CHAPTER C2. ELASTICITY AND DEMAND SPECIFICATION

Topics covered in this chapter:

1. the slope of the demand curve as a decision criterion

2. own-price elasticity of demand as a decision criterion

3. the ranges of own-price demand elasticity

4. the revenue significance of demand elasticity

5. the general applicability of the elasticity concept

6. use of the calculus in computing demand elasticity

7. the need for an average arc elasticity formula

8. income elasticity as an identifier of normal, inferior goods

9. cross elasticity as an identifier of substitute, complement goods

10. cross elasticity as an index of penetration, insulation

11. the process of estimating a demand function

12. formal vs. informal estimating methods

13. assessment of the statistical significance of an estimated

demand function

14. cross-sectional and time-series data approaches

15. causes of specification errors

16. causes of identification problems

17. remedies for specification errors and identification problems

18. the relationship between the identification problem and the elasticity

of demand

CHAPTER 2. ELASTICITY AND DEMAND SPECIFICATION

In this chapter we extend the concepts developed in Chapter C1 into the realm of the statistical estimation of the demand function. First, we consider the concept of elasticity of demand as a decision criterion. Then, after we have discussed the procedures for the specification of a demand function, we consider the implications of various specification problems for the elasticity of demand.

Revenue and Elasticity

The slope of the own-price demand curve, DQ/DP, contains some information which may be useful to the management of the enterprise. It may be interpreted as the number of units by which quantity sold can be expected to change in response to a change in the price of the item, given all other determinants of demand. If the management is interested in nothing more than predicting the number of additional units which can be sold by changing price, the slope of the own-price demand curve is an entirely adequate decision criterion. However, if the management is concerned about profitability or one of its components, the revenue generated in selling the item, the simple slope of the own-price demand curve is an inadequate decision criterion. The reason for its inadequacy is that the slope of a linear own-price demand curve never changes over its entire positive-price range, but, as became apparent in the previous chapter, total revenue does differ from one point to another along the demand curve.

Even if the slope of the demand curve does change because it is not linear, the simple slope still fails to convey information about how the revenue of the firm changes consequent upon a price change. A more useful revenue-oriented decision criterion can be constructed by computing the ratio of the percentage change of quantity demanded to the percentage change in the price which resulted in the quantity change, or

%DQ / %DP.

Economists refer to this ratio as the own-price elasticity of demand, and they interpret it as a measure of the sensitivity (or responsiveness) of quantity demanded to a change in the item's own price. The revenue-related importance of the own-price elasticity can be illustrated by demand equation Qx = 80 - 4Px, which is graphed in Figure C2-1. The linear demand curve has been divided into ranges indicated by brackets. The upper portion of the demand

Figure C2-1. Demand, Revenue, and Elasticity for Q_x=80 - 4P_x.

curve, from price of $20 down to $10, is labeled the elastic range. It is characterized by positive marginal revenues and elasticity ratios (absolute values) greater than unity. The lower portion of the demand curve, from price $10 down to $0, is labeled the inelastic range. It is characterized by negative marginal revenues and fractional elasticity ratios (again, absolute values). The midpoint of the linear demand curve (at price $10) is labeled the unitarily elastic point because the absolute value of the demand elasticity ratio is precisely 1.0 at this point. Demand at the unitarily elastic point is also characterized by zero marginal revenue.

In the elastic range of the demand curve, any particular percentage decrease of price will result in a larger percentage increase of quantity demanded. Thus, what is lost to revenue by cutting price is more than made up for in increased quantity sold, so total revenue increases. For example, if price is lowered from $18 to $16, quantity demanded will increase from 8 units to 16 units, and total revenue will increase from $144 to $256. Price fell by 11 percent, but this was more than made up for by a 100 percent increase in quantity sold.

However, in the elastic range of the demand curve, any particular percentage increase of price will result in a larger-percentage decrease of quantity demanded, thus causing a decrease of total revenue. In this case, what is gained in raising the price is more than offset by the loss in quantity sold. Thus, if the manager can verify that the enterprise is presently selling the item at a point in the elastic range of the demand curve, the appropriate direction in which to change price in order to increase revenue is down.

The opposite conclusions emerge for the inelastic range of the demand curve. A price cut in the inelastic range will result in an increase of quantity demanded, albeit one of a smaller percentage magnitude, so that total revenue can be expected to decrease. If the objective is to increase revenue, price should be raised because a smaller-percentage decrease in quantity demanded will result. In the example illustrated in Figure C2-1, a price cut from $9 to $8 will result in an increase of quantity sold from 44 to 48 units, but a decrease of total revenue from $396 to $384.

Small percentage changes of price in the near neighborhood of the unitarily elastic point of the demand curve will be offset by the same percentage changes of quantity demanded (but in the opposite direction), thereby leaving revenue unchanged. In our example, if price is raised from $9 to $11, quantity demanded will fall from 44 to 36 units, leaving total revenue unchanged at $396.

If the enterprise were to progressively lower price, moving down the demand curve from its intercept with the price axis toward its intercept with the quantity axis, total revenue would increase to a maximum (at the unitarily elastic point), and then decrease; concurrently, marginal revenue would decrease from positive values, through zero (at the unitarily elastic point), to negative values. And, elasticity would fall from (absolute) values greater than unity to (absolute) values less than unity.

The significance of own-price elasticity of demand is that it is indicative of what is likely to happen to the enterprise's revenues when it changes the price of an item which it sells. Enterprise managers may not explicitly compute elasticity ratios, and they may not use the term elasticity of demand. However, we may infer that they must have employed an elasticity thought process in making a rational decision to change price if their enterprises have survived and are profitable.

To this point we have assumed that the demand curve is linear, but only for purposes of simplicity. Since only one point on a demand curve exists at any moment (all other points are only hypothetical or virtual), it can be argued that the shape of the demand curve away from the extant point (whether curved, bent, kinked, etc.) is really a non-issue. But, even if the demand curve is curvilinear, all of the elasticity formulas introduced in this chapter can be applied to compute or estimate the elasticity of demand. Graphically, whether demand is elastic or inelastic at a particular point on a non-linear demand curve can be discerned by observing the characteristics of a tangent drawn to the curve at the point.

The demand curve for an item may take any slope, although a negative slope is expected according to the law of demand. Negatively-sloped demand curves which approach the vertical, as illustrated in panel (b) of Figure C2-2, are often said to be "inelastic demand curves." It would be more accurate to note that the

Figure C2-2. "Elastic" and "inelastic" demand curves.

relevant price range spans only the inelastic portion of the demand curve. There is an elastic range (off the vertical axis scale), but it is irrelevant under current pricing conventions. We should also note that the marginal revenues associated with points on the visible portion of this demand curve are all negative. This point is important because it is not possible for an enterprise to reach a profit maximizing equilibrium in the inelastic range of its demand curve since its marginal cost can never be negative (more about this in Chapters C5 and D₄).

A similar consideration should also be noted in regard to demand curves with very shallow slopes, approaching the horizontal, as illustrated in panel (a) of Figure C2-2. While such demand curves are often described as being "highly elastic," it would be more accurate to say that the relevant quantity range encompasses only the elastic range of the demand curve. There is an inelastic range, but only at quantities which are unattainable under current market and supply conditions. Marginal revenues associated with elastic points on such shallowly sloped demand curves will be positive, and thus can accommodate a profit-maximizing equilibrium solution for the enterprise.

Elasticity Formulas

Our discussion of elasticity to this point has focused on the own-price elasticity of demand, but elasticity is a more general concept not restricted exclusively to own-price. The demand elasticity ratio can be computed with respect to any relevant demand determinant, including own-price. Letting the symbol "X" refer to an unspecified demand determinant, its elasticity can be computed by any of the following formulas, given the requisite information:

(1) X elasticity = %DQ / %DX = (DQ/Q) / (DX/X).

A simple algebraic rearrangement of this elasticity formula yields

(2) X elasticity = DQ/Q ^. X/DX = DQ/DX ^. X/Q.

If the limit concept of the calculus is applied,

(3) X elasticity = DQ/DX ^. X/Q = dQ/dx ^. X/Q,

at the limit as DX approaches 0.

The net of this formula development process is that X elasticity can be computed as the product of the derivative of the demand function with respect to X, and the ratio of the amount of X to the quantity Q. If there are other relevant demand determinants than X, the X elasticity ratio should be computed as a partial (rather than a simple) derivative, i.e.,

(4) X elasticity = dQ/dX ^. X/Q.

This formula is referred to as the point elasticity formula because it can be computed from information about one point on the X demand curve if the equation of the demand curve is known.

Alas, this latter condition, i.e., that the equation of the demand curve must be known, may constitute a serious barrier to the employment of the elasticity ratio as a decision criterion because the equation often is not known, or cannot be satisfactorily estimated. However, an approximation to point elasticity, known as arc elasticity can be computed if information about two points along the X demand curve are known, even if the equation of the X demand curve is not known. Formula (5) can be constructed from formula (2):

(5) X elasticity = %DQ/%DX = (DQ/Q) / (DX/X)

= ((Q₂ - Q₁)/Q₁) / ((X₂ - X₁) / X₁).

where the subscripts refer to the two points identified as points 1 and 2. The expression (Q₂ - Q₁) constitutes "DQ," and the expression (X₂ - X₁) is "DX." We note that point 1 is taken as the base or starting point for the computation. However, this particular formulation exhibits a deficiency in that different values for the computed X elasticity ratio emerge if the identities of points 1 and 2 are reversed. This deficiency can be relieved by estimating the average elasticity over the arc of the demand curve between points 1 and 2 using formula

(6) X elasticity = [(Q₂-Q₁) / ((Q₂+Q₁)/2)] / [(X₂-X₁) / ((X₂+X₁)/2)]

where (Q₂+Q₁)/2) constitutes the average of Q₂ and Q₁, and ((X₂ + X₁)/2) is the average of X₂ and X₁. Finally, formula (6) can be simplified because the 2s in the denominators of the ratio cancel each other, resulting in

(7) X elasticity = [(Q₂-Q₁) / (Q₂+Q₁)] / [(X₂-X₁) / (X₂+X₁)].

This final formulation, the so-called "average arc elasticity" formula, can be computed if only two points on the X demand curve are known, but it must be recognized as only an approximation to the true elasticity at either known point, or any point on the arc between the known points. Depending upon the shape (i.e., concavity) of the X demand curve, the average arc elasticity ratio may be an over- or understatement of true point elasticity. The reader is invited to explore the conditions resulting in over- or understatement.

Elasticity and Other Demand Determinants

We now explore the conceptual sense of several specific X-demand elasticity ratios. The so-called income elasticity of demand may be computed if information about the clientele's income is known and other demand determinants remain unchanged. Any of the elasticity formulas elaborated in the previous section may be employed simply by substituting income for X in the selected formula, e.g.,

(8) income elasticity = [%DQ] / [%DI].

The computed income elasticity of demand for a normal good is expected to be positive, while that for an inferior good is expected to be negative. But conclusions should never be assumed before conducting empirical research. From this perspective, a computed positive income elasticity of demand ratio may be taken as the basis for an inference that the item is a normal good; likewise, a computed negative income elasticity ratio implies that the item is an inferior good. But even if the item is deemed normal, the value of the elasticity ratio may contain useful information. Positive income elasticities less than unity imply that the demand for the item is relatively inelastic (i.e., unresponsive) with respect to income changes. Income elasticities greater than unity suggest that the demand for the item is relatively elastic with respect to income changes. The reader is invited to review the earlier section of this chapter which suggested reasons for managerial preferences to produce normal and inferior goods.

The management of the firm may have chosen to take an aggressive approach to the demand for its item by mounting a promotional effort. The relevant question in this regard is whether the demand for the item is elastic with respect to the promotional expenditure (e.g., the advertising budget for a particular medium). The relevant elasticity formula can be expressed as

(9) advertising elas = %DQ / %D Advertising Budget.

The management might be pleased to find a positive advertising elasticity ratio greater than unity. The reader is left to imagine the management's reactions to advertising elasticity ratios less than unity (or, heaven forbid, negative!).

Finally, we consider the sense of the so-called cross (or cross-price) elasticity of demand ratio. This term may be understood in comparison with the term "own-price" elasticity of demand. A cross-price demand curve shows the graphic relationship between the quantity demanded of one item, say x, relative to the price of another item, y or z. As noted earlier, y and z may refer to substitutes and complements, respectively, for x. The cross-elasticity of demand for the substitute good y can be expressed as

(10) substitute cross elasticity = %DQ_x / %DP_y,

and that for complement good z as

(11) complement cross elasticity = %DQ_x / %DP_z.

The sign of the substitute cross elasticity ratio is expected to be positive: when the price of y rises, less of y will be demanded, but more of its substitute x will be demanded. And the sign of the complement cross elasticity ratio is expected to be negative. Again, neither substitutability nor complementarity should be assumed; empirical evidence should be compiled to reveal whether two goods appear to be substitutes or complements, and the magnitudes of the computed ratios (in absolute value, greater or lesser than unity) should indicate how good or strong is the relationship. The substitute cross elasticity ratio has been proposed as an index of the ability of a competitor to penetrate the market of the enterprise by cutting price (or the ability of the enterprise to insulate itself from competitor's price changes).

We have now considered the managerial implications of own-price, cross-price, income, and advertising elasticity of demand. The principles underlying these concepts are applicable to demand elasticities of yet other determinants which have not been specified. Each item can be expected to have a set of demand determinants which are specific to it, and which may not be pertinent to many or any other items.

While demand elasticity can be computed for any demand determinant for which sufficient information is available, we do not mean to suggest that successful managers must make explicit demand elasticity computations before each and every demand decision. Rather, the concept of demand elasticity is the economist's explanation of a thought process through which the successful manager must have passed in making the decisions which resulted in the success of the enterprise. Whether or not any demand elasticity ratio has been computed, the manager has to have asked the question of whether a contemplated demand determinant change is likely to result in a larger or smaller percentage change in the quantity demanded of the item. We shall subsequently discover that the elasticity concept can be extended into the realm of supply, production, and cost.

The Empirical Estimation of Demand

Ideally, the enterprise manager should predicate pricing decisions upon an accurately-formulated demand function for each item that the enterprise sells. This ideal is feasible only for enterprises which sell one or only a small number of items. The task of estimating a demand function is sufficiently arduous and costly that few firm managers are willing to devote the necessary resources to the task when demands for more than a few items must be estimated. In extreme cases, for example the grocery retailer or hardware wholesaler who stocks literally thousands of items, the task of estimating demand for all items becomes a physical and economic impossibility. We shall consider alternative approaches typically employed by such multi-item enterprises in Chapter D5.

For the moment we shall focus upon the procedures for estimating the demand for a single item, for example dozens of grade A large eggs, or half-gallons of 2% butter-fat milk. The first step in specifying a demand function is to model the relationship between quantity demanded as dependent variable, and all demand determinants which the analyst thinks might affect quantity demanded as independent variables. The modeling process should follow the procedures outlined in Chapter B3 to select the possible independent variables and the likely form of relationship of each (linear, polynomial) to the dependent variable and to other independent variables (additive, multiplicative). The modeling process should also hypothesize the expected sign of the coefficient of each independent variable, e.g., negative for own-price, cross-price of a complement, and income in the case of an inferior good; positive for cross-price of a substitute and income in the case of a normal good.

Once the function has been modeled, the manager can estimate the parameters of the function in a manner similar to Fritz Machlup's educated guess based upon a summing up of the situation compared to experience with similar situations in the past ("Marginal Analysis and Empirical Research," in Essays in Economic Semantics, W. W. Norton & Company, 1967, p. 167). Or, he can engage in the more-formal process which we shall elaborate in the remainder of this section. The Machlup-like seat-of-the-pants method is likely what managers do most of the time and in regard to most of the items which they sell, especially when their enterprises sell large numbers of items. Although no explicit equation results from this process, an implicit demand equation does underlie each educated guess of the number of units salable, given various values of the relevant demand determinants. This informal approach may be the only one possible in the case of a new item for which no current information or historical data can be obtained.

The following discussion of the formal estimating procedure is important both because the manager may indeed wish to estimate the demand function for some of the items sold by the enterprise, and because knowledge of the formal procedure can be beneficial to the informal summing-up process even if the demand function is not explicitly specified.

The formal estimating procedure culminates in an explicit equation which can be used to compute (i.e., predict, estimate) the unit sales of the item under various demand-determinant conditions. The equation may be linear or polynomial, additive or multiplicative, and may include as many independent variables as the analyst deems significant to the explanation of unit sales. The typical form of such a linear, additive demand equation is

(12) Q_d = a + b₁X₁ + b₂X₂ + ... + b_nX_n,

where X₁ through X_n are such demand determinants as own-price, cross-prices, incomes of prospective clients, advertising expenditures, etc.

If there is only one demand determinant, say own-price, the equation will be of the slope-intercept format similar to that of equation (1) of Chapter 6. However, if there are more determinants than one in the equation, the constant a cannot be interpreted as an intercept parameter for any one of the demand determinants.

A typical second-order (or quadratic) demand equation including only one independent variable would take the following form,

(13) Q_d = a + b₁X₁ + b₂X₁². Higher-ordered terms for X₁ can be present, and terms for other variables (X₂, X₃, ...) can be included to any order (squared, cubed) as deemed important.

Once the demand function has been modeled, and assuming that the item is already being sold so that pertinent data can be obtained, the usual procedure for estimating the parameters of the demand model is regression analysis as elaborated in Chapter B3. The associated inference statistics provide means for assessing the statistical significances of the estimated coefficients of the included variables. The analyst should attempt to include in the model as independent variables as many demand determinants as are likely to make significant contributions to explanation of the behavior of the quantity demanded. Then, any variables for which estimated coefficients are judged not to be statistically significant can be deleted from the model before it is respecified.

Occasionally the analyst will find data appropriate to the demand specification process published in industry or trade sources, or compiled by government or private agencies. More often than not, however, demand data for individual items in specific locales do not exist, and must be captured as a matter of original field research. The first field research decision which the analyst must make is whether to capture the data cross sectionally (i.e., across a number of subjects at a point in time), or as a time series (i.e., for the same subject over a period of time). A cross-sectional approach is preferred if it is thought that demand determinants not explicitly included in the model might change over time. However, a cross-sectional approach might require access to competitors' demand information, which they are likely to be reluctant to provide voluntarily.

If the analysis must be restricted to a time-series approach, the analyst should take care to include within the model all demand determinants which are likely to change over time. The analyst may also include so-called "dummy variables" (values of 0 and 1) as a means of quantifying such qualitative conditions as type of outlet (e.g., convenience store vs. full-line grocery store) or whether or not a special promotion is in effect. A student's demand specification research paper is included as Appendix C2 to illustrate the procedures and some of the problems that were encountered in estimating a demand function.

Specification Errors and the Identification Problem

A so-called specification error is often indicated by a coefficient of multiple determination (R²) which is substantially below unity. The specification error occurs either because one or more important determinants of demand were omitted from the model, or because an included variable was raised to the wrong power (e.g., linear instead of quadratic or cubic).

Another type of specification error, an identification problem, may not be indicated by any inference statistic. The best indicator that an identification problem may have occurred is a sign on an estimated regression coefficient which is different than expected, e.g., a positive sign on the own-price regression coefficient. The cause of an identification error is a simultaneous relationship between the dependent variable (quantity demanded) and some determinant (e.g., consumer income) which was omitted from the model.

As an illustration of the problem, let us suppose that a cross-sectional data capture process yielded the quantity and price data in columns (1) and (2) of Table C2-1. The row-wise pairs of observations in the quantity and price columns serve as coordinates for plotting points A, B, C, D, E and F in Figure C2-3. Because these points scatter around an upward-sloping curve, D₁, the coefficient of determination is quite low, 0.07, so a specification error may be indicated. Also, the slope of the curve D₁ is positive, thus suggesting a violation of the law of demand. The problem is that points A, B, C, D, E, and F do not lie along a common own-price demand curve. Each point lies on a separate own-price demand curve which differs from the others because another determinant which has not been included in the model, income, has varied from observation to observation. These separate own-price demand curves are illustrated in Figure C2-4.

Table C2-1. Data for specification of a demand function.

Figure C2-3. Price and Quantity Data Plotted on Coordinate Axes.

Figure C2-4. The Identification Problem Revealed.

Additional data, shown in column (3) of Table C2-1, were subsequently obtained for the average incomes of the clients at stores where the original price and quantity data were collected. Column (4) of Table C2-1 contains an index of the income data; a convenient income observation was selected to serve as the index base. The column (4) index numbers were then used to adjust the column (1) quantity data (the adjustment is analogous to the process of deflating a money-value series by a price index) to remove the effects of the income variations. The adjusted quantity data are recorded in column (5) of Table C2-1. Now, when the adjusted quantity data are plotted against the price data from column (2), points F, G, H, I, J, and K emerge in Figure C2-5. A curve D₂ has been fitted through these points which yields a coefficient of determination of 0.86. Also, the slope of D₂ is negative as expected from the law of demand.

Figure C2-5. An Income-constant Demand Curve.

The curve D₂ in Figure C2-5 can be interpreted as an income-constant demand curve. Curve D₁ exhibits an identification problem because, since the points lie on different demand curves due to the income variation, the true locus of the own-price demand curve could not be identified. The identification problem occurred because of the simultaneous change between own-price (included in the model) and income (not included in the model).

The Identification Problem and Demand Elasticity

Suppose that an analyst estimates a demand function like curve D₁ in Figure C2-3, but fails to recognize the presence of an identification problem. If the own-price elasticity of demand is computed at any point along D₁, it will have a positive sign, which indicates a perverse own-price demand elasticity. However, if the identification problem is eliminated using a procedure similar to that described in the previous section so that own-price elasticity can be computed for curve D₂ in Figure C2-5, the expected negative own-price elasticity ratio will result.

In many cases, however, an unexpected sign of a computed elasticity ratio or the wrong slope of the estimated demand curve may not occur as a clue to the presence of an identification problem. Figure C2-6 illustrates a downward-sloping path of plotted demand data points, but the

Figure C2-6. An elastic demand expansion path.

simultaneous occurrence of change of income causes a shift of the true income-constant demand curve from locus D₃ to D₄ and then to D₅.

The path traced out by points K, L, and M constitute not a true demand curve, but rather a demand expansion path. If a demand equation is estimated from data for points K, L, and M, it will have the expected negative slope, but the slope will be shallower than that of a the true demand curve at any of its loci. Also, if average arc elasticity is computed from information about points K and L, the elasticity ratio will be negative as expected, but will imply that demand is far more elastic than it truly is along any locus of the true income-constant own-price demand curve. In fact, the implication may be that own-price demand is elastic when it truly is inelastic. A price decision maker who bases a price change decision on such an erroneously computed elasticity ratio will likely lower price when it should be raised.

The moral of the story is that the analyst should take great care to be sure that the demand function is being estimated from points along a common, fixed-locus, own-price demand curve (i.e., one which exhibits no identification problem). Great care should be taken to ascertain that the two points from which the average arc elasticity ratio is computed do lie along the same demand curve.

Conclusion

The concept of the demand function provides the economist with a formalized vehicle for analyzing the demand for an item. Enterprise managers usually function to "size-up" and estimate the quantity demanded of an item without formally estimating a demand function. But more sophisticated managers who require more accuracy in their demand estimates may be willing to devote the necessary time and effort to the formal estimation procedures which we have outlined in this chapter. In Chapters D1 through D4 we shall see how demand and cost analyses can be brought together to assist the rational manager in his effort to maximize the profits of the enterprise.

CHAPTER C2 SUMMARY OF IMPORTANT POINTS

l. The slope of the demand curve is an adequate criterion for predicting a change of unit sales consequent upon a price change.

2. The own-price elasticity of demand is a more appropriate criterion for assessing the revenue implications of a price change.

3. In the elastic range of the demand curve, price must be reduced in order to increase revenue; in the inelastic range of the demand curve, price must be raised in order to increase revenue.

4. Maximum revenue is achieved at the output level for which marginal revenue is zero and own-price elasticity of demand is unitary.

5. Demand elasticity ratios can be computed with respect to any relevant demand determinant.

6. The "point elasticity" of demand may be computed using the calculus if the equation of the demand curve is known or can be estimated; otherwise, the "arc elasticity" formula may be used to estimate average elasticity across the arc between two known points on the demand curve.

7. The sign of the income elasticity of demand ratio may be used to identify whether a good is normal or inferior.

8. The sign of the cross-price elasticity of demand ratio may be used to identify whether the good is a substitute or complement for another good.

9. If the firm has survived and been profitable, its managerial decision makers must have employed a demand elasticity thought process (whether they actually computed elasticity ratios or not) when contemplating demand determinant changes.

10. Demand functions may be estimated employing either informal summing-up or formal modeling procedures.

11. Statistical regression analysis is the most commonly-used formal procedure for estimating the values of model parameters.

12. Data for regression analysis may be captured in time series or cross sectionally.

13. A coefficient of multiple determination which is substantially below unity may be indicative of a specification error, i.e., omitting some variable(s) which should be included in the model.

14. A possible consequence of a specification error is an identification problem, i.e., estimating the equation of a curve relating two variables using data for points on different curves; this is attributable to variation in some variable(s) assumed constant and thus omitted from the model.

15. A demand identification problem will likely result in an over- or under-statement of the true demand elasticity relationship.

CHAPTER C2 SIGNIFICANT TERMS

own-price demand curve
slope
elasticity of demand
elastic, inelastic ranges
revenue
unitarily elastic demand
extant, virtual points
x-elasticity of demand
point-elasticity formula
arc-elasticity formula
income elasticity of demand
cross elasticity of demand
substitute, complement
penetration, insulation index
empirical estimation
expected sign
inference statistics
contribution to explanation
data capture
field research
time-series, cross-sectional data
dummy variables
coefficient of multiple determination
specification error
identification error
demand expansion path

CHAPTER C2 QUESTIONS FOR DISCUSSION

1. Compare and contrast the decision significance of the slope of an own-price demand curve with the own-price elasticity of demand.

2. Describe the elasticity ranges of the linear own-price demand curve and discuss the decision significance of this information.

3. Explain the relationship between marginal revenue and elasticity of demand; why is this relevant to managerial decision making?

4. If management's objective is to maximize revenue, devise a price-change strategy if demand is thought to be {elastic/inelastic} at the present price.

5. Discuss the managerial implications of raising/lowering} price in the {inelastic/elastic} range of the demand curve.

6. How can the elasticity of demand at a point on a non-linear demand curve be determined?

7. Why is there no such thing as a completely {elastic/inelastic} demand curve?

8. Show how differential calculus can be used to compute the elasticity of demand at a point on the demand curve.

9. Under what circumstances can the average arc elasticity formula be used to estimate elasticity of demand when the point elasticity technique cannot be used.

10. Explain why the average arc elasticity formula may over- or under-estimate the true elasticity of demand.

11. How can the computed income elasticity of demand reveal whether a good is normal or inferior?

12. What are the managerial implications of the income elasticity of demand?

13. How can the computed cross elasticity of demand reveal whether another good is a substitute or complement for the good in question?

14. What are the managerial implications of {substitute/complementary} relationships between goods?

15. What is the possible relevance of demand elasticity concepts if real-world decision makers do not actually compute demand elasticity ratios?

16. Compare and contrast formal and informal means of estimating demand relationships.

17. Identify possible sources of data which may be used in the estimation of a demand function.

18. Discuss the positives and negatives of using cross-sectional and time-series approaches to capturing data to be used for estimation of a demand function.

19. What is a demand specification error? How can such an error be detected? What are possible remedies for such errors?

20. What is a demand identification problem? How can such a problem be detected? What are the possible causes of such a problem?

21. What can be done to eliminate or relieve a demand identification problem?

22. How are computed elasticity of demand ratios related to identification problems?

23. What are the managerial decision implications of the incidence of a demand identification problem?