Teamwork Versus Delegation

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~andtheU W O R L DECONOMYELSEVIER Japan and the World Economy 7 (1995) 139-144

Teamwork versus delegation - comparison ofJapanese and German management stylesMartin J. Beckmann *Department of Economics, Brown University Providence, R J 02912 USA

Received March 1993; accepted August 1994

AbstractTeamwork and delegation as alternative management styles are described in termsof management production functions using Cobb-Douglas specifications; a compari-

son is made between management systems with teamwork at the top (the GermanVorstand system) and at the ground level (Japanese quality circles) as extreme cases.Keywords: Management; Teams; Delegation; HierarchyJEL classification: L22; L33

1. There are two basic modes under which management can operate:teamwork and delegation. They are clearly distinguishable when the coopera-tion of manager and managed, supervisor and supervised is described by aproduction function (Beckmann, 1988).F(x,y) (1)

in which x is the contribution of the managed and y that of the manager. If(1) is a description of teamwork, then delegation means that one supervised

Corresponding author. 77 Arlington Avenue, Providence, RI 02906, USA. Phone: 401861-3559. Fax: 401-863-1970.0922-1425/95/$09.50 1995 Elsevier Science B.Y. All rights reservedSSDI 0922-1425(94)00029-8


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140 u.s. Beckmann / Japan and the World Economy 7 (1995) 139-144person receives an amount y /x of attention or managerial effort. Then xsubordinates combined will produce

XF( 1 , ~ ) . (2)Under constant returns the expressions (1) and (2) are identical. Underincreasing returns, when F is homogeneous of degree h > 1, (2) may berewritten

XF( 1,~ ) =X1 -hF( x .v) < F( x .v) (3)for x > 1 and h > 1. Thus the team mode is more productive if and only ifthe management/production technology exhibits increasing returns to scale;if not throughout then at least over a sufficiently large range of output. Theteam mode is thus more productive ceteris paribus. In a hierarchical organi-zation teamwork at successive levels is impossible. A manager either headshis/her own team or is a full-fledged member of his/her boss's team. Inprinciple, teams might be found at alternating levels but in practice team-work has been applied mainly at the extremes, the top and the ground level.The former is often proclaimed in German business firms where top man-agers consider themselves members of the 'Vorstand' or leadership team.Western views of the Japanese business firm have focussed on 'quality circles'which are seen as ground level teams composed of one supervisor and theworkers he supervises (Aoki, 1984). (Of course, one might have it both ways:teams at the top and at the bottom, but this will not be considered here.) Inthis note we wish to compare the two management styles in regard to theworkers' (and thus the firm's) productivity. A comparison in terms of generalproduction functions turns out to be impossible, but results can be obtainedusing that old work horse of economic theory, the Cobb-Douglas productionfunction. The analysis is made for a basic hierarchy of three levels, but thiscan be extended to any number of hierarchical levels (resulting merely in amore complicated model but yielding the same conclusions).

2. Reduced to its most elementary form the question is one of comparingoutput in a firm with only three levels of hierarchy staffed by no workers, n1supervisors or managers and n2 =1 president. The Vorstand as a teamgenerates

units of 'supervision' to be distributed over no workers, whose output perhead is then


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MJ. Beckmann / Japan and the World Economy 7 (1995) 139-144 141The firm's output is

Q * =noF(1'~oF(n1,1)).Alternatively, there will be n1 quality circles of 1 supervisor and c/,workers. The supervisors productivity is generated in part by the managerialeffort of the president divided through delegation among the n1 supervisors,n1/n2 Each supervisor thus contributes to his/her team an amount ofsupervision in efficiency units equal to

(4)

Thus, team output

multiplied by the number n1 of teams yields a total output under qualitycircles of(5)

We may compare the total outputs Q * and Q or compare workers' produc-tivities(6)

(7)To facilitate comparison apply the homogeneity definitions to obtain

q * =F ( 1,:~ F ( 1,: J )q =(:: r - h F ( 1,:: F ( 1,~ ))

(10)

(11)Clearly, when h =1 the two productivities agree q * =q . It seems difficult toobtain a general inequality relating q * and q. A definite conclusion can bedrawn, however, for Cobb-Douglas functions.

F( x .r) = bx"'yf3 h = a + {3 > 1 (12)


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142 M.J. Beckmann / Japan and the World Economy 7 (1995) 139-144As seen below (from (Sa there is another restriction

a + {32 < 1so that a must lie in the range

1- {3 < a < 1 - {32 .

(13)

(14)In terms of no, nl, nz the organizational production functions (4), (5) arenow

Q * =bl+f3nb-f3nff3Q =bl+f3non\-a-f32

(4a)(Sa)

Notice that 1 - a - {32 > 0 is necessary for management to have a positivemarginal product.The productivities are nowq * =bl + f3 n -f3n"'f3nf3 2o I 2{j = l+f3no-In\-a-f32nf

(6a)(7a)

Notice that q * is produced under increasing returns to scale and Q underconstant returns to scale.Having fixed the presidential input n2 =1 production in terms of no andnI shows diminishing returns from

1 - (1 - a) {3 < 1and 1- {32 < 1respectively,so that the usual marginal conditions for profit maximization apply. Theseare

bl+f3 (1 - {3)n r /nf13 =W obl+f3a{3nb-f3nff3-1 =W I

(15)(16)

orbl+f3ano-In\-a-f32 =W obl+f3(l- a - {32)noni"'-f32 =W I

(17)(18)

From now on we standardize b =1, W o =1, W I =g. Dividing (16) into (15)and (18) into (17) we obtain the spans of control(19)

(20)


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M.I. Beckmann / Iapan and the World Economy 7 (1995) 139-144 143Substituting (19) in (15) one has the presidential spans of control

( af3 ) ' / ' - a;> g(l- f3)and using (20) in (16) similarly

n , =g-('-al//32 (1 _ a _ f 3 2 ) 0 - a ) //32 aa l/32Now

(21)

(22)a+f3>l

impliesl-a


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144 M.l. Beckmann / Japan and the World Economy 7 (1995) 139-144so that

q " > q (30)From (30) it follows that the Vorstand system induces greater output perworker. On the other hand, total outputsQ*=~ 1-f3

and profits71"* =(1-a)f3Q*i T =3 2 Q

(31)(32)

are significantly larger in the" quality circles" case when conventional values(25) are assumed.It is somewhat puzzling that teamwork at the top rather than at thebottom should result in a smaller, albeit more productive organization. Whileshareholders should then prefer the organizational form of quality circles, theVorstand system may be chosen by management in a quest for power -rather than profits. We should also caution the reader that the results are

derived for a technology (or production management) that exhibits increasingreturns to scale and involves one fixed factor - the president.

AcknowledgementsThis paper was written while I was a Visiting Scholar at Nagoya CityUniversity, whose generosity I wish to acknowledge with gratitude. I havebenefitted from discussions with Professor Makoto Tawada. I am also in-debted to the referees for their careful reading and many helpful suggestions.

ReferencesAoki, M., 1984, Economic Analysis of the Japanese Firm (North-Holland, Amsterdam).Beckmann, M. J., 1988, Tinbergen Lectures on Organization Theory (Springer-Verlag, New

York).

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Teamwork Versus Delegation