Advertising's effect on the market demand elasticity: A note

Advertising’s Effect on the Market DemandElasticity: A Note

Henry W. KinnucanDepartment of Agricultural Economics and Rural Sociology, Auburn University,Auburn, Alabama 36849. E-mail: [email protected]

Yuqing ZhengDepartment of Agricultural Economics and Rural Sociology, Auburn University,Auburn, Alabama 36849. E-mail: [email protected]

ABSTRACT

Using a simple market model and Frisch’s duality relation, this report develops propositions aboutthe relationship between advertising and the market demand elasticity that may prove useful inempirical research+ In particular, we find that a parallel shift in a linear demand function alwaysalters the market demand elasticity unless supply is unitary elastic+ However, the elasticity changein most cases will be negligible+ We also find that curve rotation does not imply that the demandelasticity has changed, and vice versa+ Lastly, if the price level affects advertising’s ability to shiftthe market demand curve, it must also be true that advertising affects the demand elasticity+ Theconverse is also true, i+e+, if advertising affects the demand elasticity, the price level must affectadvertising’s ability to shift the demand curve+ @JEL citations: Q130, Q170, Q180+# © 2004 WileyPeriodicals, Inc+

+ + + promotion which stresses uniqueness of the product or alternatively its substitutability forother products in its end uses should display, respectively, less elastic and more elastic demandsof quantity with respect to price as an outcome of the advertising which is directed to achievethese ends+

—Quilkey ~1986, p+ 51!

1. INTRODUCTION

Although substantial research has been done to determine whether advertising shifts mar-ket demand curves ~for work related to brand advertising, see e+g+, Duffy, 1996; for workrelated to generic advertising, see Ferrero, Boon, Kaiser,& Forker, 1996!, relatively littleattention has been paid to the question of whether advertising rotates demand curves+ Theissue of curve rotation, or, more specifically, advertising’s effect on the market demandelasticity, is important for several reasons+ First, optimal advertising intensity ~defined asadvertising expenditure divided by firm or industry revenue! is inversely related to themarket demand elasticity ~Dorfman & Steiner, 1954; Nerlove & Waugh, 1961; Alston,Carman, & Chalfant, 1994; Kinnucan, 1999a,b; Kinnucan & Myrland, 2000!+ Thus, if

Agribusiness, Vol. 20 (2) 181–188 (2004) © 2004 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/agr.20004

181

advertising changes the demand elasticity, as Quilkey’s ~1986! analysis suggests, norma-tive decision rules based on the assumption that the market demand elasticity is constantmay be misleading+ Second, welfare effects of advertising are often measured under theassumption that advertising causes market demand curves to shift in a parallel fashion~see, e+g+,Wohlgenant, 1993; Tremblay & Tremblay, 1995;Kinnucan,Xiao,& Hsia 1996;Alston, Freebairn, & James, 2001; Wohlgenant & Piggott, 2003!+ As shown by Chungand Kaiser ~1999!, this assumption affects welfare measures and, consequently, alloca-tion decisions, in a non-trivial manner+ Third, advertising-induced changes in the demandelasticity have important policy implications with respect to generic advertising pro-grams in instances where downstream markets are imperfectly competitive+ Specifically,if advertising makes demand less price elastic, as might be expected if the ads stressproduct differentiation, this would tend to exacerbate oligopoly distortions, and reducefarmers’ returns to the advertising scheme ~Zhang & Sexton, 2002; Kinnucan, 2003!+

The purpose of this report is to advance propositions about the relationship betweenadvertising and demand elasticity that might be useful in empirical research+ We focuson two issues: the nature and extent of changes in the market demand elasticity whenadvertising shifts the demand curve in a parallel fashion ~the typical assumption in thegeneric advertising literature; see, for example, the special issue of this journal edited byKaiser, 2003!; and testing for price-advertising interaction effects+ Our analysis suggeststhat parallel demand shifts in general result in changes in the market demand elasticity,and this is true whether or not the demand curve is linear+ However, in instances where alinear demand curve shifts in a parallel fashion, assuming that the demand elasticity isconstant is innocuous from an advertising benefit-cost analysis perspective+We also findthat curve rotation does not imply that the demand elasticity has changed, and vice versa+The final point is that if the price level affects advertising’s ability to shift the demandcurve, it must also be true that advertising affects the demand elasticity+ The converse isalso true, i+e+, if advertising affects the demand elasticity, the price level must affect ad-vertising’s ability to shift the demand curve+ The latter results follow from Frisch’s ~1959!“duality relation,” a neglected concept in the literature+

2. ANALYSIS

2.1 Parallel Shift of Linear Demand Curve

As mentioned, welfare analyses of advertising effects are commonly conducted under theassumption that advertising shifts linear demand curves in a parallel fashion+ In so doing,most authors assume that the demand elasticity is constant ~typically evaluated at theinitial, pre-advertising, equilibrium point!+1 Since the demand elasticity varies along alinear curve, this latter assumption is questionable+ At issue here is whether violation ofthe constant elasticity assumption prejudices the welfare measure to any significant de-gree+ Our analysis suggests not+ In particular, we find that a parallel shift in a lineardemand function always alters the market demand elasticity unless supply is unitary elas-tic+ However, the elasticity change in most cases will be negligible+

1The one exception is the recent analysis by Zhang and Sexton ~2002! in which both the demand and ad-vertising elasticities are permitted to change in response to changes in the level of the industry tax used to raisefunds for promotion+ In so doing, Zhang and Sexton state ~2002, p+ 357! “If advertising induces a parallel shiftin demand, as is often assumed in empirical studies, this effect also makes demand more elastic+” This statementis strictly true only if supply is price inelastic, as shown later+

182 KINNUCAN AND ZHENG

To see this, let the market demand elasticity be defined as follows:

h � D~ po0qo ! ~1!

where D � �~]q0]p! is the demand curve’s slope in absolute value, and po and qo areprice and quantity, respectively, in competitive equilibrium+ Taking the logarithmic totaldifferential of ~1! with respect to advertising expenditure a yields:

d ln h0d ln a � d ln D0d ln a � d ln po0d ln a � d ln qo0d ln a+ ~2!

The first term on ~2!’s right-hand side indicates the percentage change in the demandcurve’s slope per 1% change in advertising expenditure, hereafter referred to as the “slopeelasticity+” The slope elasticity in the present case is zero, since the demand curve isassumed to be linear both before and after the shift+ Thus, advertising’s effect on thedemand elasticity reduces to how the advertising affects equilibrium price and quantity+

To determine that, let initial equilibrium in the market be defined by the followinggeneral function ~not necessarily linear! model:

qD � D~ po,a! ~demand! ~3!

qS � S~ po ! ~supply! ~4!

qD � qS � qo ~market clearing!+ ~5!

Taking the logarithmic total differential of ~3!–~5! yields:

d ln qD � �hd ln po � ad ln a ~39!

d ln qS � ed ln po ~49!

d ln qS � d ln qD � d ln qo ~59!

where a � ~]qD 0]a!~a0qo ! is the advertising elasticity and e � ~]qS 0]p!~ po0qo ! is themarket supply elasticity, both evaluated at the initial equilibrium point+

Substituting ~3' ! and ~4' ! into ~5' ! yields the reduced-form equation for price:

d ln po � @a0~e� h!#d ln a, ~6!

which, upon re-using ~4' !, yields the reduced-form equation for quantity:

d ln qo � @ae0~e� h!#d ln a+ ~7!

Substituting ~6! and ~7! into ~2! and combining terms yields:

d ln h0d ln a � d ln D0d ln a � a~1 � e!0~e� h!, ~8!

or, with the maintained hypothesis that d ln D0d ln a � 0,

d ln h0d ln a � a~1 � e!0~e� h! ~slope fixed!+ ~8a!

ADVERTISING’S EFFECT ON MARKET DEMAND ELASTICITY 183

Thus, in the absence of curve rotation, an increase in advertising will always alter thedemand elasticity unless supply is unitary elastic, as stated+ In particular, if supply isinelastic, the demand shift makes demand more price elastic; the opposite is true if supplyis elastic+

The intuition for this result is clear from the definition for the demand elasticity givenin ~1!: holding D constant, h cannot change unless the po0qo ratio changes+ If supply isunitary elastic, an outward shift in the demand curve causes quantity supplied to increaseby the same percentage amount as the percentage increase in equilibrium price+ Hence,the po0qoratio remains constant, as does h under the maintained hypothesis that D is fixed+Following the same reasoning, if supply is price elastic, an output shift in the demandcurve will cause quantity supplied to increase by a larger percentage amount than thepercentage increase in equilibrium price+ In this case the po0qoratio falls, as does h whenD is fixed+ It is only when supply is price inelastic that an outward shift in a linear demandcurve causes h to increase, as claimed by Zhang and Sexton ~2002!+

2.2 Limits of Elasticity Change

From ~8a! the limits of the elasticity change are given by:

�a � d ln h0d ln a � a0h ~slope fixed! ~8b!

where the lower limit �a obtains when price is fixed ~e � `! and the upper limit a0eobtains when quantity is fixed ~e � 0!+ Equation ~8b! motivates the second part of ourclaim, namely that the demand elasticity change associated with an advertising-inducedparallel shift in a linear demand curve is apt to be negligible, at least for generic cam-paigns+ Focusing first on the lower limit, generic advertising elasticities typically aretiny, on the order of 0+05 or less ~see, e+g+, Ferrero et al+, 1996!+ This means that to reducethe demand elasticity by, say, 5% when the demand curve is linear, advertising expendi-tures would need to be increased by at least 100%+

Turning to the upper limit, a0h indicates the advertising intensity ~� a0pq! that max-imizes profit for a monopoly with fixed output ~Dorfman & Steiner, 1954!+As shown byAlston et al+ ~1994!, a0h also indicates the advertising intensity that maximizes producersurplus in a competitive industry that raises funds for promotion through a per-unit levy+At the firm level advertising intensities in the food industry are less than 7% ~Rogers,1993!; at the industry level advertising intensities for 34 California farm products rangefrom 0+04–5+8% with a median intensity of 1+1% ~Alston et al+, 1994, p+ 161!+ The upshotis that ~8a! is apt to be highly inelastic+

This conclusion is borne out in empirical applications+ For example, in Zhang and Sex-ton’s ~2002! simulations for the U+S+ beef and dairy industries, the implied values ford ln h0d ln a are �0+0037 and 0+0387, respectively ~Table 1!+ These values, which are notatypical, indicate that unless expenditure increases are large ~say 300% or more!, adver-tising’s effect on the market demand elasticity is apt to be tiny when curve shifts areparallel+ Hence, there is little reason to believe that advertising benefit-cost analyses thatignore the elasticity-altering effects of a parallel demand shift are significantly in error+2

2This is not to say that small changes in the demand elasticity are unimportant+ In particular, in certain policysettings they can be quite important, as Kinnucan’s ~1999b! analysis of optimal fluid milk advertising policy in


2.3 Curve Rotation and Elasticity Change

Returning to ~1!, advertising can affect the demand elasticity in two ways: by changingthe demand curve’s slope, or by changing the po0qo ratio+ Specifically, if price is fixed ~2!reduces to:

] ln h0] ln a � ] ln D0] ln a � a ~price constant! ~9!

where a � ] ln q0] ln a represents the horizontal shift in the demand curve associatedwith a small increase in advertising expenditure+ From ~9!, advertising’s effect on thedemand elasticity can be decomposed into a rotation effect and a shift effect+ The shifteffect ~a! ordinarily is positive, i+e+,with prices held constant advertising in general shiftsthe market demand curve for the advertised good to the right ~see, e+g+, Basmann, 1956!+3

The rotation effect, however, may be positive, zero, or negative depending on ad content+Specifically, according to Quilkey’s ~1986! scheme there are two possibilities:

i! ads that stress unique product attributesn ] ln D0] ln a � 0ii! ads that stress substitutability in end usesn ] ln D0] ln a � 0+

With the maintained hypothesis that a . 0, in case i ~9!’s sign is unambiguously nega-tive, i+e+, advertising that stresses product differentiation always makes demand less priceelastic at any given price level+ However, in case ii ~9!’s sign is uncertain, dependent onthe relative magnitudes of the rotation and shift elasticities+ This suggests that economet-ric tests of whether advertising affects the demand elasticity is, implicitly, a joint test ofa curve rotation and shift+ Thus, the absence of a price-advertising interaction effect doesnot necessarily mean that the advertising has no effect on consumer preferences ~rotatesthe demand curve!+ Rather, it may mean simply that the rotation effect is offset by theshift effect+4

Canada demonstrates+ Rather, the issue is whether fixing the demand elasticity prejudices advertising benefit-cost analysis to any significant degree when demand shifts are parallel+ Our analysis suggests the answer is“no+”

3Instances in which advertising can have a perverse effect are discussed by Baye, Jansen, and Lee ~1992!~see also Becker & Murphy, 1993; Kinnucan, 1996!+

4As noted by a reviewer, if a linear demand curve pivots about its price axis, and price is held constant, thedemand elasticity does not change+ This is another instance in which absence of an elasticity change does notimply absence of a slope change+

TABLE 1+ Values of d ln h0d ln a for Alternative Values of Advertising Elasticity ~a!,Demand Elasticity ~h!, and Supply Elasticity ~e!

Casea a h e d ln h0d ln ab

Baseline 0+050 1+00 1+00 0U+S+ beef 0+012 0+282 1+578 �0+0037U+S+ dairy 0+035 0+507 0+208 0+0387aCases considered in Zhang and Sexton’s ~2002! analysis and associated elasticity values+bComputed using text equation ~8a!+


2.4 Frisch Duality Relationships

Additional insight can be obtained by noting that the second-order cross partial deriva-tives of any particular function are unaffected by the order in which the derivative istaken+ Thus, in terms of ~3!, this means that:

]2D0]p]a � ]2D0]a]p,

or, in elasticity notion,

]h0] ln a � �]a0] ln p ~10!

where h is ~as before! interpreted as an absolute value+ Condition ~10!, which Frisch~1959, p+ 180! terms a “Duality relation,” implies that if advertising affects the demandelasticity, it must also be true that price affects the advertising elasticity+Moreover, theseinteraction effects, when expressed in terms of percentage changes in the variables, areequal+ This implies, for example, that if advertising makes demand more price elastic,then it must also be true that an increase in price reduces advertising’s ability to shiftthe demand curve+ Conversely, if an increase in price reduces advertising’s ability toshift the demand curve, then it must also be true that an increase in advertising must makedemand more price elastic+ In short, the duality relation enriches the interpretation price-advertising interaction terms in applied demand models ~see, e+g+, Ding & Kinnucan,1996!+

Two additional duality relations can be derived by augmenting ~3! to include consumerincome y:

]h0] ln y � �]hv0] ln p ~11!

]a0] ln y � ]hv0] ln a ~12!

where hv � ~]q]y!~ y0q! is the income elasticity+ Equation ~11!, which was derived byFrisch ~1959, p+ 180, eq+ 13! and discussed in some detail by Cramer ~1973!, is of lessinterest here than ~12!+ Condition ~12! in essence states that if an increase in incomereduces ~increases! the advertising elasticity, then it must also be true than an increase inadvertising reduces ~increases! the income elasticity+ This suggests that if advertisingaffects income’s ability to shift the demand curve, then income must affect advertising’sability to shift the demand curve+ Moreover, the two effects are mutually reinforcing+

As noted by Frisch ~1959, p+ 180!, equations such as ~10!–~12! are invariant under ageneral ~non-linear! transformation of the utility function+ Thus, they can be combinedwith the classical restrictions of homogeneity, symmetry, and adding up to ensure thatdemand elasticities estimated from empirical demand models are theoretically consistent+

3. CONCLUDING COMMENTS

Advertising’s effect on the market demand elasticity depends on the extent to which thedemand curve is rotated, but also on the extent to which the curve is shifted, and on thesupply elasticity+ In the absence of curve rotation, an outward shift in the demand curvewill have no effect on the market demand elasticity if supply is unitary elastic+ If supplyis inelastic, however, the demand elasticity will increase under the same conditions, and


it will decrease if supply is elastic+ This latter result bears on the advertising benefit-costliterature in that in most instances demand shifts are assumed to be parallel and demandelasticities are assumed to be constant+ Fortunately, these assumptions are likely to beinnocuous in that theory suggests the market demand elasticity is insensitive to changesin advertising expenditure, especially when the demand curve is linear+

That advertising’s effect on the market demand elasticity can be decomposed into a“rotation effect” and a “shift effect” has implications for econometric testing+ Specifi-cally, to detect a rotation effect one, in general, needs two pieces of information: adver-tising’s effect on the demand elasticity, and advertising’s effect on the position of thedemand curve in the p0q plane+ Stated differently, a statistically significant relationshipbetween the demand elasticity and advertising expenditure does not necessarily implythat the demand curve has rotated, as the measured effect could be indicating the shifteffect alone+ This distinction is important, because inter alia in Quilkey’s formulation~1986! curve rotation is a key indicator of advertising effectiveness+

As shown by Frisch ~1959!, and discussed in some detail by Cramer ~1973!, interactioneffects in demand equations are governed by general restrictions akin to the more familiarrestrictions of symmetry, adding-up, and homogeneity+ In the case of price-advertisinginteraction, the associated “duality restriction” implies that if an increase in advertisingmakes demand less ~more! price elastic, then it must also be true that an increase in priceincreases ~decreases! advertising’s ability to shift the demand curve+ This restriction needsto be borne in mind when testing for price-advertising interaction effects in an econo-metric setting, and in interpreting the results of such tests+

ACKNOWLEDGMENTS

This research was funded in part by a grant from the National Institute for CommodityPromotion Research and Evaluation at Cornell University+ Responsibility for final con-tent, however, rests strictly with the authors+

REFERENCES

Alston, J+, Carman, H+, & Chalfant, J+ ~1994!+ Evaluating primary product promotion+ In E+W+ God-dard & D+S+Taylor ~Eds+!, Promotion in the marketing mix:What works,where and why? NEC-63Proceedings ~pp+145–167!+ Ontario: University of Guelph+

Alston, J+M+, Freebairn, J+W+, & James, J+S+ ~2001!+ Beggar-thy-neighbor advertising: Theory andapplication to generic commodity promotion programs+ American Journal of Agricultural Eco-nomics, 83, 888–902+

Basmann, R+L+ ~1956!+ A theory of demand with variable preferences+ Econometric, 24, 47–558+Baye, M+R+, Jansen, D+W+, & Lee, J+-W+ ~1992!+ Advertising effects in complete demand systems+

Applied Economics, 244, 1087–1096+Becker, G+S+,& Murphy, K+M+ ~1993!+A simple theory of advertising as a good or a bad+ Quarterly

Journal of Economics, 108, 941–964+Chung, C+,& Kaiser, H+M+ ~1999!+ Distribution of gains from research and promotion in multistage

production systems: Comment+ American Journal of Agricultural Economics, 81 ~3!, 593–597+Cramer, J+S+ ~1973!+ Interaction of income and price in consumer demand+ International Economic

Review, 14 ~2!, 351–363+Ding, L+, & Kinnucan, H+W+ ~1996!+ Market allocation rules for nonprice promotion with farm

programs: U+S+ cotton+ Journal of Agricultural and Resource Economics, 21, 351–367+Dorfman, R+, & Steiner, P+O+ ~1954! Optimal advertising and optimal quality+American Economic

Review, 44, 826–836+


Duffy, M+ ~1996!+ Econometric studies of advertising, advertising restrictions, and cigarette de-mand+ International Journal of Advertising, 15~1!, 1–23+

Ferrero, J+, Boon, L+, Kaiser, H+M+, & Forker, O+D+ ~1996!+ An annotated bibliography of genericcommodity promotion research ~Rev+ ed+! ~NICPRE Research Bulletin No+ 96–03!+ Ithaca, NY:Cornell University+

Frisch, R+ ~1959!+ A complete scheme for computing all direct and cross demand elasticities in amodel with many sectors+ Econometrica, 27~2!, 177–196+

Kaiser, H+M+ ~2003!+ Introductory remarks+ Agribusiness, 19, 273+Kinnucan, H+W+ ~1996!+A note on measuring returns to generic advertising in interrelated markets+

Journal of Agricultural Economics, 47, 261–267+Kinnucan, H+W+ ~1999a!+Advertising traded goods+ Journal of Agricultural and Resource Econom-

ics, 24, 38–56+Kinnucan,H+W+ ~1999b!+Optimal generic advertising decisions in supply-managed industries: Clar-

ification and some further results+ Canadian Journal of Agricultural Economics, 47, 57– 66+Kinnucan, H+W+ ~2003!+ Optimal generic advertising in an imperfectly competitive market with

variable proportions+ Agricultural Economics, 29, 143–158+Kinnucan, H+W+, & Myrland, Ø+ ~2000!+ Optimal advertising levies with application to the

Norway-EU salmon agreement+ European Review of Agricultural Economics, 27, 39–57+Kinnucan, H+W+, Xiao, H+, & Hsia, C+-J+ ~1996!+ Welfare implications of increased US beef pro-

motion+ Applied Economics, 28, 1235–1243+Nerlove,M+,& Waugh, F+ ~1961!+Advertising without supply control: Some implications of a study

of the advertising of oranges+ Journal of Farm Economics, 43, 813–837+Quilkey, J+J+ ~1986!+ Promotion of primary products:A view from the cloister+Australian Journal of

Agricultural Economics, 30, 38–52+Rogers, R+T+ ~1993!+ Advertising strategies by agricultural cooperatives in branded food products,

1967–1987+ ~Food Policy Marketing Center Research Report No+ 21, 61 pp+! Department ofAgricultural and Resource Economics, University of Connecticut+

Tremblay, C+H+, & Tremblay, V+J+ ~1995!+ The impact of cigarette advertising on consumer surplus,profit, and social welfare+ Contemporary Economic Policy, 13, 113–124+

Wohlgenant, M+K+ ~1993!+ Distribution of gains from research and promotion in multistage pro-duction systems: The case of U+S+ beef and pork industries+ American Journal of AgriculturalEconomics, 75, 642– 651+

Wohlgenant, M+K+, & Piggott, N+E+ ~2003!+ Distribution of gains from research and promotion inthe presence of market power+ Agribusiness, 19, 301–314+

Zhang, M+, & Sexton, R+J+ ~2002!+ Optimal commodity promotion when downstream markets areimperfectly competitive+ American Journal of Agricultural Economics, 84~2!, 352–365+

Henry W. Kinnucan is a professor in the Department of Agricultural Economics and Rural Soci-ology, Auburn University. He earned master’s and doctoral degrees from the University of Minne-sota. His current research interests include agricultural marketing, demand analysis, and benefit-cost analysis.

Yuqing Zheng is a graduate research assistant in the Department of Agricultural Economics andRural Sociology, Auburn University. He earned a master’s degree in agricultural economics fromAuburn University and is currently working on a Ph.D. His current research interests include ag-ribusiness marketing, demand analysis, and policy.


Documents

Advertising's effect on the market demand elasticity: A note