Hierarchy vs. partnership

Journal of Economic Behavior and Organization 5 (1984) 237-245. North-Hc?l!and

Brown Unit mity, Providence, r:.I 02912, USA

Received F’ebruarv :’983, final version received December 1983 Simple, organiqatio~ .c~rnpwed of qxxathes and one manager, may be organiz& as a l&w&r I@ the manti@r appropni&g ali profits or as a partnership with (say) qua f shares of @of&. Conditions 8n 1&Wit&& ty md foe optimal span of control a-~ arz_$z 9. Next, partnerships are considered and alkrnlltive incentives and distributions aw wmpar 1. When partners are free to choose their time inputs, then a sufficiently high preference for leisure as against income will rwke a partnership more attractive even though it is less !.wofitabie.

1. some

orgtizations are engaged in activiti~:s that could also k individuals, &en &I things beyond the scope of in&iduaf df~rt. III ~ZBY ~~orgaxkiz~ti~s face the task of coordinating the activities of their men&m. This act,i,ity coordination WiB be called manageme%;. in add&ion, m&mgement com;prises other planning tasks that even an individual operating on his/her own cannot escape from. Coordination re@iir~~~~ntro~. In a sirnpi~ organization (one with only two ieve&) this control mast be: centralize4i in a single person. Tlhis person may also perform $ome operative work, but the managemen”, task cAnnot be divided among several persons. The only way to retain soxne equality in an organizatiort is to rotate the management fi~nction periodically. Moreover, some choice exists a.bout the way iti M&S the o~ga&ation% profits are to be d+&ibuted, There ;appe%rto be two extremes among the possible arrangements which we shall label hierarchy and partnership respe::fively. In a hierarchy the managemerIt function is assignexi permanently to one person who also glairns the entire profits. The other extreme is that of an equal sharing of the managemen; function through rotation and of profits thl:ough an equal divisiicrn. Sixe both types occur in r~z4 We (stfthougfn the hierarchical tym mcch mom frequetitly) we want to study con&tions tinder which one or-the other foral of organization is prefi$rable. The questiou has recently come to the attent& ftr of econotiists and hg!s been addressed also by Williamson ( EW), @a!~ (19’79), Putterman (1981a, b) and Rosen. (15381). Our emphasis will h c+n ef%ciency as revealed by a production function. pdormed

by

Q16;‘-26831/S4/S3.08 cj 1984, Elsevkr Science PubIsfishersB.V. jNorth..Kolland)

239

f”!a)&” -,

171

f(q=lr),

\‘I

’

Fm k3223&$ &ftwm, r)E 9 since then /ltgp - X’A ==(WI-

t

,

condition (7) is not satisfied in the domain (5)

l)xrn > 0.

The orgahation mat operate in the realm (6) of diminishing returns. Manqemnt 31 a pa~%~rship is a f&time Mb, and the span of control i!s C-1.

U9

In a hierarchkal xganizat~on the manager is not a partner hut the o*wner. His/her obje& is to maximize profits 24fter wages to operatves. Let: these wages be the opportunity cost of operating on one’s owx ) :.e,, unity, The 0rgmiz&crrrs pl*ofitis then

The input x1 2: cxPnstrained by (I]_but x0 is tznrestrieted. Profh nmximizJ;tion yields

hierarchical orgar katisn’s

pm&s had be;cn dividad equally. For g = f (i

),/i

i!lnplies

f(a)-g+--I,<

g=

~Rlaxf(x)-(x-

f(2)-(s-

1)

l)=h.

(27)

x

CIlXlV~rselgt,

h- 1 f{f@)--x*

--_-_~----_-~

-l+f(x*). x*-II_

x”

x”

I

13-g l

‘We ccifa&x!~ TVhmeve~ a pati.ncrship is profitable, a hierp rchkal c5rgatizatio3 is even mm profitable. VVhmever a himx&isal organiz Pion is profita%lrle,a, partners&p is also profitable [as seen by (IrS)] aJthough ECSso.

4. Hmv are these conclusions afkcted when the partners’ shams ape unequa’!? fn an organkation of x = n members, let the ith partner’s shax be n

%

i

c

Czi.

i=l

The KImembers prefer adding a parttl ter if

(2 1)

We ccrnciracle that addi,.mal par?ners will be admit,te:d iif their sf-aiireIS less than the ratio of marginal product to total product. 031 the olther har& no partner will join zf the share c)f profit ;.s kS*j than the upy mtsnity wage qf mity, Thus

243

Under what conditions do partnerships yield positive utility? When do they yield 8. utility G larger than t&t achieved by the o’tifner of a hierarchical CWgati:zation, ikW&--l,k)?

(29;)

We st?ew first that memtihip in a coflec~ive is Avays preferable to being ~II quaI partner in a commune. The objecr:ive of e$atzhctsrnmune rneurber is ta c&G&I max &- ti, aif(ti + 9)). t; In

the case of equal shares, ai = l/q let t’his yield a utility ti, (30)

Since al! pazners share equally, they witi behave equaily. I’%us

ln a collecti~ e eat h member seeks to secure

rS=maxu t

(

c-t,

-&f(t+s)

.

(33)

>

Comparing (32) and (23) dho,as that

To exstine whether being a partner in 2 partnership may ever be p~ferabic to being the njarsager of a hi~:rzrchical ~rg~n~~a~~~~~~ we will limit ourselves’ to c&lectives and consider the social utility function (38). The manager of a hieraruhkal organizakn achieves utility

Cmpal~ tJ!Gstcs the utiky (34”)achieved by the owneq’manager of a tierm&icaI

orgzG2ation.

NOW,

or

fln(i4-d) ( %:==c )

0,

Nm the M&hand side can be made arbitrarily small by choosing L!large enoygh. We have tilus shown the following: Provided a partner’s (optimal) incow & nut less than h&f that of the owner of a hierarchical organization, a su%&ntly strong preference for leisure d will make being a partner mar,: =ttra&e th&n manag+jg a h&$jm$rchi& 0igatizWn. fJ?ie factor 1/S Is afbitrqy and dep& on the partMar choice of the utility function (28j.J The basic reason f?v th.s is that par,mxs may choose to work as little as they de&e w%le receiving P, share prtiportional to effort while at the same time the number of pa-3 can be adjustted is yielb the maximum ~~UII ;+r unit ef%rt g.