The problem of the principal-agent and promotion tournaments in religious organizations: choosing the next pope

The problem of the principal-agent and promotion tournaments in religious

organizations: choosing the next pope

Oliveira, Livio Luiz Soares de and Neto, Giácomo Balbinotto

Fundação de Economia e Estatística, Post-Graduate Program in Applied Economics (PGPAE) of the Federal University of Rio Grande do Sul (UFRGS)

14 February 2013

Online at https://mpra.ub.uni-muenchen.de/44679/

MPRA Paper No. 44679, posted 01 Mar 2013 17:11 UTC

THE PROBLEM OF THE PRINCIP AL -AGENT AND PROMOTION TOURNAMENTS IN RELIGIOUS ORGANIZ ATIONS : CHOOSING

THE NEXT POPE

L ív io L u iz So a re s d e O liv ei ra - Ec o nom is t a nd R es ea r c h er f or th e F u nd aç ão de Ec o n om ia e Es t at ís tic a - F E E. E- m ai l: li v i o @f e e. tc h e .br .

G iá co m o B alb in o t o N et t o - Pr of . of t h e P os t - G r ad u at e Pr o gr am i n A p p li e d Ec on om ic s ( PG P A E) o f th e F e d er a l U n i ve r s i t y o f R io G r an d e d o S u l ( UF RG S) .

E- m ai l : g iac om o. ba l b i no tt o @ uf r gs . br .

AB ST R ACT

T his p a p er s h o ws a n ap p l ic a t io n of Pr om ot i on T o ur nam e nts to r e l ig i o us or g a n i za t io ns , whic h is a p pr opr i at e, es pec i a ll y i n t he c as e of h i gh l y r ank e d i ns t it u ti o ns s uc h as t h e C at h o lic C hur c h. W it h t h is obj ec t i v e, we s eek to v er if y th e s u it a b il i t y of th e u s e T our nam en ts i n r e l i gi o us or ga n i za t i on s , r eg ar d in g t he op t im al s tr uc t ur e of c on tr ac ts in or der to s e l ec t , as we l l as , to pr om ote c l er ic s . T wo m o de ls ar e a dd r e s s ed , m od if i ed f r om th e or i g in a ls , t hr o u gh t h e i nc l us io n of ps yc h ic i nc om e, b ot h wi t h t wo c l er ic s wi t h h om og e ne o us s k il ls . F in a l l y, we d is c us s t h e ad v a nt a ge s a nd l im ita t io ns of th e T o ur n am en ts a pp l i e d to r e l i g io us or g a n i za t io ns , i nc l u d in g i ts r is k s a nd d is t or t i on s t h er e i n .

Ke y W o r d s: R el i g io u s O r g a n i za t io ns , Ca th o lic C h ur c h, T our n am ents .

J EL Cl a ss if i c at i o n : J 33 , M 5.

1. I NT RO D UCT IO N

A l l r e l ig i o us or g an i za t i on , as an y ot h er f ir m , ha v e t h ei r o b j ec t i ves , am ong wh ic h a r e wa ys t o a tt r ac t n e w c o n ver ts . T o a tt a i n t he ir a im s , e ac h r e l i gi o us or g a n i za t io n is e nd o we d wi th a d i ver s it y of o p ti o ns am on g s e v er a l or g a n i za t io n a l s tr a t eg i es . T o be s uc c es s f u l in ac h i e vi n g t hes e o bj ec t i ves wi l l be c on d it i o ne d, i n gr e at m eas ur e , t o th e s k i l ls a nd per f o r m anc e of th os e wh o ar e r es po ns i bl e f or th e l ea d er s hi p of th e or ga n i za t i on , r eg ar d in g t h e c om m itm ent of t hes e per s o ns wit h wha t h a s be en pl a nn e d. It is of the u tm os t im por ta nc e f or t h e r e l i gi o us f ir m th at i ts c l er ic s , i n t he ir s e v er al h ier ar c h ic a l l e ve ls , s up er i or s a nd s ub or d in a tes , ex er c is e a l e v e l of ef f or t s u i ta b le wi th th e r es u l ts ex pec t ed f r om eac h o n e of t h em .

T he c o n tr ac ts es t ab l is he d be t we e n r e l i g io us or ga n i za t io ns a nd i ts c l er ic s ( wor k er s ) m a y be i n s er t e d i n t he ap pr o a c h of th e p r i nc i pa l - a ge n t pr ob l em . W ithi n t his c o nt ex t , t h e f ir m wou l d be th e p r i nc i p a l a n d i ts c ler ic s , t he ag e nts . T her ef or e , ac c or d i ng to Z ec h ( 2 00 1 , p . 32 8 ) th is r e l at i o ns h i p pr i nc ip a l - ag e nt wo u ld no t b e im m une t o pr ob l em s s uc h as m or al ha za r d – i n t he c as e of s h ir k i n g b e ha v i or on t he p ar t of th e wor k er s – a d v er s e s e lec t io n – wit h h id d en i nf or ma t io n – a nd d is l od g em ent of o bj ec t i ve s – wh er e t he wor k er s m igh t ex er t an ef f or t , b u t i n ac t i v it i es wh ic h ar e n ot t hos e h a vi n g pr i or i t y f or th e f ir m .

T he c l er ic s , i n th e la c k of appr o pr ia te i nc en t i ves , wo u ld r a th er r ed uc e th e ir ef f or ts t o a m in i m um , ac ti n g i n th e ir o wn b e nef it . T hes e p r ob l em s ten d to bec om e wor s e wh e n t he m on it or i ng c os t s ar e h i gh . E v id e nt l y, t h e m or e de t ai l e d an d c om pl et e t h e c on tr ac t b et we en t he a g en t a nd t he pr i nc i p a l, t he ne ar er t h e y wi l l be t o t he o pt im um r el at i v it y of th e e qu at i o n in g of t he i nt er es t of bo t h p ar t i es in v o l ve d i n t he c on tr ac t u al r e l a ti o ns h i p, th is m ea ns , a “first-best”

c on tr ac t . Ho we v er , t h is c o ntr ac t wo u ld b e c on d it i on e d t o th e n on e x is t e nc e of h id d en i n for m at i on, t o m easurability and to the observability of the agent’s be h a v ior , t h e abs e nc e of r is k or of r e d uc e d r is k , as we l l as t h e pos s i bi l i t y of t h e pr inc i p al im pos in g s e v er e p e n al t ies o n t he a ge n t, i n th e c as e of t he a g en t n ot

c om pl yi n g wi th t h e c o ntr ac t . W hen t his is no t p os s ib l e, t h e a lt e r na t i ve is to create a “s ec on d - b es t” c o ntr ac t.

Af t er t his i ntr o duc t i on , we d is c us s i n s ec t io n 2 , i n i ti a l l y, th e ap pr o pr i a te n es s of T our n am ents f or r el i g i ous or g an i za t i o ns , r eg ar d in g th e s e lec t io n a nd pr om ot i on of th e ir c l er g y. In s ec t i on 3 , we d is c us s th e is s u e of op t im al c on tr ac t f or c l er ic s , wh er e t wo m od e l , m od if ie d f r om th e o r i g i na l , thr o ug h t he i nc l us i on of no n- m on et ar y i nc o m e or ps yc h ic i nc om e , bot h wi th t wo c l er ic s s k i l ls a nd a h o m ogen e o us p has e : a s im pl e m ode l an d o th er m ode l wi th hum an c a p it a l i n v es tm en t r el i g io us . I n t h e n e x t t op ic we d is c us s t h e a d v an t ag es an d l im it at i ons of th e T heor y of T o ur n am en t s , inc l ud i n g its r is k s a nd d is tor t io ns th er e i n . F i n al l y, th e c o nc lu d in g r em ar k s wi ll be m ad e .

2. P ro m o t i o n T o u rn a m en t s f o r r e l ig i o u s o rg an iz at io n s.

Re l i gi o us or g a n i za t io ns¹, f r om th e po i nt of v i e w of t h e T h eor y of Re l i gi o us M ar k ets , wh ic h is o n e of t h e f u nd am en ta l p il l ar s of Ec on om ic s of Re l i gi o n , ar e tr ea te d as b us in es s es t ab l is h m ents i n t h e m ar k et th at s e ek to m ax im i ze th e ir u ti l i ti es thr o u g h th e s u pp l y of r e li g i ous go o ds a nd s e r v ic es . Hu l l an d Bo l d ( 19 8 9 ) m ode l ed c hu r c h es , a c las s i c a l r e l i gi o us or g an i za t i on , as f i r m s de d ic at ed n ot o n l y to pr o d uc t i o n b u t t o th e pr o p a ga t io n of t he ir d oc tr i nes , s uc h as T he T en C om m and m ents , th er ef or e , r e d u c i ng t he c os ts of tr a ns ac t i ons i n th e s oc ie t y thr o u gh t h e ap p lic a ti o n of a s ys tem o f l a ws .

T he m ax i m i za t io n of th e ut i l it y of r e l i g i ous f ir m s is r e ac h ed wh e n, bes i d es t h e n u m ber of c hu r c h g oer s , or be l i e v er s , s e ek f or g o ver n m ent s u p po r t or ot her i ns ti t ut i on a l c on d it i o ns , wi t h t h e p ur p os e of a l lo wi n g th em to k ee p or ex p a nd t h e ir p ar t ic i p at i on i n th e m ar k et. In th is r e g ar d , as f ir m s , it is f un dam en t al to i n ves t i ga t e h o w r e li g i ous o r ga n i za t i ons , k ee p in g th is a im in v i e w, s tr uc t ur e l ab or c on tr ac ts f or t h e ir em pl o ye es , i n or d er t o c r e at e i nc e nt i v e m ec han is m s to in d uc e t hes e em p lo ye e s t o f ur t h er ef f or ts , a n d f or th em to

1 Th e f i r m r e l i g i o u s , f r o m t h e p e r s p e c t i v e o f E c o n o m i c s o f R e l i g i o n , i s n o t h i n g m o r e t h a n a r e l i g i o u s o r g a n i z a t i o n t h a t p r o v i d e s g o o d s a n d r e l i g i o u s s e r v i c e s .

c oo p er at e wi th t he t ar ge ts of th es e f ir m s . In th i s s e ns e , it is f u nd am en ta l to un d er s t a nd t h e f u n c t i on i ng of th e i nt er n a l la b or m ar k et of th e r e l ig i o us or g a n i za t io ns , m ai n l y of t hos e wh ic h h a v e be e n s uc c es s f u l i n c o nq u er in g t he r e li g i ous m ar k et.

Her e , t h e c a s e of t h e Rom an C at h ol ic C hu r c h s t r ik es th e e ye . I t i s a s u i ge n er is or g a n i za t io n wi t h ne ar l y t wo m i l le n n ia of h is t or y, s uc c es s f ul , t o s uc h a po i nt t h at , no wa d a ys , it h as o v er o n e bi l l i on be l i e ve r s s pr e a d a l l o v er th e wo r ld . A nd s om et h i ng t ha t is pec u l ia r t o i t, in vi e w of t he s i ze of th e r e l i g i ous m ar k et it ho l ds : i t pos s es s es a u n i qu e c e ntr a l le a d er s h i p i n t h e f i gur e o f the R om an P on t if f , d if f er e n t f r om Pr o tes ta n tis m , wi t h t ho us an ds of de n om in at i ons . It c a n be p o i nt ed o u t o t her r e li g i ons t ha t h a ve h a d a s im i lar s uc c es s i n c on q ue r i n g t h e r e li g i ous m ar k et. Am on g th em is Is l am , wi t h a ls o m or e t ha n o ne b i l l io n f ol l o wer s , wi t h a f ar l at er da t e of f o un d at i o n t h an Ca t ho l ic is m , wh ic h i nd ic at es th at i t c a p tur e d an i d en t ic a l am ou nt of f o ll o wer s , or b e li e v er s , i n a s h or t er i n r e la t io n t o th e r e l i gi o u s m ar k et c a pt ur e d b y th e C at ho l ic s . Ho we v e r , it do es n ot pos s es s a u n if i e d l e ad er s h ip an d, bes i de s , it p r es e nts s e v er a l doc tr in ar y c ur r en ts , b e i ng t h e m a in o n es S u nn i a n d S h ia². Am on g t he di v er s e o pt i ons f or th e a p p lic a ti o n of t he Pr om ot i o n T our nam e nts t o r el i g i ou s or g a n i za t i ons , t he Ca th o l ic Ch ur c h a pp e a r ed t o us as t h e m os t s u it ab l e f or th e f o ll o wi ng r eas o ns .

In t h e c as e of th e C at ho l ic C h ur c h , t he s it u a ti o n is d if f er en t i n r e l a ti o n to ot h er r e l ig i ous s e gm en ts . It is tr u e th a t t h er e is s p ac e t o ac c om m odat e r e li g i ous or der s wi th d if f er e nt r u les i n i ts m ids t , b ut t h is o n l y c a n be do n e wit h th e e n dor s em en t of th e H ol y S ee³. D if f er e n t to t h e c as e of Pr o te s ta nt is m , th at l ac k s a u n iq u e l ea d er s h ip a nd is s u b d i vi d e d in t o n um er o us d en o m inat i o ns , a

2 Th e Mu s l i m c a l e n d a r b e g i n s wi t h t h e H i j r a ( e m i g r a t i o n ) , o r e s c a p e o f t h e p r o p h e t M u h a m m a d , i n 6 2 2 d C , t o Me d i n a . S t a r k ( 2 0 0 3 , p . 2 9 - 3 1 ) d e v e l o p s , i n a c o n d e n s e d w a y , t h e i s s u e o f t h e f r a g m e n t a t i o n o f I s l a m i n t o s e v e r a l s e c t s , a p h e n o m e n o n t h a t b e g a n t o t a k e p l a c e r i g h t f r o m t h e b e g i n n i n g .

3 C a n o n 3 6 1 o f t h e 1 9 8 3 C o d e o f C a n o n L a w ( C C L 1 9 8 3 ) d e f i n e s wh a t i s A p o s t o l i c S e e o r H o l y S e e : “I n t h i s C o d e , t h e t e r m A p o s t o l i c S e e o r H o l y S e e r e f e r s n o t o n l y t o t h e R o m a n P o n t i f f b u t a l s o t o t h e S e c r e t a r i a t o f S t a t e , t h e C o u n c i l f o r t h e P u b l i c A f f a i r s o f t h e C h u r c h , a n d o t h e r i n s t i t u t e s o f t h e R o m a n C u r i a , u n l e s s i t i s o t h e r wi s e a p p a r e n t f r o m t h e n a t u r e o f t h e m a t t e r o r t h e c o n t e x t o f t h e wo r d s”.

.

ph e nom e no n t ha t c on t in u es oc c ur r in g . T he d oc tr i nes f or m u la te d wi th i n Ca th o l ic is m nee d th e en d or s em ent of th e R om an Po n tif f t o b ec om e a dm it te d b y its c l er ic s a nd i ts f a i thf u l . E ve n t he d i v er s if ic at i o n of th e Ca t h o lic r e l i g io us s er v ic es , as it h a p pe ns wit h t he or ie n ta l li tur g i c a l r it es , am on g wh ic h ar e t he Ma r o n it e, Co pt ic a n d S yr i ac , d if f er en t f r om th e L at i n r i t es , ar e c o ntr o l le d a n d supervised by the Holy See, that regulates the functioning of all its “branches”

s c at ter e d t hr ou g ho u t t he wo r l d , b e t h e y of t he L at i n or th e eas t er n r it es . T h e d if f er e nt i at i on of r e li g i ous pr o duc ts is l ar g e wi t hi n th e c at h o l ic m ar k et, bu t t h is is also a “m ar k e t - s ha r e” strategy. The Catholic Church is the most successful m ult in at i o na l f ir m in t he wor ld , wi t h a lm os t t wo th o us a n d ye a r s ex p er i enc e i n th e i nt er n at i on a l r e l ig i ous m ar k et.

Cer ta i n l y, th e we ll - s u c c ee d ed c as e of th is l ar g e r e l i g io us or g a ni za t i on , wh ic h has s ur v i v e d t h e pas s i n g of th e c e nt ur ies , en d o we d wi th s o li d i nt er na l s up p or t s tr uc t ur es f or th e c o nq u er in g a nd m ain te n anc e of its ma r k e t - s h ar e.

Ex t er n al f ac t or s , s uc h as t h e s up p or t a n d f a v or of s ec u lar g o ver n or s , a ls o c on tr ib u te d t o t h is , b u t h er e we do no t i nt e nd to t e l l t he s t or y of th e Ca t ho l ic Ch ur c h p er s e u n der th e p o in t of v i e w of t he T h eor y of the Re l i g io us M ar k et . T he o bj ec t i v e h e r e i s an o th er on e: t he i n ves t ig at i o n of t h e i nt er na l l ab or m ar k et of th e C at ho l i c Ch ur c h an d i ts inc en t i ve m ec ha n is m s , i n t h e f or m of op t im al c on tr ac ts , i n wh at c o nc er ns its h ier ar c h ic a l d yn am ic s , c h o ic e a nd pr om ot i o n of i ts c l er ic s u nd er t he f oc us of t he Pr om ot i o n T o ur n a m ents T h eor y or T o ur na m en ts.

A nd wh y T o ur n am e nts an d no t s t an d ar d l ab or c o ntr ac ts , as , f or e x am pl e, pa y b y pr o duc t io n ? B ec a us e t h e i nt er na l m ar k et of a lar g e s i ze d r e l i g io us or g a n i za t io n , s uc h as the Ca th o l ic C hur c h , as we l l as t h at of l ar g e s ec u l ar or g a n i za t io ns ( f i r m s an d c or por at i o ns ) , i t pos s es s s i ng u l ar s t r uc t ur es wi th s pec if ic s o l ut i ons , r eg ar d i n g t he es ta b l is hm en t of op t im al c o n tr ac ts , als o wi t h s pec if ic i nc en t i ve m ec ha n is m s , wi t h t he a im of s tim u la t in g t h e d i l i ge nc e of i ts wor k er s in t h e c om pl i anc e of t he ir du t ies . It a ls o s e ek s to c h oo s e th e b es t c an d i da tes f or th e d if f er e n t hi er ar c hic a l l e v e ls , pr i nc i p a ll y f or th e p os i t io n t ha t

is a t t he to p of th e C a th o l ic h i er ar c h y, oc c u p ie d b y th e R om an P o nt if f . Her e , is es s e n ti a l to r em em ber th at o n e of t h e m ai n c har ac ter is t ic s of t h e T o ur n a m en ts is t ha t t his m ec h a nis m s eek s f or the s e l ec ti o n of th e b es t c an d i da t es f or th e v ac a nc i es ex is t in g i n a c o r p or at i on . T h er ef or e , t h is is a s uf f ic i e nt l y es s e n ti a l j us t if ic at i o n f or t h e ap p lic a ti o n of T o ur n a m e nts f o r t he c h o ic e a n d pr om oti o n of th e c l er ic s i n t he C at h o lic C h ur c h.

A no th er f ac t s h ou l d b e m ent io n ed t h at r ec om m ends th e a pp l ic at i on of t he pr om ot i o n t our n am ent s to th e c as e of t he r e l ig i o us or g an i za t i o ns : th e ef f ec ts of c om m on n ois es o ver i ts wor k er s , ( as , f or i n s ta nc e, t h e a do pt i o n o f go ver nm en t r eg u l at i on m eas ur es f or t h e r e l ig i ous m ar k et) , ar e h ig h . T his wou l d im p l y an o th er f a v or ab l e ad v an t ag e f or t he a pp l i anc e of pr om ot io n to ur n am en ts in r e li g i ous or g a n i za t io ns o v er o th er f or m s of r e m uner a t i on .

T hus , it is a ls o ap pr o pr ia te to s a y t h at t h e pr i nc i p les th at r e gu l at e t h e r em un er a t io n s of th e C at h o lic c l er g y, as in th e c as e of ot h er lar g e or g a n i za t io ns , t he y ar e n ot l i nk ed , d ir ec t l y, to s om e c om pet i t i ve l og ic bo u n d t o th e r el i g io us m ar k et. T he h i er a r c h ic a l d yn am ic s of th e C a th o lic C hur c h, i nc l u d in g t he ir pr om ot i on s ys t em , h i er ar c h ic a l l e v els wi th t h ei r r es p ec t i v e r i gh ts an d d u ti es , a nd , a bo v e a l l, t h ei r r em un er at i on s , d o n ot de p en d m er e l y on t h e pr o d u c t i v i t y of th es e wor k er s . T hes e f ac ts ar e f u n dam en t al as s u m ptio ns of t he Pr om oti o n T o ur nam e nt s .

F or t h e qu es t i o n of es ta b l is h e d r em un er at i o n s in th e r e li g i ous m a r k et, it is im por t a nt t o em ph as i ze th a t t h e y ar e n ot m er e l y m on e tar y r em une r a t io n s , s i nc e t he r e ar e C at ho l ic c l er ic s ( as a ls o is t he c as e of m an y pr ot es t a nt c l er ic s of dif f er e nt de n om in at i ons ) wh o d o no t r ec e i ve an y s or t of m onet ar y inc om e, am ong th em the pr ies t s wh o tak e a v o w of po ver t y. T he r em u ner at i on f or t h is k ind of wor k er is g i v e n, a bo v e a ll , i n t h e f or m of ps yc h ic i nc om e ( no n - m on et ar y i nc om e) , as we s h al l s ee la te r . It is a t yp e of r em un er a t io n r e la te d t o t h e r ec o g n it i on of th e p ub l ic , s t at us, p r i v i l eg es , be n ef i ts , f ee l i ngs of a v i ta l m is s i on ac c om p l is h e d, m ean i n g, ex is te n ti a l p ur pos e, e tc .

W hen th e r em uner a t io n s of t h e h i gh er h ie r a r c h ic a l l e ve ls of th e C at h ol ic c l er ic s ar e obs er v ed , c om par in g th em to t h o s e of t h e l o wer l e v els , we r e ac h th e c onc l us io n th a t t he r e ex is ts a s ig n if ic a nt r em une r a t io n d if f er e nt i a l wit h i n t h e Ca th o l ic C h ur c h . T h is d if f er e nt i al c a n no t b e m er e l y ex pl a i ne d b y t h e pr o d uc t i v i t y of its c l er ic s bec a us e , as a m at ter of f ac t , t he ir l e v el , i n t er m s of hum an c a p it a l, is q u it e h om og en e ous . T he f or m ati on of c l er ic s in th e C at h o lic tr a i n in g s c h o o ls f or p r i es t ho o d, s pr ea d t hr ou g ho u t t he wor l d, is s ta nd ar d i ze d an d r eg u l at ed b y C a n on ic La w. T h er ef or e , th e f ac t th at a h i g h - r a nk in g C at h o lic c l er ic r ec e i v es r em u n er a t io n , e v e n if n ot n ec es s ar i l y in m one y, m uc h h ig h er th a n h is s ub or d in a te , i s n ot r ed uc ed t o a q u e s ti o n of pr o d uc t i v it y d i f f er en ti a l.

W ic h ar e th e f u nd am ent a l f ea tur es of t he T our n am ents , wh ic h m ak e this m ec han is m ap pr o pr i at e f or th e s t ud y of the op t im um c ontr ac ts f or wor k er s of a r e li g i ous or g a n i za t io n s uc h as th e C at ho l ic C hur c h ? T h e y ar e t he f o l lo wi n g :

( a) D is tr i b ut i on an d t h e m agn it u de of th e r e m uner at i on s ar e es t ab l is h e d a pr io r i an d ar e n ot r e l at e d to t h e abs o l ut e p er f or m anc e of t h e wo r k er .

( b) T h e r ec e i v in g of t he r em une r a t io n s is r e la te d t o a n as s es s m en t of r e la t i ve per f o r m anc e ( RP E – r e la t iv e per fo r ma nc e ev a lu at i o n)

( c ) T he ef f or t of t he wor k er s in a pr om o ti o n t ou r n am en t is d i r ec t l y c on n ec t e d t o th e r em uner a ti o n d if f er e nt i a l. T he hi g her t h is is , t he s tr o n g er wi l l be t h e ef f or t t o o bt a in th e pr i ze .

Re g ar d i n g f e at ur e ( c ) , i t m us t b e p oi n te d o ut t ha t t he i nc e nt i v e s ys tem w i l l be m uc h m or e ef f ic ie n t whe n th e p ar t ic i pa n ts of t he T o ur nam en t a r e m or e hom og e n eo us . If t h e r e is h et er o ge n ei t y r e gar d i ng t h e l e ve l of p r od uc ti v i t y of th e wor k er s , t her e m ig ht b e a f or m at i on of c o ll us i ons a n d s h ir k i ng be h a v ior t h at wo u ld dim i n is h t h e ef f i c i enc y of t he inc e nt i v e s .

K ee p i ng t hes e c o ns id er a t io ns i n m i nd , it m a y be ar g ue d i n f a v or of t h e us e of th e T our n am en t s , wi th th e a im of ex p la i n in g s om e of t he pr o p er t i es of th e in t er n a l la b or m ar k et of r e li g i ous or ga n i za t i ons s uc h as th e C at h o li c Ch ur c h. T h is t he or et ic a l m od el is a ls o a ppr o pr ia te , as we s h a l l s e e, i n or der t o

ex p l a in t he r em un er at i on m ec h a n is m s ado p te d b y r e l i gi o us o r g a n i za t i ons wi t h th e o bj ec t i ve of r e wa r d in g its c ler ic s . T his is or di n ar i l y d on e thr ou g h t he pr om ot i o n of t he c ler ic s to a h i g her h i er a r c h ic a l or d er , wit h i t s r es pec t i v e be n ef i ts , b e th e y m o n et ar y r em un er at i on s o r n o n - m one t ar y, wh er e th is r e wa r d is c o nd i ti o n ed t o th e r e l at i v e pe r f or m anc e of t h e c l er ic s , h ar ne s s ed t o t he ir r es p ec ti v e ef f or t l e ve l s .

T he l e v el of pa ym en t b y pr od uc t io n is no t a r u le i n th e s a l ar y s tr uc tur e of th e i nt er na l l a bor m ar k ets of r e l i g io us or ga n i za t i ons , v is - à- v is th e i nt r i ns ic d if f ic u lt i es i n m eas ur i ng t he pr o duc t i v it y of th e wor k er s of t h es e or g a n i za t io ns , m ain l y, t h os e es t ab l i s he d b y t he St at e . B es i d es , a ls o c o ns id er in g f ac t or s i n vo l v i ng m or a l h a zar d a n d as ym m etr ic i nf or m at io n, i t m a y b e c onc l u de d t h at th e T o ur nam e nt m o de l , wi th its p r om ot i ons as a s t im ul us m ec h a n is m to o b ta i n th e m ax im um per f or m anc e of t h e wor k e r s , is an ap pr opr i at e th e o r e t ic a l f r am ewor k . T his is bec a us e T our n am ent m ode l ex p l a in s h o w t o es t ab l is h op t im al c on tr ac ts , b o th f o r t he c h o ic e a n d p r om ot i on of t h e c l er ic s f or t h e Ca th o l ic C hu r c h , a n d ot h er s im i lar r e l ig i o us or g a ni za t i o ns t ha t p o s s es s h i gh l y h ier ar c h ic a l s tr uc t ur es .

Z ec h ( 2 0 01 , p .3 3 1) a f f ir m s tha t Pr om ot i on T our n am ents c o ns t it ut e a n ap pr o pr i a te m ec h a nis m in or d er t o i nc en t i v at e t he f u lf il lm en t of th e c o nt r ac ts es t a bl is h ed be t we en t he c l er ic s ( or c an d i da tes ) an d r el i g io us or g an i za t i o ns . I n th is wa y, i n or d er to a t t e n d t o t he in t er es ts , bo t h of t hes e or g an i za ti o ns , as we l l as of t h e ir c l er ic s , pr om oti o n to ur n am ents m ight be us e d as a n a lt er n a ti v e t o ot h er inc e nt i v e pr ogr a m s , am ong ot h er s : ef f i c i enc y wa g e , s or t i ng – wh ic h s e ek s to s e l ec t o n l y th e w or k er s c om m itt ed wit h t h e pr io r i t ies of th e f ir m – a n d bac k l o ad i ng r em u ner a ti o n. I n th is l as t c as e , ac c or d in g t o Z ec h ( 20 0 1, p .3 3 1) , on e of th e m ea ns to i nc e nt i v at e th e c l er ic s to s tr i ve i n t h e ir f u n c ti o n, am on g ot h er s , wo ul d b e t o of f er a s at is f ac t or y r e ti r em ent pl a n t o th o s e who s t a n d o ut or d is t i n gu is h th em s el v es thr o ug h o ut t he ir r e li g i ous c a r e er s .

W ith th e a im of pr o pos i n g a n o p tim um inc e n ti v e m ec h an is m to th e wor k er s of a f ir m , i n v i e w of h ig h - m on it or i ng c os ts , t h e T our n a m ents T he or y

was d e ve l op e d s t ar ti n g f r om th e s em in a l w or k of La ze a r a n d R os e n ( 19 8 1) . T hos e au th or s ins p ir ed t h e m ode l pr es en te d h er e , b u t it is a pp l i ed to t h e s pec if ic c as e of r e l i g i ous or ga n i za t i ons . E v en i n t he c as e i n wh ic h t her e is n o ex p l ic it o bj ec t i ve of im p lem en t in g a pr om ot io n t our n am ent t o c h oos e i ts c ler ic s , i n pr ac t ic e, t h is c a n t ak e p lac e i n m an y s i t ua t io ns , ac c o r d i n g to La ze a r ( 1 9 98 , p. 2 4 9) .

Re g ar d i n g t h is po i nt , i t is per t in e nt t o p o in t ou t wh at was s a id b y B es a nk o, Dr a v on e, S h an l e y e Sc h a ef er ( 2 00 4, p . 5 00)

A n i m p o r t a n t w a y , i n w h i c h s u b j e c t i v e a s s e s s m e n t s a r e u s e d t o d e t e r m i n e t h e p a y m e n t o f e m p l o y e e s , i s p r o m o t i o n . I n m o s t e n t e r p r i s e s , p r o m o t i o n i n v o l v e s a r i s e i n s a l a r y , wh i c h m e a n s t h e e m p l o y e e s h a v e g r e a t e r i n c e n t i v e s t o t a k e a c t i o n , w h i c h wi l l i n c r e a s e t h e i r c h a n c e s o f b e i n g p r o m o t e d . H o we v e r , t h e c r i t e r i a f o r p r o m o t i o n a r e n o t w r i t t e n i n a n e x p l i c i t c o n t r a c t . I n s t e a d , t h e r e i s a g e n e r a l u n d e r s t a n d i n g , b e t we e n t h e e n t e r p r i s e a n d i t s e m p l o y e e s , r e g a r d i n g t h e t y p e o f a c t i o n s t h a t l e a d t o p r o m o t i o n s .

T his af f ir m ati o n c an b e ap p l ie d a de q ua t el y t o c on tr ac ts i n v ol v i n g c l er ic s an d r e l i g io us or g a ni za ti o ns s i nc e, in f ac t, t h er e is n o k in d of f or m a l c o ntr ac t , i n ge n er al , c on ta i n in g c l ear , pr e d et er m in e d phr as es , s p ec if yi n g wh ic h a r e th e c r it er i a or pr e - r e q u is it es dem a nd e d f or a c a nd i d at e to t he p as tor a l m in is tr y, f or ex am p le , t o b e pr o m oted . Q u it e t h e op p os it e; s i nc e t h e f ac t t ha t t he as s es s m e nts ar e n o n - ex p l ic it , th is i nd uc es th e par t ic ip a nts i n t he r e l i gi o us T our n am en t t o s eek t o p er f o r m the d ut i es ex p ec te d of th em , i n th e bes t wa y pos s i b le . I n t he f o l l o wi ng t o pic , we s ha l l pr es e nt t wo m od e l s of op t im al c on tr ac ts f or c l er ic s .

3. O p t im u m co n t r a ct s f o r t h e c le rg y

Her e, a s im pl e T o ur n am ents m od el wi l l b e pr es en te d , bas e d on L a ze ar an d R os e n ( 1 9 81) , bu t s l i gh t l y m od if i e d t hr o u gh t h e i nc l us i on of ps yc h ic i nc om e. T he o bj e c t i v e of th is pr oc ed ur e is th e m odif ic a t io n , f or t he pur p os e of th is wor k , t ha t c ons i der s a T o ur n am en t b et we e n t wo c l er ic s , wh o p os s es s hom og e n eo us s k il ls an d a b i l it i es , t o b e ap p l ie d t o t he c as e of a r e l ig i o us or g a n i za t io n , es p ec ia l l y, t he R om an Ca t ho l ic Ch ur c h an d r e l ig i o us f ir m s wit h s im il ar hi er ar c h ic a l s t r uc t ur es . F ur t h er o n, we s ha l l d is p l a y t he C âm ar a ( 20 0 2) m ode l, wh ic h i nc or p or at es h um an c ap i ta l , wit h o n e s t ag e an d t wo c ler ic s , a ls o m odif i e d b y th e i nc l u s i on of ps yc hic i nc o m e. In m od if i ed m o de l , r e l i g io us c ap i ta l s u bs ti t ut es h u m an c a p it a l.

3. 1. T he on e s t ag e s i m ple m o de l f or t wo c l e r ic s wi t h h om og en e ou s a b i li t ies .

La ze a r a nd R os e n ( 1 98 1) d i v i de t he p r o b l em of th e o pt im a l worker’s c on tr ac t in to t wo p ar t s . T he m ode l h er e pr es e n te d is a v er s io n t ha t c o ns id er s an o pt im al c o ntr ac t f o r c l er ic s . F ir s t, t he b eh a v i or of t h e c ler ic , wh o wis h es t o m ax im i ze t he pr i ze r e c e i ve d, is m od el e d. O nc e th is b e h a v ior is u nd er s to o d, we pr oc e e d b y m od e li n g t he b eh a v i or of t he r e l i g io us o r g a ni za t i o n, wh ic h wan ts t o m ax im i ze t he ir pr of it ( i n t he c as e i n po i nt , th e n um ber of f ai thf u l/ be l i e ve r s ) , tak i ng i nt o ac c o un t t h e b eh a v i or of t he wor k er , i n or de r to o bt a i n a n o pt im um c on tr ac t .

Le t us c ons i d er a r e li g i ous f ir m wi t h t wo f unc t io n a l c ol l oc at i ons : s up er v is or c ler ic [ e. g .: B is ho p ( of t he Ca t ho l ic or pr o tes t an t c h ur c h es)] an d aux i l i ar y c ler ic [ par is h pr ies t or pr ies t ( in t h e C at h o l ic C h ur c h) or pas t or ( in t he pr o t es t an t c hur c h es ) ] . T wo hom o ge n eo us i nd i v i du a ls , th is is , w it h id e nt ic a l ab i l it i es a n d a n id en t ic a l l e ve l of r e li g io us c a p it a l, c om pet e b e t wee n

th em s el v es . W hoev er wi ns , wi ll o bt a in th e p os t of s up er v is or , s u p er in te n d en t or B is h o p⁴, r ec e i vi n g a pr i ze or r em un er at i on .

T his r em u ner a ti o n as s um es t wo d if f er en t f or m s : m onet ar y inc o m e and no n- m on et ar y inc om e [ac c or d i n g to Dur k i n an d G r e e l e y ( 1 99 1) , wh o c a l l th is i nc om e ( ), r el a ti v e t o p ur p os e a nd m ean i n g] . T his n on - m one t ar y i nc om e is a ls o k n o wn as ps yc h i c i nc om e ac c or d in g t o T hur o w ( 1 9 7 8) a n d Z ec h ( 2 0 0 1, p. 3 31 ; 20 0 7, p. 7 38) , or ig i n at i ng i n s ta tu s , pr i v i l eg es , us e o f tit l es an d i ns i g n ias , s at is f ac t io n i n p le as in g a n d s er v in g G o d an d f e ll o w m en , t es t im on y of et er na l s a l v at i o n thr o u gh a f a i thf u l l y pr of es s ed pr i es th o od , e tc⁵.

This is a necessary modification to Lazear and Rosen’s model for the c as e of o pt im al c o ntr a c ts f or c ler ic s , whe r e we as s um e her e th at t hes e m en , as r e li g i ous p eo p l e t h at t he y ar e, d o no t c om p e te f or t he p os t of s u p e r v is or h a v i ng as a n ex c lus i v e pr i or it y t h e m on et ar y r em un er a t io n, nor for “luxury parachutes”.

W e m ent io n t his bec a us e , f or ex am p le , i n s om e c as es , ec c l es i a s tic m in is t er s wi l l o n l y r ec ei v e a m on e tar y s a l ar y af t er h a v in g c l im be d s e v er a l h i er ar c h ic a l s te ps , s uc h as i n s om e pr o tes t an t d en o m inat i o ns . T her ef or e, t h e m ain obj ec t i v e of t h e p ar t ic i pa nts i n t he T o ur n a m en t m ig ht be , n ot f or th e r ec e i v in g of a m on et ar y i nc om e bu t d ue t o t he p r es t ig e or s t at us of t h e pos t i n d is pu t e or e ve n f or ex c l us i v e l y s p ir i t ua l m oti v e s .

In s e ver a l pr o tes t an t de n om in at i ons , f or ins ta nc e, t h e i n it i a l h i er a r c h ic a l s ta g es of t h e ec c l es i as t ic c ar eer d o n o t c onf er t h e wor k er s a n y r ec ei v i n g of s a lar y or m one t ar y r e m uner at i on , as i n th e c as e of th e I nt er n at i o na l Ch ur c h of th e F o ur s qu ar e G os p e l ( IC F G ) . Bef or e b ec o m ing l oc a l p as t or s , t h e c an d i da tes to b ec om e pas tor s i n t h is de n om in at i o n, n or m all y m us t g o thr o u gh the s ta g es of de ac on , wor k er , c an d id at e to t he m in is tr y a n d , on l y th e n, t h e y r eac h th e f unc t i o n of P as tor , e v en r e ac h in g t he p os it i on s of S up er i nt e nd e nt a nd N at i o na l Dir ec tor .

4 The original word in Greek, “bishop” (episkopos), means supervisor, inspector.

5 S e e a l s o S a v y c h , 2 0 0 5 , p . 5 5 - 6 3 .

In t h e c as e of t he de ac o n s , th e y ha v e, am on g s om e of t he ir f u n c ti o ns , no t on l y i n t h e I nt er n a ti o na l C hur c h of th e F our s q u ar e G os p el , bu t a ls o i n ot he r pr o t es t an t d e nom i na t i ons , t he du t y of as s i s ti n g t he pas t or o r lo c a l l ea d er i n at te n d in g t o an d f or w ar d i n g t he d em an ds of th e f o l lo we r s , r ec e i v in g v is it or s , c o ll ec ti n g of f er in gs a nd t i th i n gs , i n t he d i s tr i b ut i o n of t h e br e a d a nd wi ne – when celebrating the Eucharist or Sacrament of the Lord’s Supper or Holy Com m uni o n – am on g ot h er d ut i es . T h e wor k er or as s is t a nt gi v es s up p or t to th e pas t or b y l e ad i n g m eet i ngs i n f am i l y h o us e s , vis i t in g th e s ic k an d m in is t er i ng sermons in recently opened congregations or “preaching points”. Only those wh o h a ve m aj or ed in t he T he o l og ic a l Ins t it ut e of th e In t er n a ti o na l Ch ur c h of th e F o ur s q u ar e G os p el c a n b ec om e loc a l p as tor s . T he c a n d id at es t o th e p as t or a l m inis tr y ar e wor k er s w it h a t l eas t f o ur ye a r s ex p er i enc e a nd m us t be c om p et en t pr e ac h er s , b e in g a b le to s u bs t i tu t e t h e l oc a l m inis ter in c as e of ab s enc e . No n e of th e t hr ee pr e v io us l y m e n ti o ne d pos i t io ns , th at is t o s a y, wor k er , d eac o n a n d c an d i da te to th e m in i s tr y e nt a i l th e p r i v i l e ge of r ec e i v i ng s a lar y or m onet ar y r em un er a t io n , s i nc e t he p er s ons wh o oc c u p y t h es e p os ts , d o it v o lu n t ar i l y, wh ic h f u nc t i ons l ik e a T our n am en t. Af t er a c ti n g f or at l eas t t wo ye ar s as an as s is t an t p as t or , t he c an d i da te c a n tak e o n a loc a l c o n gr e g at i o n as a pas t or , an d on l y th e n, r ec e i v e a s a l ar y. Nor m a l l y, th is s a lar y is pr op or t i on at e to th e c o ll ec ti o n o r f un dr a i s i ng in t he c as e of t he I nt er n at i on a l C hur c h of th e F o ur s q u ar e G os p e l. T he t it l e d pas to r c an c on t in u e c l im bi ng t h e h ie r ar c h ic al p yr am i d, wh ic h wi ll de p en d of h is per f o r m anc e, an d oc c u p y th e p os t of S up er i nt en d en t, wh o is r es p o ns ib l e f or t he s u p er v is io n of s ev er a l c on gr e ga t io ns , a nd th en c o nt i nu e u n ti l oc c u p yi n g o n e of t he p os t s of Na ti o na l Dir ec tor of th e I nt er na t io n a l C h ur c h of t he F our s q ua r e G os p e l, wh o ar e r es p o ns ib l e f or th e g e ner a l s tr at e gi es f or t h e g o ver nm en t of t h e I CF G⁶.

A no th er j us t if ic a t io n f or t he i nc or p or at i o n of ps yc h ic inc om e to th e La ze a r m ode l is t h at t her e ar e s i t ua t io ns i n wh ic h i t is d em an de d, f or ex am pl e, as a c o nd i t io n t o en t e r a C at h o l ic r e l i g io us or d er , am o ng wh ic h, a n I ns t i tu t e of

6 I n f o r m a t i o n a t h t t p : / / s u p e r . a b r i l . c o m . b r / s u p e r a r q u i v o / 2 0 0 4 / c o n t e u d o _ 3 1 3 5 2 9 s h t m l d o c u m e n t c o n s u l t e d o n 0 8 / 2 3 / 2 0 1 0

Co ns ec r a t ed Lif e, in th at th e c a n d id at e t o b ec om e a c l er ic m ak es a v o w of po v er t y ( to g et h er wi t h th e v o ws of c h as t it y a n d o be d i enc e) , g i vi n g u p or r en o u nc i n g a n y m on e tar y ga i n t ha t p er c ha nc e he m ig ht r ec ei v e , af ter h a v i ng s ubm it t ed to th e r e li g i ous r u l es , in f a vor of h is or d er ( C an o ns 5 7 3 , 6 00 a nd 6 68 o f t h e 1 9 8 3 C o d e o f C a n o n L a w - C C L 1 9 8 3) . I n s uc h c as es , t h e p ar t ic ip a nt of th e T our n am en t wi ll o nl y r ec e i v e ps yc h ic i nc om e, wit h ou t r ec e i v i ng m on et ar y s a lar y, a lt h ou g h th e ir m ater ia l s us te n anc e is g u ar a nt e e d b y th e r e l i g io us or d er . Mo n et ar y i nc om e ( s al ar y) s h a ll be de n om ina t ed a nd no n - m on e tar y i nc om e ( ps yc h ic i nc o m e) wi l l b e c a l le d . T her ef or e , t h e pr i ze of a s u p er v is o r or Bis h op wi l l be , wh er e r e pr es e nts th e r em un er at i o n of t h e c l er ic wh o wi ns th e pr om oti o n T our n a me nt . T he as s is ta nt wi l l r ec e i v e a pr i ze of , wh er e a n d c on s e q ue n tl y . E ac h pr i ze wi l l on l y b e r ec e i v ed af t er th e e nd of t he T ou r n a m ent.

Rem un er at i on s ar e d e ter m i ne d b ef or e t h e b eg i n ni n g of t he T ou r n am ent an d ar e b as ed on t h e f in a l r a nk i n g t ha t r ef l e c ts th e r e l at i v e p er f or m anc e of th e ag e nts i n v o l ve d i n th e d is p ut e . I n t h e c a s e of t he C a th o l ic C hur c h , t h os e r em un er a t io n s ar e f ix e d b ef or e h a nd in t h e bo d y of t h e ir c an o n ic l a w.

T he pr o ba b i l it y of wi n n in g t h e c o nt es t , t h at is t o s a y, of be i ng pr o m oted or o bt a in i ng t h e p os t i n d is p u te as t h e pr i ze , wi ll be r e l at e d to t h e l e ve l of ef f or t ex p e nd e d b y e ac h p a r tic i p an t, r e pr es e nt e d b y t h e r e l i g io us pr a c tic e an d th e r e li g i ous s er v ic e r en d er e d b y in d i v id u a l, b e s i des a r an d om s hoc k c om po ne nt . Cl as s if yi n g th e i n d i vi d ua ls e , we ha v e :

W her e a n d ar e th e i nd i v i du a l pr od uc ts , e ar e t he l e v e ls of r e li g i ous ef f or t of th e r es p ec ti v e i n d i vi d ua ls th a t in d ic at e th e ir s k i l l or a ver a g e pr o d uc t , pr e vi o us l y c h os e n b y t he c l er ic b ef or e t h e e ve nt ; a nd a r e wh i te

no is e ( ), t ha t i n d ic a t e t h e r a nd om f ac t or s⁷ th at af f ec t t he pr od u c t of eac h c l er ic .

E ac h c l er ic wis h to m ax im i ze t h e ir ex p ec t e d r es u l ts , i n or d er to ob t a in th e h ig h es t v a l ue pr i z e, g i v en b y . C o ns id er in g th e c as e of c l er i c , we h a v e:

( )( ) [ ( )]( ) ( )

W her e ( ) is t he pr o b ab i l it y of wi n ni n g t he t o ur n am en t a nd ( ) is th e c o n vex f u nc t i o n r e l at i v e to t h e c os t of e f f or t, i n o th er wor ds , a m on e tar y v a lu e as s oc ia te d t o par t ic u l ar l e v e l of ef f o r t. I n th e c as e of c l er i c s who t ak e a vo w of p o ve r t y, s u c h as t he c a n di d at es wh o s eek t o en ter s om e c at h o lic r e li g i ous or der s or I ns ti t ut es of Co ns ec r at ed Lif e , t ha t va l u e c o ul d be m eas ur ed b y th e s a l ar y t he c an d id at e t o th e pr i es t h o od wo u ld no t b e r ec ei v i ng , wh e n h e is ef f ec t i ve l y or da i n e d a n d be g i ns pr ac ti c i ng h is of f ic e , d u e to t he l os t op p or t u n it i es i n s ec u l a r l if e , e tc .

T he f i r s t or d er c o nd i ti ons f or c l er ic ar e g i ve n b y:

[( ) ( )]

( )

T he f ir s t or d er c on d it i ons s ta te d ab o v e i n di c at e, f or a m ax im um , th at th e s pr e a d b e t wee n pr i ze s ( wh er e pr i ze s as s u m e a m onet ar y an d a no n - m on et ar y

7 R e g a r d i n g r e l i g i o u s o r g a n i z a t i o n s s u c h a s t h e C a t h o l i c C h u r c h , t h o s e r a n d o m f a c t o r s c a n b e o f d i v e r s e t y p e s o r o r i g i n s , s u c h a s : a ) r e l i g i o u s f a c t o r s , a m o n g wh i c h t h e e m e r g e n c e o f n e w c o m p e t i t i v e r e l i g i o n s , s e c t s , d i v i s i o n o r s u b d i v i s i o n p r o c e s s e s , s c h i s m a n d / o r r u p t u r e s d u e t o d o c t r i n a r y / t h e o l o g i c a l d i v e r g e n c e s ; b ) p o l i t i c a l , s u c h a s t h e i n t e r v e n t i o n o f t h e g o v e r n m e n t i n t h e r e l i g i o u s m a r k e t , t h r o u g h r e g u l a t i o n , d e c r e e s , p e r s e c u t i o n , r e m o v a l o f r e l i g i o u s l i b e r t i e s , a l l i a n c e s wi t h g o v e r n m e n t s , s i g n i n g o f C o n c o r d a t s ; c ) s o c i o l o g i c a l , d e m o g r a p h i c a l a n d e c o n o m i c a l , s u c h a s s e c u l a r i z i n g t e n d e n c i e s , a m o n g w h i c h u r b a n i z a t i o n , i n d u s t r i a l i z a t i o n , a c c e l e r a t e d e c o n o m i c g r o wt h , r e c e s s i o n o r e c o n o m i c d e p r e s s i o n , s c i e n t i f i c a n d t e c h n o l o g i c a l a d v a n c e s , v a r i a t i o n s i n b i r t h r a t e , m o r t a l i t y a n d f e r t i l i t y , e t c . R e l i g i o u s o r g a n i z a t i o n s , i n m a n y c a s e s , d o n o t h a v e a n y t y p e o f c o n t r o l o v e r t h e s e r a n d o m f a c t o r s .

f or m ) , c al l ed a m ar gi n a l b e nef it of t h e ex er c is ed ef f or t , m eas ur e d in m o ne ta r y un i ts , t im es th e c h a n ge in th e pr o ba b i l it y of win n i ng t h e d is pu te d u e t o an ad d it i o na l un i t of ef f or t , is eq u al t o t he m ar g in a l c os t as s oc i at e d to th at ef f or t ex er c is e d b y . I n o t he r wor ds , t h is m eans t ha t wil l ex er c is e t h at ef f or t u p t o th e p o i nt in wh ic h h is m ar gi na l r et ur n, c onf e r r e d b y t h e s pr ea d be t we e n pr i ze s , bec om es e q ua l i ze d t o th e m ar g i n a l c os t r e l at ed t o t h e ef f or t i nc ur r ed i n th e d is p ut e .

As an i n d i vi d ua l , wi l l wi n th e c on t es t if t he l e ve l o f h is pr od uc t is h ig h e r th a n t h at of i n d i vi d ua l ; t h is is t o s a y if . T h er ef or e , th e pr o b a bi l i t y of wi n n in g wi l l be gi v e n b y:

( ) ( ) ( ) ( )

W her e is t h e d is tr i b ut i on f u nc t i on of t h e r a n dom var i a b le . P le as e tak e n ot e t ha t :

( )

( ),

W her e is th e de ns it y f u nc t i on . H o we v er , s i nc e i nd i v i du a ls a n d ar e i de nt ic a l ex - an te , th e r e is a s ym m etr ic a l Nas h e qu i l i br i um , wh er e a nd c ho os e th e s am e le v e l of ef f or t . T h is is b ec a us e it is c ons i d er ed t h at , wi th s im il ar i n d i vi d u als , t he eq u at i on ( 1) c a n be wr it t en as :

[( ) ( )] ( )

( ) ( )

T he eq u at i o n ab o v e h as t wo f u n d am ent a l i m plic at i o ns . T h e f ir s t is t h at th e h ig h er t h e s pr e a d b et we e n pr i ze s , bo t h in m one t ar y as in no n - m on et ar y ter m s , t h e h ar d er wi l l b e t h e eq u i li br i um ef f or t, s inc e ( ) is m o no to n ic a l l y

i nc r e as i ng in . A hi g h e r e l e va t io n i n t ha t s pr ea d , bo t h in t er m s of m onet ar y, as we l l as , n on - m one t ar y r em un er at i on , wo u l d in d uc e t he c om pe t i ng c l er ic s to s tr i v e pr o po r t i on at e l y m or e in t h e to ur nam en t .

B es i d es , it c a n b e o bs er v e d i n ( 2) t ha t a l o wer s pr ea d i n m on e tar y i nc om e c a n b e c om p ens a te d b y hi g he r s p r ea d i n no n- m on et ar y i nc om e an d v ic e - ver s a . E ve n if , t h is is , s pr ea d i n m one t ar y i nc om e is nu l l, whe n th e c a nd i da t es r ec e i v e eq u a l m on et ar y i nc o m e, or if th is is , e ve n if th e c a nd i da t es do n o t r ec e i v e a n y m on et a r y i nc om e, t h e s pr ea d i n ps yc h ic i nc om e m igh t be s u f f ic ie n t as a s t im ul us f or t h e ef f or t of th e c l er ic s par t ic ip a ti n g in t he pr om oti o n t o ur nam en t. S uc h is t he c as e of c at h ol ic c l er ic s wh o b e l on g t o I ns t i tu t es of C ons ec r at e d L if e, of th e R om an C at h o lic Ch ur c h, wh o m us t t ak e a v o w of po v er t y ( t o ge th er w it h t h os e of o b ed i enc e an d c has t it y) an d do n ot r ec e i v e a m onet ar y s a lar y. T h i s i s no t a r e as o n, f or a n o v ic e wh o en t er s a n or de r or a Ca th o l ic I ns t it u te of Cons ec r at e d L if e , f or e x am pl e, n o t to s eek bec om in g a h i gh - r ank i n g a bb ot wi th i n t h is or g a n i za t io n .

In ot her wor ds , wh e n d ea l i ng wi t h pr om oti o n t our n am ents ap p l ie d t o c l er ic s , th e s pr e ad i n m one tar y i nc om e m igh t be of l it t le im por t anc e or e v en , no t m ak e an y d if f er en c e a t a ll i n s tim u la t in g t h e c ler ic s to t he ef f or t. T h is is bec a us e , ac c or d in g t o t he ex ig e nc ies m ade to th os e who wis h t o d ed ic at e th em s el v es t ot a l l y t o a r e l i g io us l i f e, th e m os t s ig n if ic a nt f ac to r , i n or d er to ex tr ac t t he m ax im um p er f or m anc e f r om t he p ar t ic i p an ts of th e t o ur n am en t, m ight b e t h e ex p ans i o n in s pr ea d of th e ps yc h ic i nc om e a nd n ot a n inc r e as e i n m onet ar y r em un er at i o n , as it h a pp e ns i n s ec u lar o r g a ni za t i o n s .

In th es e, th e s tim u lus to i nc r eas e t h e ef f or t of th e wor k er s m a y c o m e not on l y f r om the s pr ea d of the m on et ar y inc om e bu t a ls o f r om non - m o ne ta r y i nc om e, i n f or m s s uc h as pr es t ig e , inf lu e nc e, h i er ar c h ic al p o wer an d s ta t us of th e j o b, pl ac ed as p r i ze s f or th e pr om ot i on to ur nam en t, f or e x am pl e. T h is i nd ic at es t ha t, b o th in t he c as e of s ec u lar o r ga n i za t i ons an d m a in l y i n t he c as e of r e l ig i ous or g an i za t i ons , t h e L a ze ar a nd R os e n t o ur nam en t m od e l wou l d n e e d to b e on l y m i n im al l y a da p te d, i n or d er t o i nc l ud e th e ps yc hic inc o m e as we ll , as

it is be i n g d o ne h er e an d , i n t h is wa y, b ec o m ing c los er to s i tu a ti o ns as th e on e be i n g de a lt wit h i n t h is p ap er . B es id es , it is n ec es s ar y t o tak e i nt o ac c ou n t th at , i n s it ua t io ns wh er e th e c l er i c d o es n ot r ec e i v e a m on et ar y i nc om e, t he im por ta nc e of i nc lu d e th e ps yc h ic i nc om e is c r uc i a l, i n or d er to s at is f y ( 1) an d ( 2) . O t h er wis e, t h e m ar gi na l c os t ex er c is e inc ur r e d in b y t he c l er ic wo ul d b e eq u a l to ze r o , i n wh ic h c as e a pr om ot io n t ou r nam en t wo u l d b e n on e x is t e nt .

T his s p r e a d in ps yc hi c i nc om e, as a s t im ul us t o a h ar de r ef f or t of th e c l er ic s , c a n be ex em p l if i ed , i n th e c as e of Chr is ti a n it y, b y a d ia l og u e be t we e n J es us C hr is t an d t h e A pos t le P et er . T h i s d i a lo g ue is f o u nd i n t he N e w T es tam en t⁸ ( Mt 19 : 27 - 3 0) . S im on Pe t er as k ed t h e M as t er wh at wo u ld h e, P et er , as a n in d i v id u a l, an d t h e o th er Ap os t l es r ec e i v e f or f ol l o wi ng Ch r is t, r e ve a l i ng t h at , i n f ac t, his o b ed i e nc e t o t he ap os to l ic s er v ic e was no t d e vo i d of i nt er es t or wi t ho ut c o nc r e t e o bj ec t i v es . T h is pas s a ge is pr et t y i l l us tr at i v e an d i nd ic at es th e wa y i n wh ic h J es us C hr is t s o ug h t t o i ns p ir e h is d i s c i pl es t o t h e ef f or t of c on q ue r i n g s ou ls f or t he Ki n g dom of G o d , k ee p i ng t h em m oti v at e d, in s p it e of t he h i g h c os t of th e ef f or t ar is i n g f r om a l l th e r es tr ic t i ons , r en o u nc em en ts or p er s ec u t io ns t he y m a y h a v e to un d er g o .

27 T he n P et er ans we r ed a nd s a i d t o H im , " S ee , we

ha v e l ef t al l a n d f o l lo we d Yo u . T h er ef or e , wh at s h a l l we ha v e ? " 2 8 S o J es us s a id t o t hem , " As s ur ed l y I s a y t o yo u th at , i n th e r e g en er at i on , wh e n th e So n of Ma n s i ts o n th e thr o ne of H is g l or y, yo u who h a ve f o l l o we d Me wi l l a ls o s i t on t we l v e t hr o n es , j ud g in g th e t we l v e tr i bes of Is r a e l. 2 9 An d e v er yo n e wh o h as l ef t h o us es or br ot h er s or s is t er s or f at h er or m o th er or wif e or c h i l dr e n or l an ds , f or M y n am e' s s ak e, s ha l l r ec e i ve a h u ndr e df o l d, a n d i nh er it

8 B r a m s ( 1 9 8 2 ) w a s a p i o n e e r i n t h e a p p l i c a t i o n o f t h e G a m e Th e o r y f o r t h e a n a l y s i s o f t h e H e b r e w B i b l e , wh i c h i s t h e O l d Te s t a m e n t o f t h e C h r i s t i a n B i b l e . I n t h i s c a s e , t h e s i t u a t i o n a n a l y z e d i s i n t h e N e w T e s t a m e n t .

et er na l l if e . 3 0 B ut m an y wh o ar e f ir s t wi l l b e l as t , an d t he l as t f ir s t .

Peter’s religious choice, when becoming a disciple of Christ, c har ac ter i ze d i n th is p as s a g e of t h e s c r i pt ur es , h a d a th e l eo l o gic a l⁹ b as is , t ha t is to s a y, it s o u gh t f or a def in i t i ve a im : to m ax im i ze h is ut i l it y. It was a r at i on a l c ho ic e in th e ec o n om ic s e ns e of th e ter m . It was no t a r e l i gi o us c h o ic e i n th e em in e nt l y we b ber i a n s e ns e of t he wor d, gu i d ed b y v a lu es^{1 0}. Chr is t m ak es a p o in t of c a l l i ng a tt e nt i on t o th e p er s pec t i ve of th e K i n gd o m of He a ve n:

th e m ax im i zi n g of th e ut i l it y i nt e nd e d b y P et er , a t pr es en t, wo u l d h a v e t o b e pos t po n ed . F ir s t, i t w ou l d be n ec es s a r y t o c op e wi t h th e c os t of t h e i n v es tm en t i n t h e Ki n g dom of H ea v e n, a t t h at m om ent i n tim e. L at er , i n t h e f u tur e, m ax im i zat i on of th e ut i l it y t hr o ug h e t er n a l lif e wou l d b e pos s i b le , i nc lu d in g t h e pr i vi l e ge of b e in g c o - r eg e nt to g et h er wit h Chr is t, s it t in g on th r o nes . C hr is t i nd ic at es t h at P et er s ho u l d n ot th i nk in a n i m m edia t e r e tu r n bu t, t o b e c on te n t, dur i n g h is l if e o n e ar t h , wi t h t h e m ax im i zat i o n of a f u tur e ex p ec t e d r et ur n .

Un d er th e p er s p ec ti v e of t h e c o nc e pt of c o m pens a t or s , as d ef i n e d i n t h e Ra t io n al C h o ic e ( St ar k and Ba i n br i d g e, 1 99 6, p .3 6) , it m ig ht b e s a id t ha t J es us Chr is t, i ns t e a d of t h e im m ed ia te r e war d s o ug h t b y P et er , o f f er ed h im a c om pens a tor . Ec c l es i as t ic a l h is t or y t e lls us tha t, i n s p it e of h a v in g d en i e d h is Mas t er at t he m om en t of h is tr i al , P et er ac c ep t ed t he c om pe ns at or i ns t ea d of th e im m ed ia te r e wa r d h e wis he d f o r a n d p er f or m ed , as a l e ad er , a n ex c el l e nt wor k f or t he C hur c h, e ve n be i n g c r uc if ie d bec a us e of h is f a i th . O n t h e o th er ha n d, a n ot h er of J e s us ´ s d is c ip l es , J ud a s , be tr a ye d C hr is t , r ej ec t in g t he

9 R e l a t i v e t o t h e f i n a l c a u s e s.

1 0 M a r i a n o ( 2 0 0 8 , p . 4 4 ) c i t e S t e p h e n S h a r o t ´ s a f f i r m a t i o n , w h o c o n s i d e r s t h a t t h e c o n c e p t o f r a t i o n a l i t y p r o p o s e d b y R o d n e y S t a r k , b a s e d u p o n t h e Th e o r y o f R a t i o n a l C h o i c e , h a s t o d o w i t h t y p e s o f a c t i o n r e l a t e d t o a i m s , o f a n e c o n o m i c s e i g n o r a g e , w h i c h m e a n s t h a t a n a g e n t m a xi m i z e s h i s g a i n s wi t h d e t e r m i n a t e o b j e c t i v e s . A c c o r d i n g t o S h a r o t ´ s i n t e r p r e t a t i o n , t h i s t y p e o f r a t i o n a l i t y , g u i d e d b y a i m s , wo u l d b e t h e o p p o s i t e t o t h e w e b b e r i a n r e l i g i o u s r a t i o n a l i t y , o r i e n t a t e d b y v a l u e s .

c om pens a t or of f er e d b y h is Mas te r , p r ef e r r i ng a n im m edi at e r e wa r d: 30 s i l ver c o ins .

T her ef or e , we c an p er c e i ve th a t t he d em and s , q u it e r ig i d an d s e v er e , in r e la t io n to t he a p o s to l ic s er v ic e , m ad e b y Chr is t, wh ic h c ou l d i nc l u d e ab a nd o n in g f am il y a n d pr o per t ies a nd , e v e n m ar t yr d om , wer e c o un t er b a l anc e d wi t h a h i g h le v e l pr o m is es . T h at , wh en f u l f i l le d, wo ul d c om pe ns a te ef f or ts a n d r es tr ic t io ns t o wh ic h the A pos t les wo u ld s ubm it t hem s e l ves in or d er t o ac c om p l is h t h e ir m is s i on . C hr is t di d no t pr om is e m ater i a l r ic h es or f in a nc ia l r em un er a t io n t o h is A pos t les d ur i n g t h is l if e. Q ui t e th e op p os i t e: h e s t at e d th at H is K i n gd om was n ot of th is wor ld a n d r ef us ed t o b e c r o wn ed k in g, a t th at tim e, b y t ho s e t ha t i nt en d ed t o s e e h im as an e ar th l y m o nar c h ( J o 6: 1 5) . F or Chr is t, t h e c om pe ns at i ons to his A pos t l es , f o r r en o unc i n g s ec ul ar l i f e, wou l d b e r es e r ve d o n l y f or a l if e b e yo n d p h ys ic a l d e at h.

T her ef or e , wh at s ho u l d k ee p t hem m oti v at e d d ur i ng th e tim e t h e y wo u ld be ex er c is i ng t he ir m in is tr y, wo u ld b e , i n ec on om ic l an g ua g e, t h e s pr e a d of t h e ps yc h ic i nc om e. O r c om pens a tor s , ac c or d i ng t o th e R at i on a l C ho ic e T h e or y.

Chr is t c a l ls at t en t io n to th e f ac t th at a c er t a in r a nk in g i n t h e s pi r it u a l s e r vic e c an be t r a ns it or y, a nd it wi l l b e o n l y d ur i n g ete r n i t y th a t th e d ef i n it i v e r a nk i n g wi l l be k n o wn . T her e f or e, t hos e wh o no w ar e i n th e f ir s t pl ac e of th e r a nk i n g m ight e nd u p l as t a nd v ic e - v er s a. T h e as s es s m ent is no t o n l y d on e dis c r e te l y bu t is a ls o a n o ng o in g a n d c on t in u ous as s es s m ent. Co ns eq u en t l y, wha t wo u l d de t er m in e th e f i n al r a n k i ng wo u ld no t b e t h e f ac t of oc c up yi n g th e f ir s t p os i t io ns at a c er t a in p o in t in tim e, b ut ye s , th e wa y i n wh ic h th e pe r f or m anc e of t h e s p ir i t ua l s er v ic e wa s d on e t hr o u g ho ut a wh o l e tr aj ec t or y of e ar t h l y l if e.

A no th er r a th er i ns tr uc ti v e d ia l o gu e , f ou n d i n t h e N e w T es t am ent , wh ic h r ef er s t o t he wa y an d c r it er ia un d er wh ic h a pr om ot i on t our n am ent is c har ac ter i ze d i n t he B ib l e, r e gar d i ng t h e r ec e i v i ng of c om pens a ti o n c o nf er r ed f or th e ef f or t in t he s p ir it u al wo r k , c a n a ls o be f o u n d i n t h e G os p e l of Ma tt h e w, Ch a pt er t w e nt y, v er s e s 2 0 – 2 6.

2 0 Th e n t h e m o t h e r o f t h e s o n s o f Z e b ' e d e e c a m e u p t o h i m , wi t h h e r s o n s , a n d k n e e l i n g b e f o r e h i m s h e a s k e d h i m f o r s o m e t h i n g . 2 1 A n d h e s a i d t o h e r , " W h a t d o y o u wa n t ? " S h e s a i d t o h i m , " C o m m a n d t h a t t h e s e t wo s o n s o f m i n e m a y s i t , o n e a t y o u r r i g h t h a n d a n d o n e a t y o u r l e f t , i n y o u r k i n g d o m . " 2 2 B u t J e s u s a n s we r e d , " Yo u d o n o t k n o w wh a t y o u a r e a s k i n g . A r e y o u a b l e t o d r i n k t h e c u p t h a t I a m t o d r i n k ? " Th e y s a i d t o h i m , "W e a r e a b l e . " 2 3 H e s a i d t o t h e m , " Yo u w i l l d r i n k m y c u p , b u t t o s i t a t m y r i g h t h a n d a n d a t m y l e f t i s n o t m i n e t o g r a n t , b u t i t i s f o r t h o s e f o r wh o m i t h a s b e e n p r e p a r e d b y m y F a t h e r . " 2 4 A n d w h e n t h e t e n h e a r d i t , t h e y w e r e i n d i g n a n t a t t h e t wo b r o t h e r s . 2 5 B u t J e s u s c a l l e d t h e m t o h i m a n d s a i d , " Y o u k n o w t h a t t h e r u l e r s o f t h e G e n t i l e s l o r d i t o v e r t h e m , a n d t h e i r g r e a t m e n e x e r c i s e a u t h o r i t y o v e r t h e m . 2 6 I t s h a l l n o t b e s o a m o n g y o u ; b u t w h o e v e r w o u l d b e g r e a t a m o n g y o u m u s t b e y o u r s e r v a n t , 2 7 a n d w h o e v e r wo u l d b e f i r s t a m o n g y o u m u s t b e y o u r s l a v e ; 2 8 e v e n a s t h e S o n o f m a n c a m e n o t t o b e s e r v e d b u t t o s e r v e , a n d t o g i v e h i s l i f e a s a r a n s o m f o r m a n y . "

At the request of Jacob and John’s mother, called in the text as the sons of Z eb´ é de e , f or t h em to b e s e at e d at t h e r i g ht h a nd a n d th e l ef t h an d of Chr is t wh e n he be g an his r ei gn , J es us a ns wer s t ha t on l y t h e F at h er c a n r es er v e t hes e p lac es f o r t h os e wh o wer e c h os e n . W hos oe ver wa nts t o ob t ai n t he f ir s t p lac es i n t h e K i ng d om of C hr is t , oc c u p yi n g t he to p of t h e c e les t ia l r ank i n g, i t is dem a n d e d t ha t s uc h per s o n b ec om e a s er v an t of h is f e l l o wm en , t he s am e a s He , C hr is t h im s e lf , c am e to s e r ve hum an it y. T he m ar g in a l b en ef i t of t he s er v ic e in t h e K i ng dom of Ch r is t r e qu i r es i nc u r r i n g b ef or e ha n d i n th e c or r es p o nd i ng m ar g i n a l c os t r e l at i v e t o th a t s er v ic e .

In t h e f ig ur e I , n o t on l y t he m ar g i na l b e n ef it is r e pr es e nt e d, der i v i n g f r om th e ef f or t , r e pr es e nt e d i n th e ver t ic al ax is , but als o t h e m ar gi n a l c os t of th e

i nc ur r e d ef f or t ( ), bo th as a f u nc t i o n of t h e l e v e l of ef f or t , r epr es e n t ed i n t h e hor i zo n t a l ax is .

T he s ol u ti o n to t he f ir s t or d er of t h e pr o b lem is g i v en b y [( ) ( )] ( ) ( ), whe r e . If t h e m ar gi na l b en ef i t i nc r eas e d, f or ex am p le , to [( ) ( )] , t h e l e v el of ef f or t s h o ul d b e i nc r eas e d to .

Rem em ber in g t ha t [( ) ( )] ( ) ( ), an d c o ns id er i ng th at ( ) is th e i n ver s e m eas ur em ent of t h e im por t anc e of th e r a nd o m eff ec ts wi t hi n t h at c o nt ex t, t h e s ec on d im p l ic a t io n i s t ha t t he s m al l er ( ) is , th e l es s er wi l l b e t h e le v e l of ef f or t ex er c is e d i n th e b a la nc e. T h is m ea ns to s a y, as we l l , th at t h e gr ea t er th e i m por ta nc e of th e r a n dom ef f ec ts , t he s m al l er wil l b e t h e ef f or t i n t h e e qu i l i br iu m . W hen the r an d om ef f ec ts ar e n o t s i gn if ic an t, i n s uc h a wa y t ha t th e d if f er e n t i al is ins i g nif ic a n t, s o th e n, ( ) g o es t o i nf i n it y. If th e r a n dom ef f ec ts ar e s i g nif ic a n t, t h is is t o s a y, wh e n t h e d is tr i b ut i on of has a f a t t ai l , ( ) b ec om es ex tr em el y s m al l , a n d t h e c os t of t h e ef f or t bec om es ex c e p ti o na l l y b ur d ens om e, wh ic h i n duc es t o s h ir k in g b e ha v i or . T her ef or e , t he h ig h er t h e r o l e of th e r an d om ef f ec ts i n th e d is p ut e, th e m or e t he ex er c is e d ef f or t wi l l dec l i ne du e to t h e s pr e a d b et we e n pr i ze s^{1 1}.

1 1 F u r t h e r o n we w i l l e x p l a i n , t h r o u g h h i s t o r i c a l e xa m p l e s , w h a t t y p e s o f e f f e c t s c a n

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F i g u r e I - O p t i m u m e f f o r t l e v e l

If t h e d ens i t y f unc t io n wer e ̅( ) ( ), i nd ic at i ng a s i g n if ic an t r o l e of t he r an d om ef f ec ts i n t h e to ur nam en t, t he o pt im um ef f or t l e ve l wo u l d dec l i ne t o ̅, as i t c a n b e o bs er v ed in f i g ur e 1. W hen t h e r a n dom ef f ec ts pe r f or m a s ec o n da r y r o le , th e c o r r es po n di n g d ens i t y f u nc t i on wi l l b e h i gh er .

If th e r a n dom ef f ec ts ha v e a s tr o n g i nf l u e nc e i n t he f i n a l r es u lt of th e to ur nam en t, t he n t h e c om pet i tor s wi l l n ot ex er t th em s el v es as f ar as t h e y c o u ld i n or der to wi n t h e d is pu te . He nc e, i n or der to i nd uc e t hem to t he hi g h es t en d ea v or s a n d wi n th e pr i ze , a v o i di n g t he s h ir k i n g b e ha v i or of t he c l er ic s , t he s pr e a d b e t wee n pr i ze s m us t be am pl if i ed . In th e c as e of th e C at ho l ic C h ur c h, th e s pr e ad b e t wee n p r i ze s tak es o n m one ta r y a n d n on - m on e tar y f or m s . Sin c e th e r e ar e c as es of c a th o l ic c l er ic s wh o d o no t r ec e i ve a m on et ar y s a l ar y, t h e ex p a ns io n of t he s p r ea d m us t b e do n e, m ain l y, t hr ou g h t h e i nc r e as e of t he ps yc h ic inc om e. T his m eans th at th er e m us t be an ex p a ns io n of the be n ef i ts an d pr i v il e g es f or th e h ig h er r ank s of t h e c at h ol ic h i er ar c h y. T he o bj ec t i v e her e is n o t t o e nt er i n to d et a i l r e gar d i ng t he h is t or ic a l as p ec ts of t h is qu es t i o n, bu t , i n f ac t, e v id e nt l y t h is was wh at ha p pe n e d i n s e v er a l m om ents i n t he his t or y of th e Ca th o l ic C h ur c h, wh e n t h e h i g her - r a n k in g c le r ic s , wi th i n t he ir h i er ar c h y, be g an r ec e i v i ng m an y be n ef i ts .

G i v en t he wor k of f er r e pr es e nt e d b y e q ua ti o n ( 2) , t he pr o bl em of t he r e li g i ous f ir m is gi v e n b y :

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r a n d o m e f f e c t s h a v e o n t h e l e v e l o f e f f o r t e x e r c i s e d b y t h e c l e r i c s i n a t o u r n a m e n t .

W hat equ a ti o n ( 4) e x p la i ns is t h at c l er ic s m us t r ec e i v e e n ou gh , i n a ver a g e, i n or de r t o f ee l i nc e nt i v at ed , to ex er c is e t h eir m ax im um ef f or t. B e in g th e c os t r e la t ed to t h e ef f or t ex er c is ed , ^{[( ) ( )]} r ep r e s e nts th e s a lar y ex p ec te d, wh a t e ac h par t ic ip a nt ex pec ts t o r ec e i v e. W hen s u bs t i t ut i ng ( 4) i nt o ( 3) t he m ax im i za t io n p r ob l em tur ns in to :

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T he f i r s t or d er c o nd i ti ons , t her ef or e , ar e :

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T he s o l ut i on f o r t he eq u at i on s ys tem i n ( 5) im p l ies i n ( ) . T he r e li g i ous f ir m s ho u l d e s ta b l is h a r em un er at i o n s c h em e , ac c or di n g t o t he r es u l ts s ta te d a b o ve , t hr o u g h wh ic h t he c om pet i t or s ar e i nc en t i va t ed to ex er c is e a l e ve l of ef f or t, t o t he po i nt wh er e, th e ir m ar g i n a l c os t is th e s am e as t he ir m ar gi na l b e n ef it . In th is wa y, t o ur n am en t s pr o v e to be ef f ic i e nt s inc e t he y s tim u la te t h e c ler ic s t o ex er c is e an o p tim um ef f or t l e v el , thr o ug h o ut t he ir wh o l e c ar e er an d i n a l l hi er ar c h ic a l l e v e ls . S u bs ti t ut i ng ( ) in ( 2) we c a n f i nd th e o pt im al r em uner a t i on s pr e a d , g i v e n b y: