S egemann, Klaus
A icle
C oss Elas ici y and he Rele an Ma ke
Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik
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Sugges ed Ci a ion: S egemann, Klaus (1974) : C oss Elas ici y and he Rele an Ma ke , Zei sch i ü
Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s-
und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783, Duncke & Humblo , Be lin, Vol.
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C oss Elas ici y and he Rele an Ma ke
By Klaus S egemann*
An e alua ion o concep ual di icul ies ha bese he use o coe icien s o
c oss elas ici y o demand o he pu pose o de ining a ele an ma ke in
he con ex o an i us policy.
The iden i ica ion o he " ele an ma ke " has equen ly been
a he hea o monopoly and me ge p oceedings in he Uni ed S a es
and in Eu ope — o i ough o be a cen al issue whene e he ou -
come o an icombines p oceedings depends on he ma ke sha es
o he i ms conce ned o on he concen a ion o supply o demand.
Economis s adi ionally app oach he de e mina ion o he ele an
ma ke in e ms o he "closeness" o subs i u es. Concep ually, one
has o choose a measu e o closeness, has o decide wha deg ee o
closeness is equi ed o subs i u es o be included in he same ma ke ,
and can hen p oceed o mapping ou he bounda ies o he ma ke
ele an o he p oblem on hand. I is gene ally ealized ha his
p ocedu e has i s di icul ies. The choice o a cu -o poin be ween
subs i u es su icien ly close o be included in he same ma ke and
hose su icien ly dis an o be placed in sepa a e ma ke s clea ly
in ol es a ce ain amoun o a bi a iness, e en i one is able o ind
a "ma ked gap" in he "chain o subs i u es". De e mina ion o he
chain o subs i u es i sel , howe e , is in p inciple ega ded as a non-
con o e sial p oblem because i is widely belie ed ha coe icien s
o (p ice) c oss elas ici y could se e as an app op ia e measu e o
he ela i e closeness o subs i u es i only su icien da a we e a ail-
able o he es ima ion o he coe icien s1. I will be shown below ha
he concep ual di icul ies wi h his measu e a e g ea enough o make
one wonde whe he i is wo h he e o o o e come he da a p ob-
lems.
The cen al ques ion is: How should we measu e he ela i e close-
ness o he "deg ee o subs i u abili y" o subs i u es when we a e
dealing wi h mo e han wo goods? To be su e, we always need mo e
* The au ho would like o hank R. G. Lipsey, M. E. S ei , and D. A.
Va dy o ex ensi e commen s on ea lie e sions o his pape .
i See, o example, M. Howe [10, p. 42] and F. M. Sche e [13, p. 531-
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152 Klaus S egemann
han wo goods, since closeness o subs i u es is a ela i e concep .
The s a emen "ma ga ine is a close subs i u e o bu e " makes no
sense unless we ha e some o he commodi y o commodi ies in mind
which a e no "close" subs i u es o bu e o no as close as ma ga ine.
As i u ns ou he e a e se e al al e na i e ways o ela ing wo o
mo e subs i u es o a commodi y. And i will be shown ha , o some
pu poses, some o hese app oaches a e ambiguous ways o measu ing
he deg ee o subs i u abili y. We will i s demons a e he di icul ies
o using he adi ional c oss elas ici y measu e wi h a ic i ious ex-
ample, will hen look a al e na i e concep s, and inally will ela e
he indings o he pape o he p ac ical use o c oss elas ici ies in he
well-known Cellophane Case2.
I. Rela i e Changes in
Own Sales Ve sus Rela i e Changes in Sales o O he s
Le us suppose a na ional associa ion o bu e p oduce s o a policy
make wan ed o de e mine which o wo po en ial subs i u es, ma -
ga ine and peanu bu e , is he close subs i u e o bu e . One way
o doing his is o assume ha he p ices o ma ga ine and peanu
bu e a y wi hin some na ow ange while he p ice o bu e and
all o he demand condi ions emain unchanged. Using an a c o mula,
we would hen ha e o compa e he ollowing c oss elas ici ies8.
Q'b-Qb
Qb
+ Qb
(1) eQb,Pm= p, _p and
Pm + P;
Qb-Qb
sQ P Qb+Qi>
Vb'^g
—
p, _ p
P 4- P'
g ~ g
We hus compa e he pe cen changes (shi s) in he demand o
bu e which esul om a one-pe cen change in he p ice o ma -
2 Robe T i in's 1950 book [17], E. H. Chambe lin's 1951 a icle [5], and
pa icula ly R. L. Bishop's 1952 a icle [2] led o an ex ended deba e on he
use o coe icien s o c oss elas ici y o he classi ica ion o compe i i e
ela ionships be ween indi idual i ms. Since ha deba e has o e shadowed
e e y o he aspec o c oss elas ici ies a disclaime seems o be in o de :
This no e is no ano he con ibu ion o he T i in-Chambe lin-Bishop
deba e. The ocus is on di e en ques ions. Fo a discussion o he o e lap-
ping issues see he longe mimeog aphed e sion o his pape [15, pp. 13 - 20].
3 The no a ion should be sel -explana o y wi h he excep ion ha in he
second o mula I use he subsc ip "g" ( o "g ound-nu bu e ") in o de o
a oid using li le "p" as a subsc ip .
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C oss Elas ici y and he Rele an Ma ke 153
ga ine o he p ice o g ound-nu bu e , espec i ely. Le us assume
bo h coe icien s a e posi i e indica ing ha he goods a e subs i u es4.
The subs i u e which has he la ge coe icien is he close subs i u e
o bu e . This way o compa ing coe icien s o c oss elas ici y is
unambiguous as a as i goes. P esumably, his is he app oach which
many ex book au ho s ha e in mind because i ollows om he
Ma shallian way o conside ing "o he p ices" as a gumen s in he
demand unc ion o any one commodi y. Howe e , ex book au ho s
ne e wa n he eade ha his is he only alid app oach. They ha dly
e e deal wi h mo e han one "o he " good a a ime, o ha ma e 5.
Being p edominan ly conce ned wi h he e ec s o i s own p ice
policy, ou associa ion o bu e p oduce s migh be mo e in e es ed
o ind ou which o he wo o he goods is he close subs i u e when
he p ice o bu e changes and he o he p ices a e assumed o emain
unchanged. Fo his ques ion, i is emp ing o de ine he ele an c oss
elas ici ies in he ollowing way6:
(2) eQm>Pb =
4 P ice heo y ex s usually s a e ha he coe icien o c oss elas ici y o
demand is a measu e o he closeness o subs i u es when he sign o he
c oss elas ici y be ween wo commodi ies is posi i e and o he closeness o
complémen s when he sign is nega i e. Some au ho s wa n hei eade s
ha he sign o he coe icien can be misleading i we ha e he Ricksian
de ini ions o subs i u es and complemen s in mind. Fo a discussion o such
cases see Hicks [8, pp. 42 - 52] and he longe mimeog aphed e sion o his
pape [15, pp. 26 - 33]. They do no a ec he 'basic a gumen p esen ed he e.
s The o mulae (1) app oach is s a ed explici ly by Sche e [13, p. 459].
6 This app oach is pa icula ly emp ing because i uns pa allel o he
way in which Hicks [8, Chap e III] ela es di e en commodi ies o each
o he . He a ies he p ice o one good, say bu e , and looks a he changes
in demand o se e al o he goods. As is well known, Hicks employs his ap-
pa a us o subs i u ion and income e ec s a he han coe icien s o c oss
elas ici y and no c i ique o his app oach is in ended he e. Hicks could e en
a gue ha in his amewo k i would no ma e which way one compa es
he closeness o subs i u es o bu e , because o each subs i u e he absolu e
"c oss e ec s" a e equal1 unde bo h o mulae (1) and (2) as long as he
condi ions o his " ecip oci y heo em" a e ul illed [9, Chap e XIII]. Fo
c oss elas ici ies we do no s ipula e hose condi ions. Wha is mo e im-
po an , we compa e ela i e changes in demand a he han -absolu e c oss
e ec s when we employ coe icien s o c oss elas ici y.
Qm -
Qm
Qm
+
Q'm
Pb}+ Pi
Qg
+
Q'g
Ph + Pi
and
espec i ely.
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154 Klaus S egemann
Howe e , a close look a o mulae (2) e eals ha ela i e changes
in sales o subs i u es imply a misleading compa ison: The denomina-
o s a e iden ical, since we wan o ela e he e ec s on he demand
o he wo al e na i e subs i u es o he same change in he p ice o
bu e . The nume a o s, i. e. he pe cen changes o quan i ies de-
manded, hus de e mine which o he wo al e na i e subs i u es, ma -
ga ine o peanu bu e , appea s o be a close subs i u e o bu e ,
i we judge closeness by compa ing he size o he coe icien s o c oss
elas ici y. Now i is i ial o poin ou ha he alue o he nume a-
o s depends bo h on he absolu e changes in quan i ies demanded and
on he base quan i ies o which we ela e he changes in demand
caused by changes in he bu e p ice. Wi h a gi en absolu e expansion
o demand o ma ga ine, he alue o he coe icien depends on he
size o he ma ga ine ma ke p io o he change in he p ice o bu e .
The la ge he ma ke , he lowe he coe icien o ma ga ine. The
same a gumen , o cou se, holds o peanu bu e and any o he good.
I he size o he ma ke in luences he alue o he coe icien s o
indi idual goods i may also dis o a compa ison be ween hem. We
could ha e wo his o ical si ua ions whe e he esponse o consume s
o a ise in he bu e p ice is exac ly he same in e ms o swi ching
o subs i u es o bu e and s ill he coe icien s would gi e a di e en
imp ession i he ela i e sizes o he ma ke s o subs i u es would
di e in he wo si ua ions. I is also easy o cons uc examples in
which he absolu e inc ease in quan i y (measu ed in ons pe mon h)
is much smalle in he peanu bu e ma ke han in he ma ga ine
ma ke , and s ill he coe icien o c oss elas ici y makes peanu bu e
appea o be a much close subs i u e o bu e han ma ga ine. We
jus ha e o make he peanu bu e ma ke small enough ela i e o
he ma ga ine ma ke .
I is implied in he abo e c i ique ha absolu e changes in he ma -
ga ine and peanu bu e ma ke s would be a mo e ele an measu e
o compa ing he closeness o subs i u es. The measu e appea s o be
mo e ele an in he sense ha bu e p oduce s as a g oup would
conside ma ga ine as he close subs i u e i , a e an inc ease in he
p ice o bu e , hey expec o lose mo e sales o ma ga ine han o
peanu bu e — no ma e wha he pe cen age changes in he sales
o hose subs i u es. The bu e lobby would be guided by he absolu e
quan i ies (o pe cen ages o own sales los ) in i s e o s o p ocu e
p o ec i e measu es agains ma ga ine and agains peanu bu e 7. Sim-
7 I he bu e lobby we e p ima ily in e es ed in he po en ial eac ion
o p oduce s o subs i u es o a change in he p ice o bu e , i would be
mo e conce ned wi h pe cen age changes in sales expe ienced by hose o he
p oduce s. Fo mulae (2) coe icien s a e hus an app op ia e concep i he
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C oss Elas ici y and he Rele an Ma ke 155
ila ly, a policy make would eel ha he a ailabili y o ma ga ine is a
mo e impo an check on he p ice policies o a bu e monopoly han
he a ailabili y o peanu bu e , i ma ga ine could po en ially a ac
a la ge olume o bu e cus ome s. Thus he decision is o which
subs i u e is he mo e impo an componen o a ma ke labelled
"bu e and close subs i u es" would be made on he basis o absolu e
changes a he han o mulae (2) coe icien s.
A di icul y is, o cou se, ha we do no always eel con iden ha
we should use a compa ison o absolu e changes, because we ha e o
measu e hose changes in di e en uni s. Fu he mo e, when i comes
o de ining he ma ke o bu e and close subs i u es, he inclusion o
commodi ies ha ha e a la ge absolu e e ec on bu e sales, bu small
o mulae (2) coe icien s, would end o "dilu e" ha ma ke and,
acco dingly, would dec ease he sha e o bu e in he " ele an "
ma ke . Howe e , a dilu ion e ec canno be a oided by using o -
mulae (1) coe icien s, as he ma ke sha e o bu e wi h gi en cu -o
poin s o closeness, is a unc ion o he olume o sales o all sub-
s i u es included in he ma ke . Le us assume, o example, ha o al
bu e sales o a ce ain pe iod amoun o 50 uni s, ma ga ine sales
a e 150 equi alen uni s, and peanu bu e sales a e also 50 uni s. I
on he basis o a o mulae (1) compa ison only peanu bu e is e-
ga ded close enough o be included in he ele an ma ke , bu e has
a sha e o 50 pe cen . I only ma ga ine is included, he ele an
ma ke is dilu ed o an ex en ha he bu e sha e is 25 pe cen .
Thus i can happen ha in wo di e en si ua ions we measu e he
same o mulae (1) coe icien s, e lec ing and equal deg ee o closeness,
bu he conclusions conce ning he deg ee o "ma ke powe " o bu e
could a y widely. I shall e u n o he dilu ion p oblem in sec ion III
below.
Be o e his sec ion on he ela i e me i s o o mulae (1) and (2) is
closed, i mus be poin ed ou ha all c oss elas ici y concep s sha e
ce ain sho comings which in hemsel es se e ely limi he use ulness
o c oss elas ici ies as measu es o he closeness o subs i u es. One
such sho coming is ha we only compa e c oss ela ionships o ce -
ain se s o p ices, and he e is no jus i ica ion o ex apola e in o ma-
ion o o he p ice si ua ions. I could be possible, o ins ance, ha
a a low bu e p ice, peanu bu e and bu e would be close sub-
s i u es han ma ga ine and bu e , whe eas o some highe bu e
p ice peanu bu e and bu e a e comple ely un ela ed goods because
discussion is oci ssed' on he dis inc ion be ween oligopolis ic i al y and
o he ypes o compe i i e ela ionship as was he case in he T i in-
Chambe lin-Bishop deba e e e ed o in oo no e 2.
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156 Klaus S egemann
a ha p ice le el buye s consume only peanu bu e in all uses whe e
he wo p oduc s would be po en ially in e changeable. Ano he sho -
coming o c oss elas ici ies is ha hey measu e he c oss esponsi e-
ness o demand in e ms o p ice esponsi eness only. Again, he e is
no jus i ica ion o ex apola e esul s om p ice o non-p ice pa a-
me e s, unless changes in non-p ice pa ame e s o a selle 's o e can
be ansla ed in o changes in ela i e p ices o buye s8.
Finally, i mus be said ha c oss elas ici ies a e unambiguous meas-
u es o he deg ee o subs i uabili y only o he ex en ha he can
eso o an unambiguous ule o he de ini ion o p oduc s o sub-
ma ke s. Take he o mulae (1) app oach: I we lump oge he all
b ands o ma ga ine, he coe icien would be la ge han o each
b and aken sepa a ely. We migh ind ha ma ga ine as an agg ega e
is a close subs i ue o bu e han he closes b and o ma ga ine.
Now he o mulae (2) app oach: The e is no dis o ion o he ela i e
deg ee o subs i u abili y measu ed in e ms o ela i e changes o
sales o subs i u es as long as he e is li le a ia ion in he coe icien s
o he agg ega ed sub-p oduc s. To he ex en ha he e is a ia ion,
he e is dis o ion om agg ega ion. O cou se, we ound ea lie ha
o mulae (2) imply an inapp op ia e compa ison anyway9.
II. Absolu e C oss Elas ici ies and Coe icien s o Mobili y
as Al e na i e Measu es o Closeness
I bu e p oduce s wish o de e mine whe he ma ga ine o peanu
bu e is a close subs i u e o bu e when he bu e p ice changes,
he e a e wo al e na i e measu es ha do no su e om he sho -
comings o he o mulae (2) app oach. Bo h o hese al e na i es ha e
been p oposed in he li e a u e; howe e hei speci ic ad an ages o
disad an ages ha e no been discussed in he p esen con ex .
Boulding [3, p. 200] men ions he concep o an "absolu e c oss elas-
ici y o demand" which he de ines as " he absolu e change in he
quan i y o A demanded which would esul om a uni change in
he p ice o B, o he ac o s held cons an ". This de ini ion is analogous
o he Hicksian "c oss e ec s" [9, p. 127]. In e ms o ou p e ious ex-
» P ac ical a emp s a measu ing he closeness o subs i u es o en em-
phasize non-p ice pa ame e s. A Uni ed Na ions s udy o s eel subs i u es
[18], o example, closely examines he echnical ac o s a ou ing o imped-
ing he eplacemen o s eel by a ious subs i u es in a ious uses.
» In he con ex o he T i in-Chambe lin-Bishop deba e, whe e bo h
o mulae (1) and o mulae (2) ha e a pu pose, he p oblem o agg ega ion did
no a ise because p oduc s a e de ined as he ou pu o indi idual selle s;
each is assumed o be a selle o only one homogeneous p oduc .
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C oss Elas ici y and he Rele an Ma ke 157
ample, we would ha e o compa e he ollowing wo measu es o ab-
solu e c oss elas ici y:
QL
-
Qm
(3)
aQm>
pb = p, _ p and
pTW*200
aQo>Ph = Qa-Qa
Pb+P'b X 200
Fo easons o symme y wi h he o he concep s, he denomina o s
in o mulae (3) we e w i en as a one-pe cen change in he bu e
p ice a he han as a uni change. This need no be a ma e o
conce n, howe e , because we ela e he quan i y changes in bo h
subs i u e ma ke s o he same p ice change o bu e . In he case o
o mulae (1) we mus use a pe cen p ice change in o de o a oid a
p oblem o uni s in he denomina o s. In he case o o mulae (3) he
p oblem o uni s a ises in he nume a o s. The wo coe icien s answe
he ques ion o he ela i e closeness o bu e subs i u es unam-
biguously only i we can compa e uni s o ma ga ine and peanu bu e
on a one- o-one basis. I seems o be accep ed ha he p oblem o uni s
can be neglec ed when one is dealing wi h di e en ia ed p oduc s ha
ha e a common name, e. g. di e en b ands o co ee o b ands o
ciga e es o e en au omobiles. We almos daily use pe cen igu es
o ma ke sha es o pe cen age egis a ion igu es o such di e -
en ia ed p oduc s which s ic ly speaking a e o he "apple-and-pea "
ype, he idea being ha consume s subs i u e hem pound pe pound
o ca o ca . I hey do no , one could y o employ con e sion
ac o s. The changes in he demand o ma ga ine and peanu bu e ,
o ins ance, could be con e ed in o ons o "bu e equi alen ". This
app oach de ini ely has i s limi s. Had I used bu e e sus ma ga ine
and eggs o e en bu e e sus ma ga ine and elec ici y (as a sub-
s i u e o human kine ic ene gy and as a uel o hea ing) he p oblem
would ha e been mo e appa en .
I we wish o a oid he dis o ions o he o mulae (2) app oach and
also dislike he use o absolu e quan i y changes as a measu e o
closeness, we can ob ain uni - ee coe icien s by ela ing he quan i y
changes o he sales o he g oup o i m changing i s p ice. Wilhelm
K elle [11, pp. 8-12] has employed his app oach o cons uc ing his
measu e o "mobili y o demand" (Beweglichkei de Nach age). The
(p ice) mobili y o demand be ween bu e and ma ga ine, o example,
would be de ined as he pe cen age change in bu e sales los o
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158 Klaus S egemann
(gained om) he ma ga ine ma ke in consequence o a one-pe cen
ise ( all) in he p ice o bu e . We can de e mine he ela i e closeness
o he wo bu e subs i u es, ma ga ine and g ound-nu bu e , by
compa ing he ollowing wo coe icien s o mobili y o demand10:
(4) PQb n, pb=~
4 Qbm
Qb + Qj
Pb + Pi,
and
¿Qbg
Qb + Q'b
Pb-Pb
P
h
+ P'h
The o mulae (4) concep appea s o be an unambiguous app oach o
measu ing ela i e closeness o subs i u es. Howe e , se e al con-
cep ual di icul ies a ise when we imagine how coe icien s o mobili y
could be measu ed.
Fi s ly, he e could be a p oblem o uni s in he nume a o s al hough
he de ini ion seems o a oid his p oblem. How would one go abou
measu ing he sha es o bu e sales being los o (o gained om)
ma ga ine, cheese, elec ici y, and o he p oduc s when he ela i e
p ice o bu e changes? P esumably, one would measu e he quan i y
changes in subs i u e ma ke s and hen exp ess hem in e ms o bu e
equi alen s. Secondly, i mus be ecognized ha he coe icien s a e
smalle he na owe we de ine a subs i u e. This p oblem a ises when
we a e dealing wi h se e al simila subs i u es which easily can be
agg ega ed. We would, o ins ance, ind ha he coe icien s o mo-
bili y a e smalle o each indi idual b and o ma ga ine han o all
b ands o ma ga ine aken oge he , al hough — in a ood chemis 's
opinion — ce ain b ands migh be mo e simila o bu e han he
"a e age" b and o ma ga ine. As no ed abo e his p oblem o ci -
10 These de ini ions a e s ic ly analogous o he "own" p ice elas ici y o
demand. Unde he assump ion ha he p ice changes conside ed ha e no
income e ec s, coe icien s o mobili y a e sec o al own elas ici ies, and he
sum o he coe icien s o all o he goods (sa ings included) is equal o he
own elas ici y o bu e wi h espec o he gi en change in he p ice o bu -
e . Howe e , a wa ning seems o be in o de : Such sec o al elas ici ies a e
no he elas ici ies o demand in sub-ma ke s which selle s would like o
know o pu poses o p ice di e en ia ion. I we wan ed o measu e he
elas ici y o demand o he sub-ma ke in which bu e compe es wi h
ma ga ine we would ha e o ela e A Qhm o he bu e sales in ha sub-
ma ke a he han o all bu e sales.
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DOI h ps://doi.o g/10.3790/schm.94.2.151 | Gene a ed on 2023-04-04 11:51:05
C oss Elas ici y and he Rele an Ma ke 165
[17] T i in, Robe , Monopolis ic Compe i ion and Gene al Equilib ium
Theo y, Camb idge, Mass.: Ha a d Uni e si y P ess, 1962 ( i s pub-
lished in 1940).
[18] Uni ed Na ions, Aspec s o Compe i ion Be ween S eel and O he
Ma e ials, New Yo k: Uni ed Na ions, 1966.
[19] Uni ed S a es s E. I. Bu Pon De Nemou s & Company, 351 U. S. 377
(1956).
OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/
DOI h ps://doi.o g/10.3790/schm.94.2.151 | Gene a ed on 2023-04-04 11:51:05