IMPACT OF ADVERTISING ON DUOPOLY COMPETITION

Transcription

1 IMPACT OF ADVERTISING ON DUOPOLY COMPETITION Compettve paper n Marketng track POSTGRADUATE PAPER Presented at Irsh Academy of Management Annual Conference, Trnty College, Dubln nd 3 rd September 004 Malcolm Brady Dubln Cty Unversty Busness School Dubln 9, Ireland Tel Emal malcolm.brady@dcu.e ABSTRACT Ths paper proposes a model of optmal advertsng for a duopoly. The advertsng model s based on Dorfman and Stener s (954) optmalty condton. Advertsng s ntroduced nto a Cournot ncentve duopoly model (Fershtman and Judd, 987) extended to nclude dfferentated products (Dxt, 979). The paper develops the model analytcally and then examnes the behavour of the frms n a duopoly usng computer smulaton. The paper examnes the partcular case where one frm adopts a low cost generc strategy and the other frm adopts a dfferentaton strategy (Porter, 980 and 985).

2 INTRODUCTION Ths paper proposes a model of optmal advertsng for a duopoly. The advertsng model s based on Dorfman and Stener s (954) optmalty condton. Advertsng s ntroduced nto a Cournot ncentve duopoly model (Fershtman and Judd, 987) that has been extended to nclude dfferentated products. Dxt (979) suggests that two dfferent forms of dfferentaton can take place. The frst he refers to as absolute advantage and occurs when frms have dfferent reservaton prces. The second form occurs when cross prce effect dffers from own prce effect. In ths paper I assume that advertsng shfts the demand functon to the rght by changng the value of reservaton prce. If ths shftng s asymmetrc then advertsng leads to Dxt s frst knd of dfferentaton. The paper s organsed as follows. The paper develops the analytcal model and then examnes the behavour of the frms n a duopoly usng computer smulaton. Frstly two base scenaros are examned where no advertsng takes place; one scenaro has symmetrc costs and the other has asymmetrc costs. Symmetrc low and hgh levels of advertsng are then ntroduced. Asymmetrc advertsng scenaros for both hgh and low levels of advertsng are then examned. Fnally asymmetrc advertsng and asymmetrc cost scenaros are examned. Ths last scenaro s used to examne the effectveness of low cost versus dfferentaton strateges. The paper then concludes. THE MODEL The Dxt (979) model assumes a lnear downward slopng nverse demand functon where prce for a frm s product s nfluenced by the quantty placed on the market by both frms. Ths s formalsed n the expresson:

3 p = a b q d q =,; j = 3 j where p represents prce, q represents quantty, a s the reservaton prce, b s the own prce effect, and d s the cross prce effect; subscrpts and j represent the two frms n the duopoly. When d b frm products exhbt Dxt s second knd of dfferentaton. Note that the reservaton prce s the ntercept of the demand functon wth the vertcal axs. Interdependency of the two frms s represented by ths par of equatons. In each tme perod a two stage game s played where n the frst stage owners select optmal ncentve factors and n the second stage managers select frm quanttes at the Cournot equlbrum pont (Fershtman and Judd, 987; Cournot, 838). Prce s then determned accordng to the above expresson and prce, quantty, and cost determne proft for each frm usng the usual accountng dentty. Advertsng acts to ncrease the reservaton prce (parameter a n the above expresson) and ths shfts the nverse demand functon to the rght. Ths changng demand functon gves the model ts dynamc characterstc. SIMULATION I start ths examnaton wth a base case where frms have symmetrcal demand functons and cost structure and nether frm advertses. For each frm reservaton prce s set at 5, own prce effect s set at 0.000, and cross prce effect s set at Unt varable cost s set at 8 for each frm. Advertsng effectveness (φ) s set at zero for both frms. Ths scenaro yelds the symmetrc steady state result shown n fgure. Both frms place a quantty of 7,579 unts on the market. At the

4 Cournot equlbrum pont the market selects a prce of 4.6 per unt and both frms make proft after tax of 68,986 each perod for all tme. The optmal ncentve factor s for each frm for all tme. Retaned_earnngs 7,000 70,000 69,000 68,000 67, Fgure. Dfferentated ncentvsed Cournot duopoly: φ = φ =0; c = c =8 These results can be confrmed analytcally by substtutng the above parameter values nto the followng Fershtman and Judd (987) equlbrum expressons, extended by Rothschld for dfferentated duopoly: bc(b + d) ad λ = λ = = c(4b + bd d ) for the equlbrum ncentve factor, q b( a c) = q = = b + bd d for equlbrum quantty, p a(b d ) + bc( b + d) = p = = 4.6 4b + bd d for equlbrum prce, and b( a c) (b d ) Π = Π = = (4b + bd d )

5 for equlbrum gross proft. Applyng tax at 40% confrms the above fgure of 68,986 for net proft. I now ntroduce a cost asymmetry nto the smulaton model by reducng unt varable cost for frm two from 8 to 7. As expected the frm wth lower costs outperforms the frm wth hgher costs as shown n fgure. Proft for frm two s hgher than for the symmetrc case whle that for frm one s lower. Incentve factors are also asymmetrc: frm two s ncentve factor ncreased to 0.89 whereas frm one s has reduced to Owners of the lower cost frm are offerng greater ncentve to managers to maxmse sales. Quantty selected by each frm s asymmetrc wth 70,048 placed on the market by frm one and 77,3 placed on the market by frm two. Unt prces are also asymmetrc and have reduced for both frms to 4.3 and 3.77 for frms one and two respectvely. Note that the lower cost frm places a greater quantty on the market and acheves a lower prce than for the symmetrc case whereas the hgher cost frm places a lower quantty on the market and acheves a hgher prce than before. Retaned_earnngs 30, ,000 90,000 80,000 70,000 60, Fgure. Dfferentated ncentvsed Cournot duopoly wth asymmetrc costs: φ = φ =0; c = 8, c =7

6 I now ntroduce advertsng nto the duopoly model. Borden (947) suggests that advertsng shfts the demand curve to the rght or tlts the demand curve or both. Fredman (983) suggests that the mpact of advertsng s cumulatve over tme and that nteracton of advertsng may occur e. advertsng by one frm may beneft another frm. Ths model meets both of Fredman s condtons. I assume that advertsng shfts the demand functon to the rght and I express ths usng a smple lnear model: a = a * + φ A + ρφ A =,; j = 3 j j where a s the reservaton prce after advertsng, a * s the reservaton prce before advertsng, φ s the advertsng response of one frm, φ j the advertsng response of ts rval, and ρ s the advertsng nteracton factor representng the relatve response of one frm to another frm s advertsng. Where ρ s postve advertsng s cooperatve e. advertsng by one frm also asssts the other frm; where ρ s negatve advertsng s predatory e. gan n demand from advertsng by one frm s at the expense of the other frm. Where ρ s zero then advertsng by one frm has no effect upon the other frm. Note that where φ s the own advertsng effect, ρφ s the cross advertsng effect, e. the effect of one frm s advertsng on the other frm. Parameters A and A j represent the amounts of advertsng selected by the frm and ts rval respectvely. The smulaton model uses the Dorfman Stener (954) condton to select the optmal amount of advertsng for each frm. The amount of advertsng represents a cost to the frm and s subtracted from gross proft.

7 Retaned_earnngs 80,000 75,000 70, (a),500 Advertsng, (b) Fgure 3. Dfferentated ncentvsed Cournot duopoly wth symmetrc advertsng and symmetrc costs: φ = φ = ; c =c =8. I wll frstly examne the scenaro when both frms advertse but where advertsng effectveness s low. Advertsng effectveness for both frms s set at whch means that 0000 worth of advertsng wll ncrease the value of the reservaton prce by 0.3. Ths shfts the demand functon to the rght. The advertsng nteracton parameter s set at zero and so no spllover of advertsng from one frm to the other occurs. Results for ths scenaro are shown n fgure 3 where t s clear that both frms come to a termnal Cournot equlbrum and lttle advertsng s selected.

8 As levels of advertsng effectveness decrease below behavour s smlar to that shown n fgure 3 but the rate of growth s slower. Retaned_earnngs 30, ,000 90,000 80,000 70, (a) 5,000 Advertsng 0,000 5, (b) Fgure 4. Dfferentated ncentvsed Cournot duopoly wth symmetrc advertsng and symmetrc costs: φ = φ = ; c = c =8. I now ncrease the effectveness of advertsng for both frms to Results for ths scenaro are shown n fgure 4. Larger amounts of advertsng are selected causng the demand functon to shft to the rght. In contrast to the prevous scenaro demand, and consequently revenues and profts, ncrease exponentally over tme and does not come to equlbrum. As levels of advertsng effectveness ncrease above

9 behavour s smlar to that of fgure 4 but growth s more rapd. Clearly a bfurcaton n duopoly behavour has occurred: for advertsng effectveness at or below frms tend to an equlbrum above the standard Cournot level; for advertsng effectveness at or above both frms acheve exponental growth. Retaned_earnngs 80,000 75,000 70, (a),500 Advertsng, (b) Fgure 5. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and symmetrc costs: φ = , φ =0.0000; c =c =8. I now ntroduce an asymmetry nto the duopoly model. I return to the scenaro where advertsng effectveness was low leavng frm one s effectveness at and reducng that for frm two to Results for ths scenaro are gven n fgure 5

10 and show that creatng an advertsng asymmetry has resulted n asymmetrc performance: frm one advertses more heavly than and gans a compettve advantage over frm two. Both frms stll tend asymptotcally to a termnal Cournot equlbrum but frm one comes acheves a hgher level of proft than does frm two. Retaned_earnngs 30, ,000 80,000 60, (a),500 Advertsng, (b) Fgure 6. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and asymmetrc costs: φ = , φ =0.0000; c =8, c =7. I now ntroduce asymmetrc costs n addton to asymmetrc advertsng by reducng unt cost for frm two from 8 to 7. Results n fgure 6 show that ths leads to a swtch n ndustry leadershp: frm two now outperforms frm one. If we regard the

11 lower cost frm as adoptng a cost leadershp strategy and the frm wth greater advertsng effectveness as adoptng a dfferentaton strategy then we see here that the cost leader outperforms the dfferentator. Tral and error expermentaton shows that cost leadershp outperforms a dfferentaton strategy provded that unt cost of the cost leader les at or below 7.8. Fgure 7 shows results where unt cost of the cost leader s 7.9. Intally the cost leader outperforms the dfferentator but after a tme a swtch n ndustry leadershp takes place and the dfferentator outperforms the cost leader. Retaned_earnngs 80,000 75,000 70, Fgure 7. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and asymmetrc costs: φ = , φ =0.0000; c =8, c =7.9 I now ntroduce asymmetry to the scenaro where advertsng effectveness s hgh. I reduce the advertsng effectveness of frm two from to Ths dramatcally changes the behavour of the duopoly as shown n fgure 8. The more effectve advertser selects larger amounts of advertsng stmulatng demand for ts product and after a tme drves ts rval out of the market. A small change n advertsng effectveness can dramatcally rase or lower frm performance. Ths

12 suggests that when costs are dentcal t s worthwhle for a frm to mprove the effectveness of ts advertsng. Retaned_earnngs 330,000 30,000 30, ,000 90,000 80,000 70, (a) 0,000 Advertsng 5,000 0,000 5, (b) Fgure 8. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and symmetrc costs: φ = , φ = ; c =c =8 I now ntroduce asymmetrc costs n tandem wth asymmetrc advertsng. Fgure 9 shows results for ths scenaro. Note that a change n ndustry leadershp has taken place: the lower cost frm from the begnnng outperforms the more effectve advertser and eventually drves t out of the market. Tral and error expermentaton showed that for ths level of advertsng asymmetry when unt cost for frm two s at or below 7. then the lower cost producer acheves ndustry domnance whereas

13 above that fgure a swtch n ndustry leadershp takes place wth the more effectve advertser eventually domnatng the ndustry. Retaned_earnngs 500, , , , , (a) Advertsng 00,000 50, (b) Fgure 9. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and asymmetrc costs: φ = , φ = ; c =8, c =7 I now ncrease the level of advertsng asymmetry. I reduce advertsng effectveness for frm two from to Ths changes sgnfcantly duopoly behavour as shown n fgure 0. Frm two s ntal advantage due to low cost s eroded over tme untl eventually frm one s advertsng advantage predomnates. Frm two s eventually drven from the marketplace. Ths result mples that a cost

14 advantage wll only carry a frm so far. If the advertsng asymmetry s too great then the stronger advertser wll eventually domnate. Fgures 8 and 9 demonstrate the reverse: an advertsng advantage alone wll only carry a frm so far; f cost asymmetry becomes too great then the lower cost frm wll wn out. Retaned_earnngs 330, ,000 70, Fgure 0. Dfferentated ncentvsed Cournot duopoly wth asymmetrc advertsng and asymmetrc costs: φ = , φ = ; c =8, c =7 CONCLUSION Ths paper examned the behavour of two frms ntercompetng under ncentve Cournot condtons e. a two stage game s played where owners select ncentve factors for managers n the frst stage, and managers select quantty at the second or market stage. The examnaton was carred out usng a computer smulaton model founded on ndustral organsaton economc theory. A partcular scenaro examned was that where one frm adopted a cost leadershp strategy and the other adopted a dfferentaton strategy where that dfferentaton was acheved through advertsng. Several specfc results were determned. The smulatons demonstrated the exstence of a bfurcaton pont above whch frms advertse relatvely heavly and greatly

15 beneft from that advertsng and below whch frms advertse lttle wth lttle consequent change n demand. The bfurcaton pont s a functon of advertsng effectveness. Ths fndng suggests an explanaton for the emprcal observaton that some ndustres advertse and some do not. In general the results demonstrate that the mpact of advertsng s uncertan and unpredctable, even though the models used are determnstc. Markedly dfferent duopoly behavour was demonstrated when advertsng effectveness crossed threshold levels or became asymmetrc. The results suggest that frms cannot be certan about the mpact of ther advertsng polces. A small change n behavour by the rval frm may lead to very dfferent results for the frm. For example, f the rval frm mproves the effectveness of ts advertsng the model demonstrates that frm performance may swtch from exponental growth to exponental decay. The results also demonstrate that dfferentaton by tself does not necessarly confer an advantage on one frm or the other. Under Dxt s second form of dfferentaton (I wll label ths symmetrc dfferentaton) both frms behave symmetrcally and acheve equal profts for all tme. It s only when an asymmetry s ntroduced nto the model that one frm gans a compettve advantage over the other. Advertsng s one mechansm for ntroducng demand growth nto the model. However, whle advertsng may mprove the proft poston of both frms, as long as the model remans symmetrc no compettve advantage wll be conferred on one frm or the other by advertsng. Asymmetry may be ntroduced n a number of ways: by varyng advertsng effectveness, cost, manageral ncentve, or a combnaton of these

16 parameters. Asymmetry s also ntroduced by nature; ths may be smulated by ntroducng a random element to the mpact of advertsng. The results also shed lght on the theory of compettve strategy. Whether a low cost or a dfferentaton strategy s domnant s shown to be contngent on crcumstances. Porter (980, 985) advses frms that when adoptng a strategy based on one attrbute that frms mantan close proxmty n other attrbutes. The smulatons bear ths out. When adoptng a low cost strategy frms must mantan a mnmum level of advertsng effectveness to reman compettve, or when adoptng an advertsng effectveness advantage frms must mantan proxmty n costs. The paper suggest a role for management: to dentfy sources of asymmetry and to ntroduce such asymmetry nto the compettve envronment. BIBLIOGRAPHY Borden, Nel (947). The economc effects of advertsng, Irwn: Chcago (4 th prntng, frst prntng 94). Cournot, Augustn (838). Researches nto the mathematcal prncples of the theory of wealth, translated nto Englsh by Nathanel T. Bacon, Macmllan, 897; reprnted wth notes by Irvng Fsher, New York: Macmllan, 99; orgnally publshed as Recherches sur les prncpes mathématques de la théore des rchesses, L. Hachette, Pars, 838. Dxt, Avnash (979). A model of duopoly suggestng a theory of entry barrers, Bell Journal of Economcs, v.0, n., pp.0-3.

17 Dorfman, R. and P. O. Stener (954). Optmal advertsng and optmal qualty, Amercan Economc Revew, v.44, n.5, pp Fershtman, Cham and Kenneth Judd (987). Equlbrum ncentves n olgopoly, Amercan Economc Revew, v.77, n.5, pp Fredman, James (983). Advertsng and olgopolstc equlbrum, Bell Journal of Economcs, v.4, n., pp Porter, Mchael (980). Compettve strategy, The Free Press Porter, Mchael (985). Compettve advantage, The Free Press. Rothschld, R. (00). Dscusson of unpublshed workng paper wth author, Unversty of Lancaster.