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.