs—total $25 per unit?
With marginal costs of $25 and _P = –2, the profit-maximizing price is
Therefore, the profit-maximizing price on The Kingfish fishing reels is $50. To see how Equation can be used for planning purposes, suppose Stevens can order reels through a different distributor at a wholesale price that reduces marginal costs by $1 to $24 per unit. Under these circumstances, the new optimal retail price is
Thus, the optimal retail price would fall by $2 following a $1 reduction in The Kingfish’s relevant marginal costs.
Equation can serve as the basis for calculating profit-maximizing prices under current cost and market-demand conditions, as well as under a variety of circumstances. Table shows how profit-maximizing prices vary for a product with a $25 marginal cost as the point price elasticity of demand varies. Note that the less elastic the demand, the greater the difference between the optimal price and marginal cost. Conversely, as the absolute value of the price elasticity of demand increases (that is, as demand becomes more price elastic), the profit-maximizing price gets closer and closer to marginal cost.
Determinants of Price Elasticity
There are three major influences on price elasticities: (1) the extent to which a good is considered to be a necessity; (2) the availability of substitute goods to satisfy a given need; and (3) the proportion of income spent on the product. Arelatively constant quantity of a service such as electricity for residential lighting will be purchased almost irrespective of price, at least in the short run and within price ranges customarily encountered. There is no close substitute for electric service. However, goods such as men’s and women’s clothing face considerably more competition, and their demand depends more on price.
Similarly, the demand for “big ticket” items such as automobiles, homes, and vacation travel accounts for a large share of consumer income and will be relatively sensitive to price. Demand for less expensive products, such as soft drinks, movies, and candy, can be relatively insensitive to price. Given the low percentage of income spent on “small ticket” items, consumers often find that searching for the best deal available is not worth the time and effort. Accordingly, the elasticity of demand is typically higher for major purchases than for small ones. The price elasticity of demand for compact disc players, for example, is higher than that for compact discs.
Price elasticity for an individual firm is seldom the same as that for the entire industry. In pure monopoly, the firm demand curve is also the industry demand curve, so obviously the elasticity of demand faced by the firm at any output level is the same as that faced by the industry. Consider the other extreme—pure competition, as approximated by wheat farming. The industry demand curve for wheat is downward sloping: the lower its price, the greater the quantity of wheat that will be demanded. However, the demand curve facing any individual wheat farmer is essentially horizontal. Afarmer can sell any amount of wheat at the going price, but if the farmer raises price by the smallest fraction of a cent, sales collapse to zero. The wheat farmer’s demand curve—or that of any firm operating under pure competition—is perfectly elastic. Figure illustrates such a demand curve.
The demand for producer goods and services is indirect, or derived from their value in use. Because the demand for all inputs is derived from their usefulness in producing other products, their demand is derived from the demand for final products. In contrast to the terms final product or consumer demand, the term derived demand describes the demand for all producer goods and services. Although the demand for producer goods and services is related to the demand for the final products that they are used to make, this relation is not always as close as one might suspect.
Price Elasticity and Optimal Pricing Policy
In some instances, the demand for intermediate goods is less price sensitive than demand for the resulting final product. This is because intermediate goods sometimes represent only a small portion of the cost of producing the final product. For example, suppose the total cost to build a small manufacturing plant is $1 million, and $25,000 of this cost represents the cost of electrical fixtures and wiring. Even a doubling in electrical costs from $25,000 to $50,000 would have only a modest effect on the overall costs of the plant—which would increase by only 2.5 percent from $1 million to $1,025,000. Rather than being highly price sensitive, the firm might select its electrical contractor based on the timeliness and quality of service provided. In such an instance, the firm’s price elasticity of demand for electrical fixtures and wiring is quite low, even if its price elasticity of demand for the overall project is quite high.
In other situations, the reverse might hold. Continuing with our previous example, suppose that steel costs represent $250,000 of the total $1 million cost of building the plant. Because of its relative importance, a substantial increase in steel costs has a significant influence on the total costs of the overall project. As a result, the price sensitivity of the demand for steel will be close to that for the overall plant. If the firm’s demand for plant construction is highly price elastic, the demand for steel is also likely to be highly price elastic.
Although the derived demand for producer goods and services is obviously related to the demand for resulting final products, this relation is not always close. When intermediate goods or services represent only a small share of overall costs, the price elasticity of demand for such inputs can be much different from that for the resulting final product. The price elasticity of demand for a given input and the resulting final product must be similar in magnitude only when the costs of that input represent a significant share of overall costs.
Price Elasticity of Demand for Airline Passenger Service
Southwest Airlines likes to call itself the Texas state bird. It must be some bird, because the U.S. Transportation Department regards Southwest as a dominant carrier. Fares are cut in half and traffic doubles, triples, or even quadruples whenever Southwest enters a new market. Airport authorities rake in millions of extra dollars in landing fees, parking and concession fees soar, and added business is attracted to the local area—all because Southwest has arrived! Could it be that Southwest has discovered what many airline passengers already know? Customers absolutely crave cut-rate prices that are combined with friendly service, plus arrival and departure times that are convenient and reliable. The once-little upstart airline from Texas is growing by leaps and bounds because nobody knows how to meet the demand for regional airline service like Southwest Airlines.
Table shows information that can be used to infer the industry arc price elasticity of demand in selected regional markets served by Southwest. In the early 1990s, Southwest saw an opportunity because airfares out of San Francisco were high, and the nearby Oakland airport was underused. By offering cut-rate fares out of Oakland to Burbank, a similarly underused airport in southern California, Southwest was able to spur dramatic traffic gains and revenue growth. During the first 12 months of operation, Southwest induced a growth in airport traffic on the Oakland–Burbank route from 246,555 to 1,053,139 passengers, an increase of 806,584 passengers, following an average one-way fare cut from $86.50 to $44.69. Using the arc price elasticity formula, an arc price elasticity of demand of _P = –1.95 for the Oakland–Burbank market is suggested. Given elastic demand in the Oakland–Burbank market, city-pair annual revenue grew from $21.3 to $47.1 million over this period.
A very different picture of the price elasticity of demand for regional airline passenger service is portrayed by Southwest’s experience on the Kansas City–St. Louis route. In 1992, Southwest began offering cut-rate fares between Kansas City and St. Louis and was, once again, able to spur dramatic traffic growth. However, in the Kansas City–St. Louis market, traffic growth was not sufficient to generate added revenue. During the first 12 months of Southwest’s operation in this market, traffic growth in the Kansas City–St. Louis route was from 428,711 to 722,425 passengers, an increase of 293,714 passengers, following an average one-way fare cut from $154.42 to $45.82. Again using the arc price elasticity formula, a market arc price elasticity of demand of only _P = –0.47 is suggested.
With inelastic demand, Kansas City–St. Louis market revenue fell from $66.2 to $33.1 million over this period. In considering these arc price elasticity estimates, remember that they correspond to each market rather than to Southwest Airlines itself. If Southwest were the single carrier or monopolist in the Kansas City–St. Louis market, it could gain revenues and cut variable costs by raising fares and reducing the number of daily departures. As a monopolist, such a fare increase would lead to higher revenues and profits. However, given the fact that other airlines operate in each market, Southwest’s own demand is likely to be much more price elastic than the market demand elasticity estimates shown in Table. To judge the profitability of any fare, it is necessary to consider Southwest’s revenue and cost structure in each market. For example, service in the Kansas City–St. Louis market might allow Southwest to more efficiently use aircraft and personnel used to serve the Dallas–Chicago market and thus be highly profitable even when bargain-basement fares are charged.
The importance of price elasticity information is examined further in later chapters. At this point, it becomes useful to consider other important demand elasticities.
How Prices Plunge and Traffic Soars When Southwest Airlines Enters a Market
CROSS-PRICE ELASTICITY OF DEMAND
Demand for most products is influenced by prices for other products. Such demand interrelationships are an important consideration in demand analysis and estimation.
Substitutes and Complements
The demand for beef is related to the price of chicken. As the price of chicken increases, so does the demand for beef; consumers substitute beef for the now relatively more expensive chicken. On the other hand, a price decrease for chicken leads to a decrease in the demand for beef as consumers substitute chicken for the now relatively more expensive beef. In general, a direct relation between the price of one product and the demand for a second product holds for all substitutes. Aprice increase for a given product will increase demand for substitutes; a price decrease for a given product will decrease demand for substitutes. Some goods and services—for example, cameras and film—exhibit a completely different relation. Here price increases in one product typically lead to a reduction in demand for the other. Goods that are inversely related in this manner are known as complements; they are used together rather than in place of each other.
The concept of cross-price elasticity is used to examine the responsiveness of demand for one product to changes in the price of another. Point cross-price elasticity is given by the following equation:
where Y and X are two different products. The arc cross-price elasticity relationship is constructed in the same manner as was previously described for price elasticity:
The cross-price elasticity for substitutes is always positive; the price of one good and the demand for the other always move in the same direction. Cross-price elasticity is negative for complements; price and quantity move in opposite directions for complementary goods and services. Finally, cross-price elasticity is zero, or nearly zero, for unrelated goods in which variations in the price of one good have no effect on demand for the second.
Cross-Price Elasticity Example
The cross-price elasticity concept can be illustrated by considering the demand function for monitored in-home health-care services provided by Home Medical Support (HMS), Inc.
Here, QY is the number of patient days of service per year; PY is the average price of HMS service; PD is an industry price index for prescription drugs; PH is an index of the average price of hospital service, a primary competitor; PT is a price index for the travel industry; i is the interest rate; and I is disposable income per capita. Assume that the parameters of the HMS demand function have been estimated as follows:
The effects on QY caused by a one-unit change in the prices of other goods are
Because both prices and quantities are always positive, the ratios PD/QY, PH/QY, and PT/QY are also positive. Therefore, the signs of the three cross-price elasticities in this example are determined by the sign of each relevant parameter estimate in the HMS demand function:
HMS service and prescription drugs are complements.
_PH = (+10)(PH/QY) > 0
HMS service and hospital service are substitutes.
_PT = (+0.0001)(PT/QY) ≈ 0, so long as the ratio PT/QY is not extremely large Demand for travel and HMS service are independent.
The concept of cross-price elasticity serves two main purposes. First, it is important for the firm to be aware of how demand for its products is likely to respond to changes in the prices of other goods. Such information is necessary for formulating the firm’s own pricing strategy and for analyzing the risks associated with various products. This is particularly important for firms with a wide variety of products, where meaningful substitute or complementary relations exist within the firm’s own product line. Second, cross-price elasticity information allows managers to measure the degree of competition in the marketplace. For example, a firm might appear to dominate a particular market or market segment, especially if it is the only supplier of a particular product. However, if the cross-price elasticity between a firm’s output and products produced in related industries is large and positive, the firm is not a monopolist in the true sense and is not immune to the threat of competitor encroachment. In the banking industry, for example, individual banks clearly compete with money market mutual funds, savings and loan associations, credit unions, and commercial finance companies. The extent of competition can be measured only in terms of the cross-price elasticities of demand.
INCOME ELASTICITY OF DEMAND
For many goods, income is another important determinant of demand. Income is frequently as important as price, advertising expenditures, credit terms, or any other variable in the demand function. This is particularly true of luxury items such as big screen televisions, country club memberships, elegant homes, and so on. In contrast, the demand for such basic commodities as salt, bread, and milk is not very responsive to income changes. These goods are bought in fairly constant amounts regardless of changes in income. Of course, income can be measured in many ways—for example, on a per capita, per household, or aggregate basis.
Gross national product, national income, personal income, and disposable personal income have all served as income measures in demand studies.
Normal Versus Inferior Goods
The income elasticity of demand measures the responsiveness of demand to changes in income, holding constant the effect of all other variables that influence demand. Letting I represent income, income point elasticity is defined as
Income and the quantity purchased typically move in the same direction; that is, income and sales are directly rather than inversely related. Therefore, ΔQ/ΔI and hence _I are positive. This does not hold for a limited number of products termed inferior goods. Individual consumer demand for such products as beans and potatoes, for example, is sometimes thought to decline as income increases, because consumers replace them with more desirable alternatives. More typical products, whose individual and aggregate demand is positively related to income, are defined as normal goods.
To examine income elasticity over a range of incomes rather than at a single level, the arc elasticity relation is employed:
Arc income elasticity provides a measure of the average responsiveness of demand for a given product to a relative change in income over the range from I1 to I2.
In the case of inferior goods, individual demand actually rises during an economic downturn. As workers get laid off from their jobs, for example, they might tend to substitute potatoes for meat, hamburgers for steak, bus rides for automobile trips, and so on. As a result, demand for potatoes, hamburgers, bus rides, and other inferior goods can actually rise during recessions.
Their demand is countercyclical.
Types of Normal Goods
For most products, income elasticity is positive, indicating that demand rises as the economy expands and national income increases. The actual size of the income elasticity coefficient is very important. Suppose, for example, that _I = 0.3. This means that a 1 percent increase in income causes demand for the product to increase by only .3 percent. Given growing national income over time, such a product would not maintain its relative importance in the economy. Another product might have _I = 2.5; its demand increases 2.5 times as fast as income. If, _I < 1.0 for a particular product, its producers will not share proportionately in increases in national income. However, if _I > 1.0, the industry will gain more than a proportionate share of increases in income.
Goods for which 0 < _I < 1 are referred to as noncyclical normal goods, because demand is relatively unaffected by changing income. Sales of most convenience goods, such as toothpaste, candy, soda, and movie tickets, account for only a small share of the consumer’s overall budget, and spending on such items tends to be relatively unaffected by changing economic conditions. For goods having _I > 1, referred to as cyclical normal goods, demand is strongly affected by changing economic conditions. Purchase of “big ticket” items such as homes, automobiles, boats, and recreational vehicles can be postponed and tend to be put off by consumers during economic downturns. Housing demand, for example, can collapse during recessions and skyrocket during economic expansions. These relations between income and product demand are summarized in Table.
Relationship Between Income and Product Demand
Firms whose demand functions indicate high income elasticities enjoy good growth opportunities in expanding economies. Forecasts of aggregate economic activity figure importantly in their plans. Companies faced with low income elasticities are relatively unaffected by the level of overall business activity. This is desirable from the standpoint that such a business is harmed relatively little by economic downturns. Nevertheless, such a company cannot expect to share fully in a growing economy and might seek to enter industries that provide better growth opportunities.
Income elasticity figures importantly in several key national debates. Agriculture is often depressed because of the low income elasticity for most food products. This has made it difficult for farmers’ incomes to keep up with those of urban workers. Asomewhat similar problem arises in housing. Improving the housing stock is a primary national goal. If the income elasticity for housing is high and _I > 1, an improvement in the housing stock will be a natural by-product of a prosperous economy. However, if the housing income elasticity _I < 1, a relatively small percentage of additional income will be spent on houses. As a result, housing stock would not improve much over time despite a growing economy and increasing incomes. In the event that _I < 1, direct government investment in public housing or rent and interest subsidies might be necessary to bring about a dramatic increase in the housing stock over time.
ADDITIONAL DEMAND ELASTICITY CONCEPTS
The most common demand elasticities—price elasticity, cross-price elasticity, and income elasticity—are emphasized in this chapter. Examples of other demand elasticities can be used to reinforce the generality of the concept.
Other Demand Elasticities
Advertising elasticity plays an important role in marketing activities for a broad range of goods and services. A low advertising elasticity means that a firm must spend substantial sums to shift demand for its products through media-based promotion. In such cases, alternative marketing approaches—such as personal selling or direct marketing—are often more productive.
In the housing market, mortgage interest rates are an important determinant of demand. Accordingly, interest rate elasticities have been used to analyze and forecast the demand for housing construction. To be sure, this elasticity coefficient varies over time as other conditions in the economy change. Other things are held constant when measuring elasticity, but in the business world other things do not typically remain constant. Studies indicate that the interest rate elasticity of residential housing demand averages about –0.15. This means that a 10 percent rise in interest rates decreases the demand for housing by 1.5 percent, provided that all other variables remain unchanged. If Federal Reserve policy is expected to cause mortgage interest rates to rise from 6 percent to 8 percent (a 33 percent increase), a 4.95 percent decrease (= –0.15 _ 33) in housing demand can be projected, on average.
Not surprisingly, public utilities calculate the weather elasticity of demand for their services. They measure weather using degree days as an indicator of average temperatures. This elasticity factor is used, in conjunction with weather forecasts, to anticipate service demand and peak-load conditions.
Time Factor in Elasticity Analysis
Time itself is also an important factor in demand elasticity analysis, especially when transactions costs or imperfect information limit the potential for instantaneous responses by consumers and producers. Consumers sometimes react slowly to changes in prices and other demand conditions. To illustrate this delayed or lagged effect, consider the demand for electric power. Suppose that an electric utility raises rates by 30 percent. How will this affect the quantity of electric power demanded? In the very short run, any effects will be slight. Customers may be more careful to turn off unneeded lights, but total demand, which is highly dependent on the types of appliances owned by residential customers and the equipment operated by industrial and commercial customers, will probably not be greatly affected. Prices will go up and the quantity of electricity service demanded will not fall much, so the utility’s total revenue will increase substantially. In other words, the short-run demand for electric power is relatively inelastic.
In the long run, however, an increase in power rates can have a substantial effect on electricity demand. Residential users will buy new and more energy-efficient air conditioners, furnaces, dishwashers, and other appliances. As electricity rates rise, many consumers also add insulation or temperature-control devices that limit energy use. All such actions reduce the consumer’s long-run demand for power. When energy costs rise, industrial users often switch to natural gas or other energy sources, employ less energy-intensive production methods, or relocate to areas where electric costs are lower. The ultimate effect of a price increase on electricity demand may be substantial, but it might take years before its full impact is felt.
In general, opportunities to respond to price changes tend to increase with the passage of time as customers obtain more and better information. There is a similar phenomenon with respect to income changes. It takes time for consumers’ purchasing habits to respond to changed income levels. For these reasons, long-run elasticities tend to be greater than short-run elasticities for most demand variables.