The terms of authority

Journal of Economic Behav;,:,-and Organization 2 {I?~1) 237-255. North-Hollan, l

TIlE TERMS OF AUTHORITY James D. HESS U uv~rsity ofSouth~ rn Cal~lbrn~a, Los Angeles, CA 90007, USA Receivea June 1980, final version received October 1981 Many exchanges involve only a !~artial transfer of ownership righ'.s. The employmeat :elation is the standard example ~ an employer purche.ses the authority tt; use the worker's tim,~ in the most profitable way, within specified limits. Tats paper develops a model of fl~e fare-':; which deternfine the terms of authority.

i. introduction The exchange of commodities is a transferral ~.f ownership rights pertaining to two bundles of goods. There are m~ny ways ir~ which economists have .,nodelted the corLtractual form of scch exchange. First, much of received micreecc;,:~mic th~mry assumes that the contract stipulates that complete ownership rights to :,l quantity of a good is exchanged for a quantity of the mlit of account (money) equal to the prod~:ct of the unit price and the quahlky of good. For examd!,, when we purcl.ase groceries at a supermarket the checkout person computes a bill of sale which evaluates in money terms the value of our market bas "et. When we pay for the goods, we assume that we may t, se the groceric" in any fashion .'.c desire {v,'itl'..hl prescribed legal or social limits). Second, in the modern rcrsiort of exchange individuals make payments ao~ for the complete ownership rights to a quantity of a goed contingent on tbe occurrence of some random event [see ATrow (!97Ia) or Debreu (1959)-]. If the event does not oe.cur the individual has r.o ownership rights over the goc ~ls in question. Third, ir~ the literature on sequential markets [Grandmm, t {1977), Radncr (lg72)] some contracts are ,'es~;ned but never made for,qlaliy t:inding tmtii the event is actually reaiiz,sd some time in the future, ffour~h, Sim,:,r (i9571 has investigated contrac|uai mode.~, which he calls 'emp~oyr.~enr con~.acts" in which a payment is made now |br the right to select the quant;i',es of some c~,mmodities after • evenls ha'~e urn|bided. The em~lovm~:n~ ,, on~,-:.~c,• ,;-~ecifies ~he uncertain .~. . . . . . limi~,s on the qu:mtitie~; permitted. ]his does not exhau:...'he iist of contractua! modes; see alsv Wilharason, Wachter and Har, i~, 11975}, Stigiitz {i975}. Che.'..~.~g (I9¢,8} ard Mirr!ees {1076!. h.t fbis paper, ii ~vili be assttrnc{{ th~.i iab,-~: ..
0167-2681/81/0000-(R)00/$02.75 (("~, 1 )8; N.')rth-.Hoiland

23~

ZD. He.~g T~Je1ettm of authority

co~,~:racts which permi{ the buyer to deterr:tine, within prescribed tfinits, the ia~:rer's ~caivX~es in an authoritarian mam:~er, tt is important to notice ~hat ~ e aath~mty relationship is not forced oa the worker by the employer. Audmri~ is a mutualy advamta£eous arrangement for allocating resour~:es, as Siu~on ~ s poi~:*ed out:~lt is a h o Lmp~>rtant to remember vhat authority is fm~t:.d. ID a n o r ~ ! setting the worker can always refuse to fotow the d.;:'~ates of the employer and the wors~ sanction that can be imposed is to {er ~irr~{e the emplo>ment (aR,5ough the govermnent, as o p ~ s e d to pdvate e~:.,Ae~yers, may pm you in jail if you refuse to submit to authority). worker is a potential souro= of many t,¢~r of labor [see Lancaster {.~966) l,%r a more gener#, model]. When a worker takes a job (that is, agrees to an emplo,3,ment relationS, a composite c,mrnodity is being exchanged for t ~ urdts, l~Lor ser',ices, like any commodity, can be distingvJshed by phys~ca; characteristics, lecation ir~ space, date in time and state of nature. It mi#d ~e ~ s i ~ to write a contr~tct for a worker that specifies in detail how much of each t y ~ of labor service is provided, where, when and in what cite, noes. This DIJe of contract is not used for several reasons spelled e~m by Simon ( D 5 7 ) a n d Wiliiamson (1975). A traditional explanation is that tran , costs wou|d b.~. too l a r g e - - c o n s t r u c t i o n and enforcement of s ~ h a c o m F f i ~ a t ~ contract weuld be difficult. In this paper, the most appmp!~ mtionalb'ation wou,id have t o do with u n c e ~ i n t y and m differem:m~,. Radner (1968) has demonstrated that contingent coramoditi~s; "~1 opA!y be t:raded wbJich are based on the c o m i o n a~.-ion ~ both pardes. For e ~ a p b a sappose that die employer of construction workers only has tt'~e ~att~b~'ty to dete~.m~- whether the temperature is above or bel~)w 80°F, w~le e o ~ ~ t i a n workers can only distingmsh temperatures is being above or bele~w !~°F. Even when the work, m~ and employers hax'e strong reasons for va~4~g the salary with the ,~emperature of the work ,ite, their ring ~.t,titi~ to verify the te~lz~ratare force them to pay' a uniform ~a~'. b,~ wage differed m 75' from that at 85 °, the workers would be va~eo~bM to a d~shonest empicT'mr's misrepresentation of the ~omperature and wo~!d the~e~%re r~e< sttch a wage schedule. :Similarly., a wage schedule w~th di~erem wages at 35 ~ and 95 ° would be rejected by the empto).;~. The ord~~ m~t~11y accep~Ne contract is ~ne with a uniform wage for all tem~ramr~. W}th SimurFs e~plo3c~meat conWact, a mutt~aiiy adwantagem~s resoluti(m of tan og mformatiov,ai ~iifferenoes may be... found. For example, a ~ y cenlract to type, rNe reports, ~ k e shor|hand dictation, answer ~,e},ephon~ or perfor~v many other tasks, a;1 at the dis~c:retion of the boss. The ~',,o~,

thcLv~,se]ves

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,I.D. Hess, The. ~erms of authorit)

239

in~rmafio:~ is obtained may b, very valuable to the employer, ffhc emp!oyer may, therefore, be wilting t ~ pay salary premiums ~c the workers fo~ the authority to unitate,ra!ly aajust work tasks as t~is personal information is acquired, Workers may f~,d these premium,, ~ttractive enoug~ ~ :,o that they accept some ur ce,_tamty about the exae, job con!itions. The employment ,:ontract must describe the ~.~b in some fashion. Simon assumed that th~ d;.:scription was simply to state the set of possible tasks that might be as .ed of the worker. In this paper, a slightly more general formulation of j~.~ description will be used. The employment contract will specify the frequ,mcy w!hieh the employer expects the tasks to occur. For example, the agreement between boss and secretary might Sl;Vecify that t~e secretary is required to brew coffee for the boss only in very un!ikely circumstances (or in the limit, as Simon might require, never~. L job will b~: characterized by a probability distribution defined on the set of possible time allocations between var;ous types of tasks. This paper' presents models of job selection and the determination of work conditions in an uncertain world. A major distinction between these models and the trathtional labor supply models is the assumption made here of fu~ttime employment. Workers either give an employ?r all their labor time ~r they do not work for him at all. This assumption is based on the mode of contractual exchange. When authority is granted to the employer by the worker, this means that the ~vorker is on-call to perform any task asked of him withir~ the agreed to limits. Even if r ature turns out to be such t~at the worker is performing the task of 'wa~t t-.ut do nothing', he cannot use this freetime to moonlight at another job. He is paid a salary r~remium to zssure the employer that he is available for any task assignment. ~ e worker canr, ot make such an agreement with two employers. The aim of this paper k,. to develop a model of labor market equilibrium which eaptt~res two reafistic institutional features - - indivisible, full-time work and an authority relationship between employer and employee. The economic rationale for authority is doceloped in section 2. The fulMime nature ~f the employment cowtract may lead to difficulties in matching workers and jobs. This is anaty~ed in section 3. The terms of a,athori~y a~c determh:~,e-'~ by the tastes and the technology of employees and employers, in section 4, the equilibrium terrn,~ of c.rnt,loyment contracts are studied as :~ thnction of the authori'~y aversion ~f workers and ~:he riskinc.~s c,f ~h,cmp~oy~':r's technology. 2, A~th,~r~ty i~

empioy~eut ~d~tiio~.s~ips

Work consists of a finite n~ ~..,. . . . . . .

.........

by ranOom events. The fir~e :hat ~ worker devotes to a task i is ~enoted ~

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' obabifity denmy,' ~:(0,e), defined on,the ate s

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on e mdica:: ;v" that employers may have different beliefs

T~ ~~Yes utGty from ~ ~ :~anhffected"by thetasks his em#oyee p~fforms. His t: ~tes are giwm by the yon Neumann--Morgcnstern ~ t~hty f u n c t i o n

G(LeL

(41

ZO, Hess, The terms of authority

241

The only thir.~g which needs to be specified about the economic eavironment is the inibrmation systems of the employers and workers. It will ~be ass~med that the emp,oyert can o.:bserve the true state of natm'e, 0, before the production activities are selected. The employer can also observe the revenue, R, deft'red from the productive enterprise and can costlessl2~ monitor the actions, t, of his employee. The worker, on the other hand ~, is assumed to learn r~otMng about the state of nature or the revenue of his employer. All he can observe are the tasks he performs. As a r e s a l t o f these infomaational assmnptions the payment of the worker cannot depend directly on the revenue or the state of nature. In parti2ular, the worker cannr0t~ be paid by giving him a share in the resulting re'~::nue. [When sharing is possible the employment relationship takes on characteristics of the princip~!!-agertt relatiocship discussed by Ross (i973, 1974), Harris and R~,,iv'~l~7~i~, ShaveU (19"79) and Holmstrom (1979).] If ~ y m e n t w a s based u g o n R or 0, the workel would not be able to enforce the contract. It w0:tfld seemthat ~imilar reasoning would imply that the task select~d by t h e employer c a n n o t depend on the state of nature. If it did the worker would ,!M:~unable t o erffome the continrsent features of the employment contract.: However, there are onport~m;_tLs lost when the task is not the most propitious: activity for the trac ~tate of nature. The remainder of the section provides a rationale for an emp;eyment contract with a fixed wage but with state contingent work selected un laterally by the employer. Suppose that tke worker has o~iternative uses of his time which provide a level of utility,

tT(w),

i5:

If the employer does not adjust: tasks when he observes the state of nature, the best he can do is to select a task, t, and a salary, S, to rn~,x~mize his over expected ulility

.[ G(R(t, O,e)- S, e)';(O,e)dO,

',61!

subject to the employee's r Nuirement that

U(S, t, w)> (TIwt. Denote the solution of this problem (t~,S*). The solution depends v~ca whicl~ particular employer e ~e are tooking. ~.,t but t,~,;~ wilt be suppressed for notational simplicity. If the empl,~yee a~to~s the t~s~ to be selected by the empl~yer after he observes 0 he is ~?~king a "hancc of having an undetectab:c breach of contract. However, if the col~[r"ct dOeS aPow t to vary width O, t:.e

~0~ployer will sel~t a de~i~ition rule t(O) and salary S ~o m a x ~ z e

j C4R(t(0),~;e)-. s, e)#, e~0,

(8)

j t~t&.a~ v0#, e)~0 ~.. ~(w~.

(9)

subjee~ to %

Denote the, solution of th~s problem (tZ(0), 8~). S i n ~ (tl,$~) saiisfy (7} it is clear that they a l ~ :~tisfy (~9),~The-o p ~ a l i t y of (t~0),8 :) mapliesthat r

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j C~R(tz(0), rL:~V.,S~..ep](O,e)dO~JC~R(tt.OiO--Si,e)~l(O,e)dO. (10) 3 ~ , emp!c}~er should be able to share these benefits with his worker by ~ying a s a l ~ p~u~:a;~:~ove "32. I~ should be noted that i~f~ worker ~ obsexv.e t~ fl~t:~ ~:no~ ~ason that the salary =hould be independent of the task in gen,:ral. However, if the empk~yer is r~sk neutral t!he worker risk averse~ wi~ r ~ t to income and the marginal utility of irtc~)me is unaffeeteA by~ changes in tasks, the optimal s ~ r y slm~d not delx,~ul on the actual task. The intuitive explanation is this; ff the worker is t4sk averse he world give u p ~ m e expected: salary to eimtrate u n c e m t y about the salary a n d since the employer is risk neutral, he is better off when tmyin,g a lower e~'pected mlary andi having a ridder net revenue. To be more precise, s~ppose that (ts(O),SZ(t)) maximizes the employers expected intcom,e

{ r(R(r(~ O,ell--S(t(O))]7(O, e)d0,

t t0

j u(s(t(o)), t(o~,.~;(o, e)dO>=O(w).

¢12)

subject to

Let u~; assume that the worker'~ utility is separable so that changes in income do nc,t affect the relative desirability of tasks. The first-order condition for t?i~e~.a~a~¢,~ule is d

U ~(,.-(t~(0))~t3(0), w)= 1 for all 0,

A

(13)

w~-~"e ~ ~ ,:he t ~ a n g e multiplier of (12). Holding 0 constant, differentiating

J.D. Hess, The terms of authority

Solve for

24?

OSa/Ot~to get (15)

OS3/Oq = - O ~ , / t i u .

The assumption that utility is separable in income and work implies that

OS3/Ot~=O,

i= 1,2,...,n.,

(!6)

or

S3(t)== constant.

(17)

Since it is rezsonable to assume that the employer is risk neutral [see Bailey (1974)], in the remainder of th0~ p a ~ r it will be assumed that employers are i~terested in maxim'zing "1"-'",:,~,e×pected income. This will be acb.ieved by employment contracts whtch make a fixed salary payment to the w~,;kers and which permit the employer to adjust the assignment of tasks. Although workers cannot observe 0 to check if the task asked of them corresponds to the aathorized task, t(0), the salary is large enough to compensate. If the worker and employer have a recurring contractual relationship, the employee may be able t~ detect misuses of authority when the empirical frequency with wh~..h tas
3. Job-worker matching with full-time employment workers are hired by employers to pe:fo~'m work lasks~ Salaries are paid the workers unconditionally and emplo3..',rs are granted the right to select work tasks after nature has determined il:; s~:ate, 0. The employer is asaumed to select the work t e T to maximize tl:e ~revenue generated by a worker conditional upon the state of nature. Wit ,out specifying marginal concitions, let us denote the optimal choice of work by e,mployer e in stare s by

t(O,e).

'1~!

Given this decision rua, and the subjective, probability of O, the employer determines the frequercy with which his worker may be called upon to per¢,,,-m each pos:fibne task combination. Denote t!~e resulting probabiiit) dcasi~y of work t w~.h er%~Ioyer e by ~(t,e), v, here

~(t,e)> 0,

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Gwen t.~ese e>; "~.~ ~.~~.~rk decisions tl3e cnplo)e~ mt ,;t ~ae~.'~e ii a. ,a.,;rne.~ saouhi be hired. The expected optimal reven,ue associ~tt~-.d wi~h the worker of --,~-

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244

J.D. Hess, Tlie te~ms of authori~,

employer e is

R(e) = ~ R(t(O:,e), O, e)~(O, e)d0.

(20)

t9

The ¢.-nployer c can afford to hire a work~,r ff the salary ae pays, S(eL does no~ exce~ the expected optimal ~:evenue of the worker, R(e). ji~saiary exceeds R(e) ~ n the employer hires no worker. The employer makes a jeb offer to all workers consisting of a job ,.?es,~ipt~p~ #(t,e):. and a salary, S(e). Workers whe accept such a contract will be paid a known salary but will aot know wi,.h certainty the actual task revolved.. For example, a ~eeretary m/ght tx~ IGed for a fixed weekly salary and !old only that there i.,; an ~ probability that the week wfli be s ~ a t t y i n g or t ~ g shorthand dictati0n~ Workers ~ : free to choose any jo'b offer which has been made. They observe the entire ~ # x u m of potential job contracts o ,n ,=,..

(21)

The wth wc,rker can calculate for each e the expected utility derived :from ~:he announced salary income and job description,

V(S(e), 2, w)= ~ U(S(e), t, W)la(~,e)dt.

(:;!2)

"Fae we~ke~." r is- not concerned witlt the manner that t;'e probabiity distribution is derived from the work assignment rule ( 1 8 ) r o d the state probability density (3). Workers select the employer which mal'es the most attractwe job offer. This choice of employer may be forrv,tated as :&c follovAng linear integer prograiaming problem: maximize by choice of aw~O, a , ~ l , . . . , a.,,~

e,.,V(S(ek e, w) + a-.o V(O, O, w),

(23)

e--I

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Y a~,~= 1,

The c ~

i24)

vaz~nN~ ea~.~} ~fe i~teger as,'iqnment variabks with the

245

,I.D. Hess, The terms oJauthorit~'

if employer e h~s the most attractive job available. The constraints specify that eacli ~orker w must choose one and only one employer for whom to work. "['l~e job c,:,,,sists of the full-time submissio;a to the authority of the employer. A job offer spect,um like (21) would lead to equilibrium in the job markets if the ~ptimall assigm~aent vectors from the above problem, A = {a~}, also satisfy the cortditie n t w, = 1 if

S(e)
e = 1,2, ..... :~1,

(26)

aw,=0

S(e)>R(e),

e=l,2,...,M.

(27)

w=l in

if

w=l

Condition (26) sta:es that each employer rec:ives only one acceptance of his job offer and condition (27) implies that the ;ob offers are profitable to the employers. I,, tins simple model where emr,loya,'2 hire only one worker, the job des,,ription, V(t,e), is fixed by the technology [the revenue function R(t. 0.e) and the ~liefs y((?,e)]. Only the salary is adjustable. The market is ass~,m-~d to increase salaries of jobs which ,.re not selected by any worker and to decrease the salaries of jobs which ara desired by more than one wor/,:er. Eouilibrium cart be illustrw:ed ~Ls in fig. 1. s~2~

A I

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i-~te~ are two em#oyers and two workers. Line AA' in ~ e salary s p a ~ ret~,ct~nt~ rite dividing ~ between prefit and loss for employer e--=1. To .the

be.- ~ ~ : ~-~~!y~-:----:~-:-di~- ~-tM;-:~~::,~ace:"ia~ording >to the . . . . . . . . . .... ...~-.: r~the s~ lary pr~..~~bi-~t~• ~--ff.a .. .~ .r k. e. r. ._-.fo.~:----em~oye: .e--' : . .~urve,~:~.--divi~,: ... "" " ' " m m d i n g to the pr~eren~:~:.of worker w='l.i Belo~ ..~d:.:-m m e ieft--a ~ n t C lx~th sMacks-are so low t;'~at worP.~r 1 - . t ~ ~ m , : : ~ t ~ ~ ¢ n t . SMaries below tl~ c~rve C C , ~ . ~ . the: workcr_l. tO eh.oose.-emp!oyerl-e=.! .since his ~ r y h) sigv,i.-Cmantlyla~r them that of-:--~!Oye,r 2, C ~ v e . . D D . ts- the analogo),~ cu~e for worker ,.---I. ~ n salar~-'es are in-the shaded re#on, CEFG, the workers and empMyers "~ve reached an equiiibfium where ~'orker w = I l~c.epts the offer of em.piovee e = 2 a n d worker w = 2. ~ccepts the offer of ¢~ployer ~ = 1. It should .~.. ~,~.-~_,ted~ .~.~t.~t~i!i~-'_ .urn.:may result, m-one~-or-mo~:pairs workers and emptoym d ~ . that ::-the~e.~_-r~~mmuatly.bene~r~al empio~t In fig, 2 the eqaiiibrium ..salaries must ~y in r e # o n . E C G F . In ~ . the worker w.- 1 dec~des t o ..~...,~eif~em.played.-~and.employer e = 2 not to employ-a worket~ Worker w =2-:and.,:,¢mpl~yer e = - ! s t ~ e an etnploytl~-xtt .barga~ ~ .-shmdd .not-view-:this- as a situation of unem#oyment. The remainder of. the._pape~ will-presume that all workers fred we. = w~th the e m ~ and are not .selfemployed. "

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J.D. Hess, The terms of authority

247

In ;:he above simple modei the job conditions arc: determined cnly on the supply :fide: the function relating optimal work and state of nature, t(O,e), and the sut,je~,ive beliefs about nature, ?(0,e), toge~ther determine the job description, ,,.,(:,,e). This is completely independent of labor market conditionsi~The next task~ is to show how the job description may be et:dogcnousiy determined, in part by the preferences c,f workers. The only change to be made in the above model is to permit employers t!he t,ption of hiring several workers. (There is no longer a need to assume that the nmnber of employers equals the number of workers.) Let x be the n u m ~ r of workers employed by the employer and denote the total contribution of those workers ~oward revenue by

R(x,t,O,e).

(28)

The employer e with work force x observes the state of nature 0 and selects the task assignments for the typical worker, t(x, 0, e),

(29)

to maximize revenue. By the nature of the employmen! relation, the work selection is done after woL kers are hired and nature is ob,;erved. Prior to ~ n g workers tt~e employer calculates that the expected net revenue associated with x workers is

.I R(x, t(x, 0, e) 0, e)y(0, e)d0- S(e)x,

(30)

0

wh~re S(e)x is the cost ¢4 hiring x full-time employees. The employer selects the work force to maximize the expected net revenue. Denote the optimal numOer of workers by

x(e,S(e)).

(311

When this has been done the employer can calculate the jcb conditions (a probability density of T) from the composife function t(xte, S(e)t,O,e) and ti~c subjective belief3, ?(0, e). Denote the calculated job des:ription by ~(r, e, S(e)), where

g~t,e,S(e))>O, toT

and

I #(t,e,S(e))dt= 1.

(32)

T

Unlike the previous model the job conditions are endoge~ousty determined. :\~ ::alary adjusts, ~,) do the optimal work |orce sizes and hence so do tl;e optimal work tasks.

2~

1~,~ t.1~, T~i, terms :.ofaua~omy

Workers observe_ ~.heS l ~ t r u m of job 9ffers (S(e), flit, e, S(e))>~_-~,

(33)

and ~ t the , , ~ # o y ~ w~ose effe.J" maxim~es their e x p i r e d : mility, exa~fl' as before. M o ~ t~han one worket may find ,employer e's offer the most attractive, it" A=(a.,,,J ~ the a r r a y of workers' assignment variables, equilibrium wi:~ c~:ur when ~,.~,-: x ( e 8(e)),

for all e.

(34)

If ~¢ven~e is ze:'c, when the number of workers is zero (R(O, t, s, e) =- O), ,then e~tlilibfit,~ may c~ccur with some employers hiring no workers. The c.r:oice o~" :~ptimal w~rk fo,rc~e rem6ves the ~ u i r e m e n t tha,t S(e)6K(,~) as in eq. (27)

Eq , ~ m

~md~s: An e x a m l ~

In t [ ~ ~cli~m a market for workers who operate or repair machines is a n M ' ~ d fo~t~'gag on the market impacts of en~ploy(;'s changing, riskiness of techJ~,~ogyo ~ exan~pl¢, is s p ~ e d numetieal:y a~ an expository aid. More g~.~ra! specifications will ~ left l~:.~rother~ studies. 71"he example illustrates the stret~gt:t'a and weakne L.~e~of the gem.ral naodel ~:ffthe l,,revious section. ~ o r ~ r s are hired in this exana,ple because tliey car operate machinery or repair machinery when it malfimcdrms. For a p:trticule,r ~mployer, e, let 6~ be the number o r wc~rker-6ays ac,,,~d to repair machine,,1. This is a random va~b~_. Let La d ~ o t e the mt~ll worker-daytl of la,bor used in otx:radng rnacb~es a~d let /~ ~ n o t e the: tomt worker-days used for repair w~rk. Labgr can be tr",.-: ~'o~.anedinto revenue by the eth employer according t o t h e ~ia'6en R =- a{c~ Lo - ~ L ~ ---t~-(Lr - 0e)2.

~ e Lrs~ ~.wo ierr.ls are the ~c,tal re,;enue product of machine operating labor and t~e iast b : ~ is the loss in revenue which occurs if there is a deviation from the roq~ir~:i number of repairmea. The: ~3efficient a(e) varies with emp~oy~.-r, reflec~ir~!~ perhaps the size of tiI~eempioye~'s capital stock. Labor i~ iamxl as m the previous secti~3n. If the er~plo)er has x workels and ,-~,-.~,~ worker°s time is allocated t:etween operating and repaiiring ~cordi~g to t :~(t~.r,) tlL~er~total b.bor is

d D, ltess, The term~ ,of authority

240

It is assumed that each worker supplies orte worker-day of h~bor, so

(37}

T = { t i t o - t - t , = 1}.

Non-negativity constraints will be ignored. Suppose the emplc.yer believes that the number of wort:er-day~ needed tc repair machines has a mean ~t~ and a standard deviation &. To assure that non..negativity constraints are not violated it might also be assumed that rb is large compared to 6, and that the i,robability density has a compact sapport. The employer maximizes the exl:ectation of (35) subject to (36) and (J;7). The optimai time spent operating mazhines will be

(38)

to(X, 0~, e)= 1/2 + (a(e) - O~)/2x, and the optimal size work force will be

{ ':t~B

x(e,S(e))=rle +a(e)-- :; 7(e).

t h e workers hired by the employer e grant the empic :¢er the authority :o select operation time to with a frequency given by a :?robability distribu',t n with mean ~r

,lg'

E{to} = 112 + (a(e)- r/,)12(r?~+ a i e ) - 25,e)),

{40}

and standard deviation

g(e) = x//E {(to - E {to })z} = 6,,/2(,1,, + a(e) - 2S( e')L

(41)

To simplify the analysis assume that all employers befiev:, th,: tb-. expected number of worker-days needed for repair work ¢qus:-:r~.e ~:oeff~cient of productivity of the machines, ~'l~=a(e). Because o: t;,:s wh.r.n tae salary increases the job description changes only by an iacr,.asv, in the authority required, o'(e), and there is no chang~ i~ ihe expected time ~peot c,l~'.rating machines. See', fig. 3. For emInoV,aS with less l~r~:dtctabte a n d ~epamng " ~" ' ~ .e machines the authority curve in fig. 3 will be urMormly higher and sl;,~eper. Assume that workers have atilitv lunctions of the separable ;orm 1; { ', t, w) = V(I, w ) - D i t , w).

~'+=i

V is the ,.'-, ~,= of inc~..::ae and D is the di~utility of labor. Sep;~rabilit .' impth:. ,hat the ;,.arvna~ utih*:y of i:~come is no~ i:jfluer, ced by t~,: ..c~ J:.. ma',~ a i a y i o . s~:ries approximation of expected utility around

I

Ll@-m

~t

ale;) •

Fil~3

.

.

~

-:

t=(t/2, I/2) |:coping only terms o~ :g~r~: two or less: Z { U(S(e), t, w)} =

(43)

V($Ce[ w ) - I / 2 A ( w ) ~ ( e ) : - r[:,

where

(44) and

A(w) is , ~ a l ~ . ~ approxu,aa~

equal

t=(1/2, t/'E); T'rt," w o A e r :w:.~ou~: tmy :an i ~ o u u t to

I/~2g(G A.(~,)~!V~$(e), w)

: _

:

:~:

~ .~:

-

,

(46)

to e ~ e ~ . , e L~ authority which employer e:=~ks for. A(~)will ~ troatcd as a ~ncasu~ of the worker's aversion to authority. When t~e worker vie~es the u~,ks as p c ~ t substitute,

the worker do~,s not care how much authority the c m p l o y e wants so lone as

J.D. Hess, The terms of authc,rit.~

251

the total supply of labor time is the same. In this ,;ase the value of A(w) will be zero and the worker will not pay to reduce the auth,:,rity of the employer This brings into relief the assumptior~ made here that the amount authority is measured by the spread of tLe dismoution of the random variables to(x, Oe,O and t,(x, O,, e). The tastes of a worker can be d:~scribed by a family of indifference cu~es as in f~g:. 4. [~Arrow (i971b) aa~ Pratt (1964) use a •imilar analysis.] o(e)

,,

.

.

.

.

s ~..-)

Fig. 4

~Vorkers with greater aversion to authority will have flatter indifference curries.

Suppose ,there are two employers where 3(1) > 6(2). TJ~e first employer has less predi~ble machines and must have greater authority to adjust the r e p ~ r / o ~ r a t i n g task assignment. Also suppose there are two types of workers where A(I)
2~ e{o)

-

.-:-:~.:

-

.

. ..,'.z,-t.x2

.

..i ¸

.,

.

;

7 :

-.

,L

.

_-.-,

aOl-½x~ Fig, 5

cff-,¢ # the., 3¢lk~rebut will. stit~ choose the authorivarian employer's offer. ./..:-al'., not c~.ar~ge. if one member of type ! work.er; w'e,s to change ave :sion to authority and ,.~~,or.-v.er, ~ u i h ' h n u m s a l ~ e s > ~ d j~b~,":deseriptions must adjm,-t. ~i'k~ ~ offe~.d by employer 2 wilt fall along the at>.'.th0fity curve t~

~ ~alary~ g .by l:z toredu~, h~:.ex~ ~ d i J f o f work-e~, The employer 2-r .s-t z mhority he req,:••from>•ihis,workers while If the r~-3drva;~dty of a-.-• . . .. f . ~ t ~ n", . ,- I a ~ r i n c r e a s e s at t h e s a m e t i m e 'that the ,:xrm:)~ dr.,_e ~ u i r e d ~br macI~.,ine repair increases [a(e)=~h goes up] the ,~v,'.,#,.. e wilt i ~ the s ~ h ~ ~ offers. If the num~mrs of workers r~miai~ constant the ~ l a ~ mcre~"-wili •be jus ,su~;ei¢nt •":~ so that job a,atho.fity ~ unchanged. There is a shift in the authority curve aswell as a mo::~ne;,,.t along it._ The wv~-ke.~ of the employer '~tI be ~ t t e r off •than !f ,hr. p,-~Ic*,ab~: of ~ c h i ~ decreases .the s ~ l a r y . o f ~ workers is ~affe~t,.:d bu.~. H-.,e re~:-.'ired authority necessary to ;,,~tifv that ,~alar" and w : , ri~e w~... w~r!
J.D. Hess, The te,ms of

authority

253

1

w=l

....

J,',J~mm

t

it

~(,2)

A

.

.

.

.

.

.

.

.

.

L

.

.

.

.

.

.

.

.

.

.

.

.

.

.

" .

.

.

S(e)

.

a(2)

s(1)

a(1)

Fig. 6 1; Equilibrium m job markets ,.ke these may not produce an efficient allocation of resources. Consider an et.~, ao,uy witl two employe, rs and t h r ~ types of workers as in fig. 6. Only one iao.~"rence curve ~ drawn for each w o r ~ r type. Workers of type 1 are the learnt a , , . ' , ' ta a~'.thorlt? and workers ". of ty!ze 3 are the most averse ;o a u t h o i,v. Tl~e p-t~:L-..~, :'es arc ¢.,I ,.ne,~en such that workers of type t w o u l d accept ofier j rath,:r than ~:,7"~ 1: workers of t y p e . , would accept I rather than d. ~..~,. smg~e wJrker ~,. type 2 is indifferent betwc.en the two offers but as.~,.~m',: t b ~ ' : has ~-lected o.7-~ I. If the salary of employer t were to fall by 1/2 ~;nits ~e wc,:.~ld w a n t .:, !:ire ~ ',~'

addkicnal

work~r;

if the ~alarv o r cmp!-'-::~7,~,

'

~ uni~.; h,:

would want ~o fire one worker. By construction of the indifference c, irves all

e { g }..

S(e))::

V2(a(e) +

-

+ (S(e)- a(e)p.

S(~ is m a ( e ) the llhtter the expected profit relationsMp. By S(21 is d ~han S(1) is to a(t). From this we conclude a ~ ia S{2) by d a fall in S{1) by 1/2 units will increase the ~o~! ex ed [aofiis of ~ e empl+~ye~ ! a n d 2, In au¢, ~ ; ' 5 mte~; a~ ec~nom~with multiple equilibria. Not all eq are e f f : ~ n t ~cx~.equi_tJbdum l - J is dominated by L - K . All better off: if work~.~ 2 worked fbr:emp|oyer I. However, ~N.~e is a,~ t e n ~ n c y for I - d 1:o change s i n ~ salaries are determined 'by the labor marl;.:t~ not by fiat

is a tentative step toward a general model of the equilibrium a u t h ~ y . The contractual mode studied here peru!its the employer ~o ..... tL',e t~Ks pe by wor ~:ers. The motivation for o~cb an in on is simp|e. Authoritarian aLlocatiora of t'esourT,e e s i"s a Fev t t~hnique for distributing scarce lest ,.c~s. not only in centralized i ~ bu~ aL~o in ~ono~des with strong pr,~.~v:y fights. Mos't of us .~.r~,~,~-~.~ ~ . . ~ ~ work for a b~ss who te~+ us ~ow to use a large - e~orfion of our Not oMv s~o~ztd eco~omists invesxig~ conditions whieh~ result in s.~ w d u ~ d ' authority, but they s h o e d a~.,o ~o investigate" ''" the L~its i~ ~ rk

~ a m ~ i h e eq~il/brima of a system of job a ~:~a pfir~ ingredient. Employers au~,~,~y ~eeau=e of ~he unc-erta~nties tb; ~accA and workers were

:~0'~+-':~,: By p~stul~a:i~N s

c

chanm~es :in

wo::kers a t f i t u ~ , toward

J.D. Hes.s, The terms of .,mth,~"!~y

autt~:ority or changes in employei's' beliefs about uncert~tmt~t-3, the ~ d e i alzle to pre~'ct changes in salary levels as well as levels ,~f authorty.

23:,

w~s

Re~enees Arrow K.J., t971a, The role of securities in the optimal aiJocatior4 of risk-oearmg, in: K.J. Arrow, ed., Essays in the tht:ory of risk bearing (Markham Pub~i:~hing C~,mpany, Chicago. IL). Arrow, K.J., 1971b, The theory t,f risk aversion, in: K.J. ,~rrow, ~.. l:.~.;ays in the theory of risk beating. Bailey, M.N, 1974, W !,es and employment under uncertain demand Yeview of Economic Studies, Jan. Cheang, S., 1968, Private properly rights and share-cropping, Journal (,f Political Eco,omy Debreu~ G., 1959, Theory of valt; ~ (Wiley, New York) GrandmonL J.M.. 1977, Tempor-d general equilibriurn theory, Econon~.c~ric~, April Harris, M. and A R~viv, 1978, '..t~me r~ults on incentive contracts, A ,~erican Ecc,nomic Revi,~w 68. Holmstrom, B, 1979, Mora~ haz '~d and observability, Bell Journal of ~icc,zomics~ Sp.,i.-_? Lancaster, ICJ., 1976, A new ap[i,~.ach to consumer theory, Journal of Political Economy. Mirrlees, J.A., I976, The optim;.l structure of incentives and authority within an o:rganizati, m. The Bell Journal of Economi "s, Spring. Pratt, J.W., 1964, Risk aversion n the small and in the large, Economv tdca. Radner, R., 1968, Competitive e, ~uilibrium under uncertainty, Econome(rica. Radner, R., 1972, Existence of~ :luilibrium plans, prices and price expectations in a sequence of markets, Eeono~netrica. Ross, R., 1973, The economic theory of agenc2,: The principars proi~Iem, American Economic Review 63. Ross, S., 1974, On the economic theory of agmcy and the principle ,~f similarity, in: r). Balch D. McFadden and S. Wu, eds., Ess~,ys on behavior under un~.rtainty (North-Holla,d, Amsterdam). Shave.It, S., 1979, Risk sharing and incentive in the principal and agc~ :elationship, Bell Jour,:m] ot Economies, Spring. Simon, H., t957, A formal theory of the employment cc,ntract, in: H. Simon, ed., Models of n-~an (Wiley, New York). Stiglit~ J.E., 1975, Incentives, risk, and information: Notes towards a theory of hierarchy. The Bell Journal of Economics, Autumn. Williamson, O.E., 1975, M[arkets and hierarchies (The Free Press, New York). Wiltiamson, O.E., M.L. Wachter and J.E Harris, 1975. Understanding ~he employment retat~o:~: The analysis of idios)ncratic exchange, The Bell Journal of Econorr its. Spriag.