S e ano , Ya osla
A icle
Powe heo y o exchange and money
Economies
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Sugges ed Ci a ion: S e ano , Ya osla (2022) : Powe heo y o exchange and money, Economies,
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Ci a ion: S e ano , Ya osla . 2022.
Powe Theo y o Exchange
and Money. Economies 10: 24.
h ps://doi.o g/10.3390/
economies10010024
Academic Edi o : Robe Czudaj
Recei ed: 4 Decembe 2021
Accep ed: 6 Janua y 2022
Published: 12 Janua y 2022
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economies
A icle
Powe Theo y o Exchange and Money
Ya osla S e ano
Facul y o Mechanics and Ma hema ics, Lomonoso Moscow S a e Uni e si y, 119991 Moscow, Russia;
[email p o ec ed]
Abs ac :
Mode n exchange heo ies model a la ge ma ke , bu do no explain single exchanges. This
pape conside s he phenomenon o single exchange and o mula es he gene al exchange p oblem
in he o m o a sys em o wo equa ions, subjec i e and objec i e. Subjec i e equilib ium is gi en
by he Wal as–Je ons ma ginal u ili y equa ion. Objec i e equilib ium equa ions by Wal as and
Je ons a e a e aged o e all ansac ions in he ma ke and can only gi e a ough gene al pic u e
wi hou explaining he speci ic p ice o an indi idual exchange. An exchange mic o-condi ion mus
be ound ha , when a e aged, will gi e he Wal as ma ke equilib ium mac o-condi ion. The s udy
o he in e nal s uc u e o exchange leads o he need o conside powe . The concep o gene alized
powe is in oduced. I is gene alized powe ha se es as he p ima y compa able and measu able
objec i e basis o exchange. The powe heo y o exchange p o ides he objec i e p ice-equa ion.
I is demons a ed ha money is a measu e o gene alized powe in exchange and a ce i ica ion
o gene alized powe in subsequen exchanges. This me hodology is based on an in e disciplina y
analysis o an abs ac exchange model in he o m o a sys em o equa ions. The p oposed heo y is
able o uni o mly explain any exchange, including a single one, which is impossible wi h he exis ing
heo ies o exchange.
Keywo ds: exchange; exchange heo y; money; money heo y; powe
JEL Classi ica ion: A10; A13; A14; D00; D41; D46; D51; E40; G00; Z13
1. In oduc ion
Many au ho s, ega dless o hei scien i ic iews, assign a key ole o exchange in
economic esea ch. In Ka l Ma x’s book Das Kapi al, he second chap e is dedica ed
exclusi ely o exchange (Ma x 1909). Ludwig on Mises, a ep esen a i e o a comple ely
di e en mo emen and an ideological opponen o Ma x’s, w o e ha “ he exchange
ela ion is he undamen al social ela ion” (Mises 1998). Acco ding o William S anley
Je ons: “I is impossible o ha e a co ec idea o he science o Economics wi hou a pe ec
comp ehension o he Theo y o Exchange” (Je ons 1924).
Theo is s ha e achie ed ema kable esul s in cons uc ing models o ma ke exchange
unde condi ions whe e a la ge olume o ansac ions a e conduc ed (he eina e “la ge
ma ke ”). Howe e , in he case o a simple disc e e exchange, he exis ing app oaches
do no p o ide a comple e explana ion. The cen al elemen o mode n economics is he
Wal asian gene al equilib ium model, which is designed o a la ge ma ke , when supply
and demand a e gene a ed by many buye s and selle s. Howe e , his model does no
explain he case o a simple exchange. A he beginning o his book, Wal as men ions ha
“O cou se, ou heo y should co e all such special cases
. . .
. Ma ke
. . .
in which he e is
a single buye , a single selle
. . .
”, bu la e in he book he deals only wi h “exchange as
i a ises unde
. . .
compe i i e condi ions [o he la ge ma ke ]” (Wal as 1954). As Al ed
Ma shall (1890) no ed “in a casual ba gain ha one pe son makes wi h ano he
. . .
, he e
is seldom any hing ha can p ope ly be called an equilib ium o supply and demand”.
F ancis Ysid o Edgewo h (1881) was mo e de ined: “Con ac wi hou compe i ion is
inde e mina e”. To ob ain an unambiguous solu ion o exchange p oblem, hese heo ies
Economies 2022,10, 24. h ps://doi.o g/10.3390/economies10010024 h ps://www.mdpi.com/jou nal/economies
Economies 2022,10, 24 2 o 16
e e o he condi ions caused by he la ge ma ke . F anco Donzelli w o e in de ail abou he
ole o hese condi ions in he a icle “Negishi on Edgewo h on Je ons’s law o indi e ence,
Wal as’s equilib ium, and he ole o la ge numbe s: a c i ical assessmen ” (Donzelli 2012)
so I will no explo e he issue in dep h he e. Ins ead, I will conside only hose aspec s ha
a e impo an o u he easoning. The aim o his pape is o build a comple e model ha
will be able o desc ibe any exchange uni o mly, i espec i e o whe he i occu s on a la ge
ma ke o i i is a one-o e en .
Sec ion 3conside s he impo an ole o he la ge ma ke in exis ing exchange heo ies.
Sec ion 4p esen s he o mula ion o he exchange p oblem as a sys em o wo equa ions
wi h wo unknowns. Then, one o he equa ions is de e mined. Sec ion 5examines he
concep o powe and in oduces he concep o gene alized powe . The applica ion o
hese concep s in he case o exchange is in oduced. Sec ion 6ou lines a powe heo y o
exchange and de e mines he second equa ion. Sec ion 7p esen s a powe heo y o money.
2. Me hodology
This esea ch is based on he cons uc ion o an abs ac model o a single exchange,
exp essed in ma hema ical o m. The explana o y componen o he heo y is in e disci-
plina y in na u e; i essen ially uses concep s om sociology and poli ical science. Analysis
o he model allows me o apply hese concep s o unde s and he measu able basis o
exchange and he essence o money. Fu he easoning allows o de e mine he posi ion o
he p oposed heo y in he exis ing mode n s uc u e o he exchange heo y.
3. Role o he La ge Ma ke on Exchange Theo ies
I is bes o s a by conside ing he assump ions o mode n exchange heo ies, which
a e dependen on he in luence o he la ge ma ke . Acco ding o Wal asian exchange
heo y, p ices a e de e mined by he compe i i e ma ke as a esul o supply demand
equilib ium. In pa icula , Wal as illus a es his posi ion by he example o ade in
whea : he p ice “does no esul ei he om he will o he buye o om he will o he
selle o om any ag eemen be ween he wo” because p ice is a “na u al phenomenon”
(Wal as 1954). This quo e clea ly shows he di e ence be ween he cases o a simple ex-
change and a la ge ma ke , because in a simple exchange, he exchange a e depends
p ecisely on he will o he pa icipan s and on hei ag eemen .
Unde an al e na i e app oach, he Je ons exchange heo y, he addi ional condi ion
is he “law o indi e ence”, which alone allowed Je ons o cons uc a sys em o wo
equa ions. He w o e ha “ he wo equa ions a e su icien o de e mine he esul s o
exchange; o he e a e only wo unknown quan i ies conce ned, namely, x and y, he
quan i ies gi en and ecei ed” (Je ons 1924). La e , Edgewo h, w i ing on he Je ons
equa ions, c i icized he axioma ic in oduc ion o an addi ional condi ion and o e ed his
way o sol ing he p oblem h ough he in oduc ion o “pe ec compe i ion,” which is in
ac he la ge ma ke (Edgewo h 1881). Despi e subsequen a emp s by Takashi Negishi
o de end Je ons’ conclusions (Negishi 1989), hey we e challenged by Donzelli. Donzelli
w o e: “The ailu e o Negishi’s a emp con i ms, in he las analysis, ha Edgewo h’s
esul s canno be imp o ed
. . .
s onge esul s depend on he special assump ions adop ed”
(Donzelli 2012).
Bo h Wal as and Je ons’ models a e based on ma ginal u ili y heo y (MUT), whe e
exchange is iewed h ough he subjec i e es ima ions o he pa icipan s. In o de o ind
a solu ion in each model i was necessa y o add objec i e condi ions o he subjec i e
equa ions o ma ginal u ili y. To Wal as, his addi ional condi ion was he law o one p ice
caused by supply–demand equilib ium on he ma ke . As o Je ons, when analyzing his
equa ions, Edgewo h demons a ed ha he inco po a ion o “pe ec compe i ion” wi h a
la ge numbe o ac o s in o he model allows one o ob ain a single solu ion. In o he wo ds,
o sol e he p oblem, Edgewo h was o ced o go beyond he only subjec i e assessmen o
u ili y and o in oduce an objec i e ac o , pe ec compe i ion, which is he esul o a social
phenomenon, a la ge ma ke . The necessi y o adding objec i e ci cums ances o subjec i e
Economies 2022,10, 24 3 o 16
assessmen s is no acciden al, as will be seen la e . In addi ion, i will be emphasized ha he
ma hema ical o m o he co esponding Wal as and Edgewo h–Je ons’s p ice-equa ions
does no depend on he pa ies in ol ed in he exchange (a he same ime, hei equa ions
o ma ginal u ili y depend on he pa ies o exchange in an explici o m). These equa ions
se a uni o m p ice o he en i e ma ke . Howe e , in eali y, e en in a la ge ma ke , he
pe sonali ies o he pa icipan s in he single exchange can in luence he p ice, and in he
same ma ke , di e en p ices a e possible in di e en exchanges.
Thus a , I ha e only ocused on he models ha a e based on MUT. Howe e , he e is
also ano he app oach, which is based on he labo heo y o alue (LTV). I will co e i
la e . I s a by conside ing a simple exchange in gene al e ms.
4. Two Condi ions, Two Equa ions
A simple single exchange is he in e ac ion o wo ac o s (pa icipan s, subjec s, pa ies,
o commodi y owne s) whe eby nego ia ion (ba gaining) is conduc ed and he a io o
exchange is de ined. A e an ag eemen has been eached, objec s (goods) o exchange a e
ans e ed mu ually in speci ied amoun s. The concep o a ans e will equi e special
a en ion la e .
I wo pa icipan s H1 and H2 exchange objec s O1 and O2, hen hei common ask
is o de e mine he numbe x o objec s O1 and he numbe y o objec s O2 ha will be
ans e ed mu ually in he cou se o exchange. Exchange is hus a p oblem wi h wo
unknowns. When hey bid, he pa icipan s in he exchange a e se ing he speci ic alues
o he a iables x and y wi h a iew o sol ing he p oblem oge he .
A wo old in e p e a ion o he ac o s o he objec o exchange has o med g adually
since he ime o A is o le. On he one hand, he exchanged i ems can sa is y human
needs, be use ul and hus ha e alue o indi iduals as objec o u ili y. This ac o is
called use alue. On he o he hand, objec s can be exchanged o o he hings, and hus
hey ha e alue o indi iduals as a means o ob aining o he goods. This ac o is called
exchange alue. Bo h ac o s ha e oles o play in exchange and bo h in luence i s ou come.
Resea che s ha e explained hem in di e en ways. Fo example, o Ma x, he a ionale o
exchange alue is ma e ialized labo . To Wal as, i is sca ci y. Böhm-Bawe k deeply s udied
he ques ion o he duali y o exchange and use alues and especially poin ed ou ha
alues can be subjec i e and objec i e (Böhm-Bawe k 1886).
Exchange alue mani es s in he in e ac ion be ween he exchanging pa ies as a
quan i a i e a io. I a ises as a comp omise be ween he in e es s o he pa icipan s in
he exchange. Exchange alue is he esul o economic in e ac ion be ween wo membe s
o socie y. This esul has an objec i e basis because when speci ic alues a e es ablished
du ing exchange, a decision is made join ly by wo pa icipan s, each o whom is o ced o
conside he wishes o he o he . In addi ion, o he ex e nal ci cums ances o a social na u e
may exe cise an in luence on he a ios o exchange. Fo example, he p esence o a la ge
numbe o selle s in he ma ke can change he exchange a io compa ed o he case when
he e a e no o he selle s. The e o e, in he case o exchange alue, he e is some objec i e
condi ion o exchange ha is es ablished du ing an in e ac ion be ween wo subjec s. I
exchange is conside ed a solu ion o a p oblem wi h wo unknowns, hen he ci cums ance
o exchange alue can be ep esen ed in a e y gene al o m as a unc ion OB ha imposes
es ic ions on he a iables x and y.
OB (x, y) = 0— he equa ion o objec i e equilib ium o p ice equa ion. (1)
The OB unc ion is objec i e in na u e, ha is, i does no e lec he pu ely pe sonal
assessmen s o each side bu ins ead a ises om he in e ac ion o he pa ies, and i may
depend on social ci cums ances.
The use alue ha pa icipan s can ex ac om he objec s o exchange is subjec i e.
Pa icipan s mus ake his ac o in o accoun when exchanging since e e yone seeks o
bene i hemsel es. Thus, use alue can be unde s ood as a subjec i e condi ion o exchange
ha each pa icipan es ima es o hemsel es. Howe e , hese es ima es also a ec he
Economies 2022,10, 24 4 o 16
exchange and se i s condi ions. I exchange is cons ued as a solu ion o a p oblem wi h
wo unknowns, hen he ci cums ance o use alue can be ep esen ed in a e y gene al
o m as a unc ion SU ha imposes es ic ions on he a iables x and y
SU (x, y) = 0—subjec i e equilib ium equa ion o quan i y equa ion. (2)
Thus, wo condi ions o exchange can be disce ned, one ha is objec i e (public) and
ano he ha is subjec i e (pe sonal). Each condi ion imposes a es ic ion on he unknown
a iables. Mo eo e , by hei na u e, hese condi ions a e independen : wha e e he
pe sonal p e e ences and needs o each subjec (condi ion o he SU), hey collide wi h he
opposi e in e es s o he o he in he cou se o ba gaining, o cing he wo o de elop a
minimally objec i e comp omise (condi ion OB).
Ma hema ically, inding he alues o wo unknowns equi es wo independen equa-
ions ha es ic he wo a iables. One equa ion gi es he a io o he a iables (p ice),
and he second de e mines he absolu e solu ion ( inal amoun ). The e o e, p oceeding
om gene al conside a ions, one can expec ha he pa icipan s in he exchange mus
sol e a sys em o wo equa ions ha ha e al eady de ined be o e, connec ing he a iables
x and y.
OB(x, y)=0
SU(x, y)=0(3)
This sys em o equa ions may no ha e solu ions, and hen he exchange will no ake
place.
Wha a e he equa ions in sys em (3)? Ea lie , I discussed wo models o exchange ha
a e based on MUT. These models p opose equa ions ha desc ibe he subjec i e condi ions
o exchange as hey compa e he subjec i e ma ginal u ili ies o he pa ies. Mo eo e , as
Wal as showed, he ideologically di e en models o Je ons and Wal as a e ma hema ically
iden ical. Wal as w o e ha o he case o exchange be ween wo indi iduals “Je ons’s
o mula is iden ical wi h ou own, excep ha he used quan i ies exchanged whe e we
use p ices” (Wal as 1954). The e o e, he MUT p o ides one independen equa ion o
compa ing ma ginal u ili y in exchange. Conside he Je ons equa ion in he o m gi en by
Edgewo h (1881):
ϕ1(a−x)
ψ1(y)=ϕ2(x)
ψ2(b−y)(4)
whe e
ϕ1
and
ψ1
deno e he ma ginal u ili ies o wo p oduc s o pa icipan H1, and his
pa icipan su ende s x uni s o one p oduc ou o a o al o a ha hey hold. In e u n,
hey ecei e y uni s o ano he p oduc . The unc ions
ϕ2
and
ψ2
ha e he same meaning
o pa icipan H2. Since his equa ion imposes a condi ion on he u ili y a ios o he wo
pa icipan s, I can employ (4) as a subjec i e equilib ium equa ion SU (x, y). To main ain
consis ency wi h chosen o m, I ew i e i as
SU(x, y)=ϕ1(a−x)ψ2(b−y)−ϕ2(x)ψ1(y)=0. (5)
Be o e con inuing, i should be no ed ha bo h Wal as and Je ons p oposed hei
a ian s o equa ions as he i s equa ion OB in his sys em (3). Howe e , he equa ions
hey p oposed do no desc ibe he condi ions o his pa icula exchange, bu ep esen
en i e ma ke gene aliza ions. Fo mally, his can be seen om he ma hema ical ep e-
sen a ions o hese condi ions. In case o Je ons, i is
dx
dy =x
y
, and in case o Wal as i is
Fa(pa)=Fb1
pa1
pa
, o in e ms o x and y
Fay
x=Fbx
yx
y
(5.2) (F
a
and F
b
ep e-
sen demand o goods A and B, x/y is p ice). No indices o pa icipan s (1, 2) a e in ol ed
in hese equa ions, in con as o he equa ions o ma ginal u ili y, whe e hese indices a e
explici ly p esen ( o example see (4)).
Economies 2022,10, 24 5 o 16
I he gene al sys em o Equa ion (3) is w i en mo e igo ously, hen bo h he
pa icipan s (1, 2) o he exchange and he objec s being exchanged (A, B) mus be ex-
plici ly p esen in i as pa ame e s:
OB1,a,2,b(x, y)=0
SU1,a,2,b(x, y)=0
These pa ame e s a e explici ly ep esen ed in he ma ginal u ili y equa ions p oposed
by Wal as and Je ons. Howe e , ano he exchange condi ion p esen ed by each o hese au-
ho s does no con ain he speci ied pa ame e s 1 and 2. Thus, Je ons simply axioma ically
in oduces he o mula o he “law o indi e ence”, and Wal as gi es easoning when some
supply–demand cu es a e a e aged o e he en i e ma ke , and hus a common p ice o
all is ob ained. In bo h models, he p ice equa ion is independen on indi idual exchange.
Howe e , in eali y, e en in a la ge ma ke , he p ices o indi idual exchanges can a y
and he co ec model should e lec his ac . I am no sugges ing he e ha he e ms hey
p oposed we e inco ec . In ac , Je ons’ condi ion was w ong, and Wal as’ condi ion was
ue. Howe e , hese we e no he condi ions o his pa icula exchange, bu he ma ke
condi ions a e aged o e pa ame e s 1 and 2.
Wha can he i s OB equa ion in sys em (3) be? LTV migh come in o play. Acco ding
o LTV, when hey engage in exchange, he pa ies compa e he amoun o socially necessa y
labo ha is needed o he c ea ion o he exchange objec s. The condi ion o he exchange
is he equal con en o labo T in he objec s o exchange. In o he wo ds, he exchange will
occu i
T(x) = T(y), whe e x and y a e he quan i y o he exchange i ems O1 and O2. (6)
This equa ion o e s an objec i e c i e ion o exchange and could be he i s equa-
ion in sys em (3). Howe e , he LTV is incomple e, ha is, i is incapable o explaining
e e y possible exchange uni o mly, as any coun e example p o es. Ma x ga e one such
example in Das Kapi al. He w o e: “Objec s ha in hemsel es a e no commodi ies, such as
conscience, honou , &c., a e capable o being o e ed o sale by hei holde s, and o hus
acqui ing, h ough hei p ice, he o m o commodi ies” (Ma x 1909). He e, Ma x ied o
escape a p edicamen — he con en o labo is no ound in he named objec s o exchange,
which means, acco ding o his logic, ha hose objec s canno be exchanged. Howe e ,
in eali y, hey do become objec s o exchange, which o ced Ma x o seek explana ions
beyond he LTV. The e a e nume ous examples o ins ances whe e no labo can be ound in
he objec s o exchange, up o cases whe e money is paid o delibe a e inac ion, ha is, he
gua an eed absence o labo . Thus, LTV is no sui able o sol ing he exchange p oblem.
To disco e he condi ion ha is necessa y o compose a comple e sys em o equa ions, I
p opose o ega d exchange in mo e de ail.
Conside he ollowing p oposi ion: bo h he exchange alue and he use alue o a
desi ed objec become a ailable o he pa icipan s in exchange only when he objec s o
exchange a e a he disposal o each pa icipan . As long as an i em does no belong o a
pe son, hey canno access any o he alue in ha i em. Wi hin he amewo k o ma ke
ela ions, i is impossible o exchange o use an objec ha a pe son does no con ol. Ma x
w o e abou i as ollows: “In o de o ela e hese [exchanged] hings o one ano he as
commodi ies, he gua dians o commodi ies mus ela e o one ano he as pe sons whose
will disposes o hese hings, so ha each acqui es he o eign commodi y only wi h his
will and he will o he o he , bo h he e o e only wi h hei common will can app op ia e
someone else’s goods, aliena ing hei own”. ( ansla ed by he au ho ) (Ma x 1867). Ma x
no es he need o an abili y o dispose, an abili y o ul ill he will o he commodi y
owne in ela ion o he commodi y o , as I will discuss la e , he necessi y o “ inding he
commodi y in he powe ” o he commodi y owne . He e, I need o discuss he concep o
powe in mo e de ail.
Economies 2022,10, 24 6 o 16
5. Powe and Gene alized Powe
The e a e se e al app oaches ha look a he concep o powe om di e en angles.
He e, he si ua ion wi h di e en iews on he concep o powe in sociology and poli ical
science is o some ex en simila o he si ua ion wi h di e en app oaches o u ili y in
economics, when di e en au ho s o e di e en de ini ions when hey conside his
phenomenon om a ious pe spec i es (Kelle 2015). I will b ie ly ecall now he di e en
poin s o iew on he concep o powe .
Max Webe de ined powe as “ he p obabili y ha one ac o wi hin a social ela ionship
will be in a posi ion o ca y ou his own will despi e esis ance, ega dless o he basis on
which his p obabili y es s” (Webe 1957). The wo ks o Ha old D. Lasswell, Ab aham
Kaplan, Robe Dahl, Do win Ca w igh , S e en Lukes, and An hony Giddens p esen s
a concep acco ding o which “powe a ises in hose social in e ac ions whe e one o he
subjec s has he abili y o in luence he o he , o e coming his esis ance” (Ledyae 2015).
In ano he app oach, ollowed by Talco Pa sons and Hannah A end , “powe is iewed
as a collec i e esou ce, as he abili y o achie e some public good; he legi ima e na u e o
powe is emphasized, i ’s belonging no o indi iduals, bu o g oups o people o socie y
as a whole” (Ledyae 2015).
Each o hese app oaches a emp s o explain he mechanisms o exe cising powe
h ough ei he coe cion o ag eemen . To he p esen ends, he mechanisms o powe a e
less impo an han a desc ip ion o powe in e ms ha a e applicable o exchange. The
quo e om Ma x abo e indica es ha he no ions o will and disposal a e likely o p o e
use ul. I will be shown la e ha he concep o will plays an essen ial ole in explaining
exchange. Thus, o he pu poses o his a icle, i would be easonable o ake Webe ’s
de ini ion as a basis, because i also elies on he concep o will. Now, an app op ia e
de ini ion o powe can be gi en. No hing new has o be in en ed o his pu pose. I need
only highligh and sligh ly ans o m pa o he quo e by Webe : powe is he abili y o
ealize (exe cise) he will ( he abili y o dispose) o he subjec in ela ion o he objec .
Powe is o en desc ibed in compa a i e e ms. Ph ases such as “ hey ha e a lo o
powe ” o “ his pe son has much mo e powe han ha pe son” can o en be hea d. Some
esea che s ha e a gued abou he measu abili y o powe . Thus, in he wo ks o Lasswell,
Kaplan and Mills, he model o powe is a ze o-sum p oblem, ha is, “ he e is a ixed
‘quan i y’ o powe in any ela ional sys em and hence any gain o powe on he pa o
A mus by de ini ion occu by diminishing he powe a he disposal o o he uni s, B, C,
D” (Pa sons 1963). Thus, powe u ns ou o be quan i a i ely measu able, and in ac he
“law o conse a ion o powe ” is p oclaimed. I adop a simila quan i a i e app oach,
albei wi hou he conse a ion law (pe haps Pa sons’ conside a ion o his law is based
on he kind o misunde s anding o he wo k o he a o emen ioned scien is s, as shown
by (Baldwin 1971)). No e ha he wo d “p obabili y” used by Webe in his de ini ion o
powe is in ag eemen wi h he quan i a i e measu abili y o powe . Howe e , ollowing
Pe e M. Blau, I used “abili y” in he de ini ion. The eason is ha ma hema ical alue o
p obabili y canno exceed 1. Howe e , in he case o powe , he gene al measu ing scale
canno be limi ed because one powe can always be se e al imes g ea e han ano he . As
o he e m “abili y” in he de ini ion o powe , pe haps an example om physics would
be app op ia e, when ene gy is de ined as he abili y o do wo k. Acco ding o Be and
Russell “ he undamen al concep in social science is Powe , in he same sense in which
Ene gy is he undamen al concep in physics” (Russell 2004). Jona han Hea n s udied in
de ail he analogy be ween social powe and physical ene gy and belie ed ha he analogy
is deep, ubiqui ous, and some imes mo e han an analogy (Hea n 2012).
I should be cla i ied ha I am no men ioning economic heo ies o powe he e, since
hey do no o e he idea o measu abili y o powe . Fo example, he e olu iona y chain
o heo ies o he i m (Alchian and Demse z, Coase and Williamson, Ha and Moo e)
signi ican ly add ess he issues o powe ela ions, bu powe is no a measu able pa ame e .
I p opose o e u n o he concep o ans e ing an objec be ween exchange pa -
icipan s. T ans e ing is key o he pa ies o gain access o he bene i s ha hey wan .
Economies 2022,10, 24 7 o 16
How is he ans e ac ua ed? Fi s o all, as Ma x igh ly no ed, “ he will o [ he pa ies]
disposes... o hings [objec s o exchange].” In o he wo ds, he p econdi ion o exchange is
ha he will o he pa icipan can dispose o hei objec o exchange. How does he will o
his subjec ela e o he objec be o e and a e he exchange? The na u e o exchange i ems
can a y. Ma e ial and in o ma ional objec s (o mo e gene ally: angible o in angible
objec s) can be exchanged, as can ac i i y and inac i i y. When i comes o he possibili y
o exe cising he will in ela ion o an inanima e objec , i is possible o speak o a igh o
owne ship in ela ion o he objec . Howe e , in eali y, i ems a e some imes exchanged
ha a e no owned by he pa icipan s. Fo ins ance, a hie may well exchange a s olen
objec , e en hough he hie does no ha e owne ship igh s. The hie can dispose o he
objec wi hou hose igh s because he objec is in hei powe and hey ha e he abili y o
exe cise hei will is-a- is he objec , e en wi hou legal igh s. The implica ion is ha i
is mo e accu a e o speak no o owne ship bu o inding an objec in powe . In gene al,
one can ega d “owne ship as he powe o exe cise con ol” (G ossman and Ha 1986).
G ossman and Ha also e e in he same a icle o he Oli e Holmes’ quo e, which mo e
ully exp esses he idea: “ he owne is allowed o exe cise his na u al powe s o e he
subjec -ma e ” (G ossman and Ha 1986). In he cou se o an exchange, objec s mus be
swapped and a ans e mus occu . In his way, he objec passes om he powe o one
pa y o he con ol o ano he . Then, each pa icipan loses he abili y o dispose o hei
objec s. Howe e , hey a e able o dispose o , ha is, o exe cise hei will in ela ion o he
ecei ed objec s.
The case is di e en when ac i i y o ms he objec o exchange. Suppose ha a wo ke
ansac s in labo a a cons uc ion si e. In his case, e e y wo king day, o eigh hou s, he
wo ke does no con ol hei ac i i ies. Ins ead, a o eman does. By gi ing ins uc ions o
subo dina es, he o eman exe cises hei will in ela ion o he subo dina es. The o eman
says wha needs o be done; he wo ke obeys and pe o ms he necessa y wo k. Thus,
wi hin he amewo k o he con ac ual ela ionship ha has a isen in he cou se o he
exchange, he o eman exe cises powe o e he wo ke . Fo eigh hou s, he wo ke is
unde he powe o he o eman, who can dispose o his ac i i y. In gene al, “A e he
exchange, powe is in he hands o he capi alis , and i s mone a y equi alen in he pocke s
o he wo ke ” (Pale mo 2016).
In exchanges o bo h ma e ial objec s and ac i i ies, ans e akes he o m o a mu ual
ansmission o he objec o exchange o he powe o he o he pa y. To emphasize he
uni ied na u e o he e en s ha anspi e du ing he exchange, I use he e m “gene alized
powe ,” ha is, he abili y o he subjec o exe cise hei will in ela ion o he objec bo h
in he case o ma e ial o in o ma ional objec s and in he case o ac i i ies. Then, “ ans e ”
in exchange is he mu ual ans e o objec s o he gene alized powe o he o he pa y.
In gene al, no undamen al obs acles p e en he ex ension o he concep o powe
in o he concep o gene alized powe . Gene alized powe includes bo h powe o e people
and powe o e hings o in o ma ion. Gene ally speaking, he wo cases di e only in
he objec o which he human will is applied. The abili y o dispose o a ma e ial o
in o ma ional objec , powe o e such an objec , means ha a pe son can exe cise hei will
in ela ion o an objec and do wha hey wan wi h i . The abili y o con ol he ac i i ies
o a pe son, powe o e a pe son, means ha one can exe cise one’s will in ela ion o
ano he , a subo dina e, and gi e o de s ha he subo dina e will obey. Wal as w o e: “The
objec o b inging he human will o bea upon na u al o ces, ha is o say, he objec o
ela ions be ween pe sons and hings, is he subo dina ion o he pu pose o hings o he
pu pose o pe sons. The objec o exe cising he human will on he will o o he s, in o he
wo ds, he objec o ela ions be ween pe sons and pe sons, is he mu ual co-o dina ion o
human des inies” (Wal as 1954). P obably i would be logical o supplemen his s a emen
o Wal as by saying ha in he case o human ela ions, simila o he case o ela ions
be ween pe sons and hings, he objec o exe cising he human will is he subo dina ion
o he pu pose o one pe son o he pu pose o ano he pe son. In bo h cases, powe is he
abili y o ac ua e will. In ac , possession (o an objec ) and dominion (o e a pe son) me ge
Economies 2022,10, 24 8 o 16
na u ally because bo h conce n he applica ion o he will o an indi idual o some objec .
Powe is exe cised in bo h cases, and i is di ec ed a ei he objec s ha do no ha e hei
own will (ma e ial o in o ma ional objec s) o o objec s ha do (people). This shows he
na u al essence o he e m “gene alized powe ,” which combines di e en mani es a ions
o powe .
I ollows ha , a i s , he objec o exchange A is unde he gene alized powe o he
i s pa icipan in he exchange, H1. A e nego ia ions wi h he second pa icipan , H2,
and he de e mina ion o he pa ame e s o exchange be ween objec s A and B, he wo
a e ans e ed. A his momen , he gene alized powe o H1 o e A disappea s, as does
he gene alized powe o H2 o e B. The e immedia ely a ises a new gene alized powe
o H1 o e B and, acco dingly, o H2 o e A. In e es ingly, powe is no ans e ed in he
same way as ma e ial objec s—i does no pass physically om hand o hand. A e all, he
powe o exchange pa icipan H1 o e objec A, which exis s be o e he exchange, is no
exac ly he same powe as ha o pa icipan H2 o e objec A, which appea s a e he
exchange. (I is impo an o no e in pa en heses ha he beha io o gene alized powe
in exchange is e y simila o he beha io o u ili y, because he u ili y o he same objec
a e he exchange is a di e en u ili y han i was be o e he exchange.) Ne e heless,
he e is a ans e o powe . Ini ially, H1 had powe o e A. Now, H2 has powe o e A. I
u ns ou ha he ue essence ha is ans e ed a he momen o exchange is gene alized
powe . Only a e he ans e o gene alized powe can he pa icipan s in he exchange
consume o exchange he ecei ed objec s. The e o e, in he cou se o exchange, he ans e
o powe is p ima y is-à- is he ans e o use alue and exchange alue. The possibili y
o command o powe mus be ans e ed be o e he subjec may enjoy he bene i s ha
he objec o exchange embodies. One o he ounde s o MUT Ca l Menge w o e abou he
exchange, ha command (powe ) o a ce ain amoun o goods om one side is ans e ed
o he o he side and ice e sa (Menge 2007).
I eme ges ha gene alized powe plays a key ole in he second s age o exchange, he
momen o ans e ing objec s. Now, in o de o e eal he ole o powe in es ablishing
he p opo ion o exchange, I u n o he ba gaining p ocess. Le us model a s anda d
nego ia ion. Suppose ha wo indi iduals, H1 and H2, engage in exchange. H1 o e s
goods A, and H2 o e s goods B. The ba gaining p oceeds along he ollowing lines:
1. H1 o e s an exchange a io o 2A o 7B (2/7 ≈0.28);
2. H2 p oposes 3A o 8B ins ead (3/8 ≈0.37);
3. H1: 3A o 10B (3/10 = 0.30);
4. H2: 3A o 9B (3/9 ≈0.33);
5. H1 accep s he o e .
The numbe s in b acke s indica e p opo ions ( he numbe o A is di ided by he
numbe o B). In he cou se o ba gaining, H1 is ying o lowe he a io and H2 is ying
o inc ease i . In ba gaining by he me hod o successi e app oxima ions, a ce ain inal
a io is sough ha will sui bo h pa ies. Di e en quan i ies o goods A and B a e equa ed.
These goods may no ha e any hing in common. Howe e , in he cou se o exchange, some
commonali y is ound and compa ed quan i a i ely. So, wha is measu ed o compa ed
du ing he ba gaining p ocess? Is i labo , as Ma x claimed? O is i sca ci y, as Wal as
w o e? As shown abo e, gene alized powe is mu ually ans e ed du ing he exchange.
The ans e o he objec is he ans e o powe o e he objec , which means ha i is
p ecisely gene alized powe ha mus be compa ed du ing he ba gaining p ocess. H1
and H2 compa e wha hey ans e o each o he and his is exac ly and exclusi ely he
gene alized powe . Mo eo e , gene alized powe mus be compa ed be o e he exchange.
A e he exchange, o he gene alized powe s will eme ge on bo h sides.
Appa en ly, i is mo e impo an o an indi idual o measu e he loss o wha hey
had be o e he exchange han o e alua e hei gains om i . A is o le, in his analysis
o exchange, w o e ha “wha belongs o us and wha we gi e away always seems e y
p ecious o us” (A is o le 1906). Kahneman and T e sky’s well-known p ospec heo y la e
explained he ela i e impo ance o loss and gain in subjec i e assessmen s. The heo y
Economies 2022,10, 24 15 o 16
-
Fo a co ec desc ip ion o he exchange, bo h equa ions mus depend on he pa ici-
pan s in he exchange. In he classical app oach, only one equa ion depends on he
exchanging pa ies, and he second has a global a e age cha ac e .
-
The concep o “gene alized powe ” has been in oduced, which makes i possible o
unde s and he pa icipa ion o powe in he exchange p ocess.
-
A new powe exchange heo y is p oposed, which explains he objec i e equa ion
o exchange by compa ing he magni ude o he gene alized powe o he exchange
pa icipan in ela ion o he objec .
-
A new powe heo y o money is p oposed, which explains he essence o money
by measu ing he magni ude o gene alized powe in he cou se o exchange and
ce i ying his powe in subsequen exchanges.
10. Conclusions
This a icle p oposed a o mula ion o he exchange p oblem in he o m o a sys em
o wo equa ions wi h wo unknowns. One o he equa ions ep esen s objec i e condi ions
o exchange, and he o he equa ion ep esen s subjec i e condi ions o exchange. This
app oach esol es he long-s anding dispu e be ween wo app oaches o he exchange
model, MUT and LTV. These heo ies a e iewed as compe ing, bu i anspi es ha hey
ep esen di e en and complemen a y condi ions o exchange: MUT ep esen s subjec i e
ci cums ances, while he LTV ep esen s objec i e ones. I may appea ha combining
he wo app oaches would sol e he exchange p oblem, bu as no ed in pape he LTV
is incomple e and i is e u ed by simple coun e examples. The e o e, o es ablish he
objec i e condi ions o exchange, I p oposed ano he idea whe eby he objec i e basis o
exchange is he compa ison o gene alized powe . This idea gi es ise o a powe heo y o
exchange ha is comple e and ha applies o any exchange. In addi ion o explaining he
na u e o exchange, he powe heo y cap u es he essence o money. Money u ns ou o
be a measu e and a ce i ica e o gene alized powe in exchange.
The limi a ions o his s udy should be no ed. The p oposed model desc ibes economic
exchange, bu , o example, social exchange is a anged di e en ly. Cases ou side he scope
o he p oposed model should be conside ed sepa a ely.
As no ed, some hough s se ou in his a icle a e ound in economic and sociological
esea ch in sca e ed and pa ial o m. Howe e , i is only when hey a e colla ed in o a
powe heo y o exchange ha hese hough s coalesce in o a single logical ab ic. Mo eo e ,
he connec ion and in e dependence be ween economic, sociological and poli ical heo ies
becomes clea .
The powe heo y o exchange and money opens up b oad p ospec s o u he
esea ch. He e, a e some examples o di ec ions o u u e esea ch on his opic. Many
sociologis s poin o he key ole o powe ela ions in he eme gence o poli ical s uc u es
in socie y. Based on he powe heo y, one can y o ind a gene al app oach o he
eme gence o bo h poli ical and economic s uc u es. Fu he , i o ca e ully conside
he possibili ies o ans o ming eal powe in o he symbolic o m o money and ice
e sa, one can s udy he poli ical signi icance o some economic phenomena, such as p o i .
Unde s anding money as a symbolic o m o powe allows also o ake a esh look a he
heo y o he i m.
The u he de elopmen o he powe exchange heo y will enable a deepe examina-
ion o bo h economic and socio-poli ical phenomena.
Funding: This esea ch ecei ed no ex e nal unding.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Con lic s o In e es : The au ho decla es no con lic o in e es .
Economies 2022,10, 24 16 o 16
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