The comparison of collective learning, specialisation, informal and formal exchange in the model is purely analytical in terms of exploring the characteristics of hierarchies and networks. However, while it entails a high degree of abstraction, I also hope to provide a conceptual framework for explaining different organisational characteristics of T.V.Es. In particular the model attempts to formalise the main arguments in this chapter through exploring three related issues: The first is a trade-off between collective learning and specialisation depending on whether exchange is informal or formal. The second is a trade-off between collective learning and specialisation in the distinct group and extended sector. The third is to consider the effect of an exogenous increase in the size of the T.V.E sector on the first of the trade-offs.
First, consider the trade-off between collective learning and specialisation depending on the extent to which exchange is informal or formal. To do this let us assume that a T.V.E allocates labour to three activities. The first is specialisation, the second is collective learning and the third is building its reputation or discovering the reputation of other firms. Moreover assume the following: (a) the T.V.E must choose its optimal participation in each process at the start of the period (this is a one period model), (b) the firm can substitute between processes without cost (this means that factors such as the initial cost of training labour in different processes is overlooked), (c) the returns to each process depend on, and are increasing functions of, the amount of labour assigned to them, and (d) the T.V.E seeks to maximise a given utility function:
U = E n u (X Cltr) (1) c=d,i
where U is satisfaction, Xc is a composite which denotes two “states of outcome” or “two states of the world" - (i) when contracts are formal (xd) and (ii) when contracts are informal (xj). n denotes the probability of state c. Let xd occur with probability n and Xj occur with probability (1 -11) where 0 < n < 1. n refers to the probability that contractual rights are certain and tr denotes the net benefits of devoting time to nurturing reputation or discovering others’ reputation where:
x„ = (B , - Cs)NU(ls) + (B, - C s)u(l5) + (B„ - C c)NU(lc) ^ = S NU(ls) + S u(ls) + C NU(lc) (2 )
x, = (Bc - Cc)NU(lc) + (Bo - Cc)u(lc) + (B , - C S)NU(IS) X, = C NU(I0) + C u(lo) + S NU(ls) (3)
and tr=f(lr) where lr 0 as JT-^ 1 (4) subject to: L=lr + lc + ls (5) (endowment constraint) and lr> 0, lc>0, ls>0 (6) (non-negativity requirements)
[c is labour allocated to collective learning, Is is labour allocated to specialisation,
Bs and Cs are the benefits and costs of specialisation, and Bc and Cc are the benefits and costs of collective learning
The relationships in (2) and (3) endeavour to formalise a trade-off between specialisation and collective learning, dependent on the value of n (the extent to which contractual rights are certain). There are other formal models which attempt a similar trade-off in the context of the J-mode (see eg Aoki 1984, 1986, 1989, Itoh 1987) and the ideas here borrow from those models. The underpinning premise in equations (2) and (3), consistent with Aoki’s and Itoh’s writings, is that (a) formal exchange reaps economies of specialisation, but at the expense of collective learning, while (b) informal exchange results in economies of collective learning, but at the expense of greater specialisation.
The net benefits fro m specialisation
Snu=(Bs - CS)NU and Su=(Bs - Cs)u represent the net benefits from specialisation. SNU=(Bs - CS)NU denotes the net benefits and costs associated with specialisation that exists with both formal contracting (xd) and informal contracting ( X j ) . The rationale is that even when all exchange is informal, specialisation exists. Yang & Wills (1990) give a formal proof that specialisation within the firm and exchange occur simultaneously whether exchange is formal or informal.19
Su=(Bs - Cs)u represents economies of specialisation due to formal exchange. This depicts the net benefits associated with specialisation (over and above the general benefits) as exchange becomes more formal. The benefits arise because as the amount of arms-length exchange increases, labour is released from gathering and processing information through informal channels. This can be reallocated to specialised production in the firm. The costs denote the net benefits of collective learning from informal exchange which are foregone.
The net benefits fro m collective learning:
Cu=(Bc - Cc)u and CNU=(Bc- Cc)NU are the net benefits from collective learning.
Cnu=(Bc - Cc)NU denotes the net benefits and costs associated with collective learning that exists with both formal contracting (x^) and informal contracting (X j).
Even when exchange is formal, some opportunities exist for collective learning within the firm and to some extent between firms through information exchange.
Cu=(Bc - Cc)u represents net benefits to collective learning specific to informal exchange. The benefits (Bcu) include inter-firm learning due to more flexible exchange which generate innovations which are in excess of value creation when exchange is at arms-length. The costs (Ccu) relate to the extra time and effort that need to be diverted from specialised processes to facilitate inter-firm integration and value creation. These include the extra costs of bargaining, as well as coordination and communication in the absence of formal exchange.
The condition in (4) suggests that as exchange becomes more formal, labour devoted to "reputation issues” decreases. The T.V.E devotes labour time to nurturing its own reputation and discerning the reputation of potential contractees. When exchange is informal (ie. low n ) nurturing and discerning reputation will be important ex ante when deciding whether to contract because of the absence of explicit sanctions. As exchange becomes more formal, reputation will be less of an issue. Having said this, I am not suggesting that the polar extreme (11=1) exists. The existence of court/arbitration costs means that even in high n societies such as Western Europe some contracts will be negotiated on reputation (see eg Macauiey 1963, Williamson 1975 pp. 103-108).
If we substitute (2) and (3) into (1) the problem is now to maximise:
subject to (5) with respect to the choice variables lr, lc and ls
Thus, taking the first derivative, the Kuhn-Tucker conditions are as follows:
au/ai < X
(au/ai).i<x
(8)
l>0where I denotes the optimal values for lr, lCl k and X (the Lagrangean multiplier) denotes the marginal utility of labour or marginal utility of the firm’s time (5U/dL).
We are interested in how the firm allocates labour between collective learning and specialisation as the degree to which contractual rights are certain varies. If we assume that labour allocated to reputational issues (lr) is given (for a given n), the optimal allocation of labour between specialisation and collective learning, in the case of an interior solution, must meet the first order condition:
A (cu + cw ) - ^ ‘7cM/ - ( s " u + su) 1-
=n
U ' (X d )/(1 -n ) U- (Xi) (9 ) where: cu=rfCu« lCl cNU =dCm/d\c, / u =</SNU« ls, and su=rfSu« lsThe term on the left hand side of (9) is the slope of a production transformation curve (PTC) of the composite variable Xc between the two states of the world (Xd and Xj). The term, on the right hand side of (9) is the slope of an indifference curve (defined along dU*-0). The PTC, in figure 6.2, is defined between the points A and B because of the conditions in (4) and (5). The vertical and horizontal intercepts, drawing diagonals from A, are (CNU+Cu)(lc) + SNU(ls) where ls+lc=L-lr, and lr >
0.
The horizontal intercept at B is (SNU+Su)(ls) + CNU(lc) where L=ls+Ic,lr=0
whenn=1
given (4). Three indifference curves, in figure 6.2, (Ui, U2 and U3) show three possible outcomes. A and B are both corner solutions denoting outcomes when contractual rights are ex ante certain(11=1)
at B and contractual rights are ex ante uncertain(n=0)
at A. These are polar cases. The point C shows the first order condition for the optimal allocation of ls and lc givenan interior solution (/'e when 0<
n <1)-
The point C is a strict global maximum provided that (a) indifference curves are convex to the origin and (b) the PTC is linear or concave. The first implies diminishing marginal rate of substitutionXd.Xi while the second suggests diminishing marginal rate of transformationXd.Xi.Equations (8) and (9) together with figure 6.2 can be used to consider the firm's allocation of labour between specialisation and collective learning as n varies. At point B (11=1) a required condition to allocate more labour to collective learning is that the absolute value of the slope of the PTC exceeds the absolute value of the slope of the indifference curve (Ui). The reverse is true at A. At
FIGURE 6.2
Xj
X d
point A ffl=0) a required condition to allocate more labour to specialisation is that the absolute value of the slope of the indifference curve (U2) is greater than the absolute value of the slope of the PTC. When we take into account marginal returns to collective learning and specialisation this suggests the following:
Proposition 6.1:
If the extent to which contractual rights are certain increases (decreases) the firm will substitute Is for l c ( l c for Is ) provided that the marginal returns on economies of
specialisation due to formal exchange [ie. su ] are greater than (are less than) the marginal returns on economies o f collective learning due to informal exchange[/e. cu ].
Second, consider the trade-offs between collective learning and specialisation determining the size of the regional network/distinct group and extended sector.
Let Un=otYE+(1-a)YH (10) where:
Un denotes T.V.E willingness to contract for a given value of II,
Yh refers to the number of T.V.Es in the regional network/distinct group, Ye refers to the number of T.V.Es in the extended T.V.E sector,
and a is a positive function of the size of the T.V.E sector in terms of both (i) the actual size of T.V.Es and (ii) the number of T.V.Es.
The relationship in (10) captures the dualistic structure of the expanded T.V.E sector. The parameter a is a positive function of the size and number of T.V.Es where 0<a<1. When a=0 YE does not exist. This is the traditional and still predominant T.V.E regional network denoted here as YH. However, as the T.V.E sector grows it was suggested above that two things happen: (i) institutional innovation draws other parties into the distinct group and (ii) the T.V.E starts to contract outside of the distinct group forming a series of inter-regional relationships with other parties. The growth in the T.V.E sector is depicted in (10) via an increase in the parameter a. When a is greater than zero a dualistic
structure emerges. When this occurs there is a core of informal exchange (with some formal exchange) in a distinct group (YH) and a core of arms-length exchange (with some informal exchange) in the extended sector ( Yh).20
Let:
Y H=[Pd(ls) - M ls ) ] + [ C u*(lo) - Ri(lc)] (1 1 )
and
Ye=(Pi(Io) - Vii(lc)]+[SU* (I5) - Rd(ls)l (1 2 )
where:
pd - |Lid are the net benefits of specialisation over and above the general benefits associated with limited formal exchange in the distinct group. Cu*- Rj are the net benefits of collective learning in excess of the general benefits associated with informal exchange within the distinct group.
pi - pi are the net benefits of collective learning in excess of the general benefits associated with limited informal exchange in the extended sector.
Su*- Rd are the net benefits of specialisation over and above the general benefits associated with formal exchange in the extended sector.
and
L *= ls+lc (13) is the relevant labour constraint
Equations (11) and (12) are specified so that there is both informal and formal exchange in the distinct group and extended sector. The reason is that not all exchange in the distinct group is informal, nor is all exchange in the extended sector formal. Members of the regional network or distinct group are assumed to enter into some arms-length exchange and, in the extended sector, parties who normally exchange at arms-length are assumed to enter into some informal
relationships. However, economies of collective learning due to informal exchange in the extended T.V.E sector (pi - pi) are assumed to be a strict subset, in terms of degree, of economies of collective learning due to informal exchange within the distinct group (Cu* - Ri). This seems reasonable given that informal exchange is much more extensive in the latter. Thus, let (Cu* - Ri)=(pi - pi)+(j>i where (j>i denotes the difference in the net benefits from informal exchange between extended sector (YE) and distinct group (YH). The same assumption is made, but in reverse, for the net benefits from formal exchange. Economies of specialisation from formal exchange within the distinct group (pd - pd) are assumed to be a strict subset, in terms of degree, of economies of specialisation from formal exchange in the extended sector (Su* - Rd). Thus, let (Su* - Rd)=(pd- Pd)+<j>d where (|)d depicts the degree to which net benefits from formal exchange in the extended sector (YE) exceed the net benefits from formal exchange within the distinct group (Y h). This also seems reasonable given that casual empiricism suggests formal contracts are more widespread in the extended T.V.E sector. If we substitute (11) and (12) into (10) and maximise (10) with respect to (13) we set up a first order condition for an interior solution which is analogous to (9):
- 1 (cu* - n) - (/&- //,,)/ (/?,- //,) - (su* - rd) I = aU n’ (YE)/(1-a) Un ' (VH) (14) where: ^^dC^Vcftu rFdR\/cJ[u Pd~d\)Jd\^ m~d\xdd\^ pj=dfyld\u fii=d\.ijd\u
^*=6/Su*/6/ldl rci=dRJd\d
The expression on the left hand side, as in (9), is the slope of a PTC. The expression on the right hand side is the slope of an indifference curve. If a=0 we have a corner solution where all exchange occurs within a regional network and there is no extended T.V.E sector. If we start from a position where a=0, under what conditions will the T.V.E sector extend outside the regional network? Equation (10) suggests that an extended sector will emerge when a>0 where, as noted above, a is a positive function of the size and number of T.V.Es. An
increase in the size and number of T.V.Es will effect the marginal net benefits to collective learning from informal exchange - [(cw* - ri)+ (/?,-juj)] - and the marginal net benefits to specialisation from formal exchange - [(su* - rd) +((3d- fid)].
The precise effects of an increase in the number and size of T.V.Es on marginal net benefits of collective learning and specialisation is an empirical issue. Nonetheless, some observations, although somewhat arbitrary and impressionistic, are still possible. Consider the effect of an increase in the numbers and size of T.V.Es on the marginal net benefits to collective learning from informal exchange. As the number of contracting parties increases we would expect that the marginal net benefits would decrease. This is because the marginal costs of collective learning specific to informal exchange (ie. dCculd\c or ;•/+ fii) will increase. First, with larger numbers, more time and effort will need to be diverted from specialised production in the firm in order to collect and process information through informal channels. Second, with larger numbers, the costs of communication, co-ordination and bargaining in the absence of formal exchange will increase with more complex horizontal integration.
The effect of an increase in the size and number of T.V.Es on the marginal net benefit to specialisation from formal exchange, however, might not be the same over the entire range of a. First, it seems reasonable that the marginal net benefits to specialisation from formal exchange will increase with larger firms and more contracting parties for low to middle values of a. First, in terms of size, opportunities exist for economies of scale with vertical integration, but the marginal costs of specialisation due to worker alienation or boredom are likely to be small for low to middle values of a. With respect to an increase in the number of T.V.Es, the costs of facilitating specialisation through formal exchange is likely to small over low to middle values of a. It seems plausible
that for low to middle values of a an increase in the number of contracting parties will reduce the marginal cost of stipulating ex ante contractual rights because for the nthcontractor most of the formal details will be in place.
However, for higher values of a we might expect that the marginal net benefits of specialisation from formal exchange will decrease with more contracting parties and larger firms. In terms of size, there is likely to be diminishing returns to scale economies. In terms of numbers, the marginal cost of ex ante stipulating and ex post enforcing contractual rights will be high. The reason is that for high values of a casual empiricism suggests the transactions will be ex ante more complex and, therefore, cost more (in terms of legal expenses) to enforce. We can summarise the suggested effects of an increase in a on the marginal net benefits of specialisation from formal exchange as follows: For low to intermediate initial values of a such that a is less than some specified value a*, an increase in the number and size of firms will have a positive effect on the marginal net benefits of specialisation from formal exchange. However, for higher initial values of a (values of a greater than a*), an increase in the number and size of firms will reduce the marginal net benefits to specialisation from formal exchange. Thus a* is the value of a for which (su*+ /y - {fd+jnJ) changes from an increasing to a decreasing function of labour allocated to specialisation (ls). Given these observations (14) suggests the following three part proposition:
Proposition 6.2:
Given that cpi >0 and that cpd >0,
(i) with an increase in the size of the T.V.E sector a dualistic T.V.E sector will emerge provided that the marginal net benefits of specialisation from formal exchange in the extended sector (.vw* - i\i) are greater than the marginal net benefits of collective learning from informal exchange within the distinct group {cu* - r t).
(ii) for values o f a < a * (/<?. values for which the marginal net benefits o f specialisation from formal exchange are an increasing function o f ls given 10) with an increase in the number and size of firms, the size of the extended sector will increase provided that the marginal net benefits o f specialisation from formal exchange in the extended sector (su* - r j) are greater than the marginal net benefits o f collective learning from informal exchange within the distinct group (cu* - r,-).
(iii) for values o f a > a* (Je. values for which the marginal net benefits of specialisation from formal exchange are a decreasing function o f ls given l0) with an increase in the number and size of firms, the size o f the extended sector will increase provided that (a) the marginal net benefits of collective learning from informal exchange (cu* -rf) are greater than the marginal net benefits of specialisation from formal exchange ( f i d - / / , /) within the distinct group, (b) the
marginal net benefits o f specialisation from formal exchange (su* - are greater than the marginal net benefits of collective learning from informal exchange (fit - //,) in the extended sector and (c) the marginal net benefits o f specialisation from formal exchange in the extended sector are greater than the marginal net benefits of collective learning from informal exchange within the distinct group.
Third, consider the effect of an exogenous increase in the size of the T.V.E sector on the relationship between collective learning, specialisation, informal and formal exchange. To do this we must spell out what, to this point, has been implicit: (i) S u= ( S u* - R d)+ (pd - pd) and (ii) C u= ( C u* -R i)+ (p j - pi). When the equality in equation (14) holds (first order condition for an interior solution) there will be a value of n for a given a which corresponds to the optimal value of n in equation (9). This corresponds to the value of n at C in figure 6.2. To show the effect of an increase in a on 11 in terms of both equation (9) and figure 6.2 consider figure 6.3. Assume that there is an exogenous increase in the number
FIGURE 6.3
and size of firms. The intercepts of the PTC in figure 6.2 will change. With an increase in a, the maximum possible Su will increase while the maximum possible Cu will decrease provided that <)>i>0 and tj>d>0. This follows when equations (11) and (12) are inserted into (10). The PTC will rotate as shown in figure 6.3. A1 will lie below and to the left of A and B1 will lie to the right of B.
Point C in figures 6.2 and 6.3 correspond. The dotted PTC in figure 6.3 has the same M R TXd.xi as A1 B1 for given values of xd and xi (ie for given values of