Two forms of workers' enterprises facing imperfect labor markets

Economics Letters 41 (1993) 121-127 0165-1765/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved

121

Two forms of workers' enterprises facing imperfect labor markets Ernst Fehr

*

Department of Economics, University of Technology, Argentinierstrasse 8/175, A-1040 Vienna, Austria

Murat R. Sertel Department of Economics, Bogazi#i University, Bebek, 80815 lstanbul, Turkey Received 9 December 1992 Accepted 20 January 1993

Abstract

We analyse workers' enterprises (WEs) facing an imperfect labor market with two different internal property rights structures. One type, the discriminatory W E (DWE), admits new members sequentially, charging each the maximum he is willing to pay as entrance fee. The non-discriminatory W E ( N D W E ) , on the other hand, admits new members in a single block, charging them all the same entrance fee. All except the marginal member in the D W E earn strictly more than their opportunity wages. The behavior of both types of W E is derived from the interests of individual members. U n d e r perfect competition the two types coincide in their employment behavior, behaving efficiently. Under imperfect competition, while the D W E remains fully efficient, the N D W E becomes inefficient, although less so than its profit-maximizing twin acting as a non-discriminatory monopsony.

I. Introduction

Starting with the contributions of Ward (1958), D o m a r (1966) and Vanek (1970), there now exists a large literature which assumes that labor-managed firms (LMFs) maximize income per worker. 1 It is well known that this type of LMF exhibits perverse supply and employment responses to changes in output prices or in fixed costs, and generates in general an inefficient allocation of resources. Sertel (1982, Ch. 2, 1987, 1990, 1991) showed that the introduction of tradeable membership rights cures these perversities and renders worker-run firms efficient if output and membership markets are perfectly competitive. 2 To distinguish LMFs with tradeable membership rights from other types of LMFs, Sertel termed them worker's enterprises (WEs). The decisive feature of a W E is that the workers and the partners of the firm coincide, so that entering

* Corresponding author. For a recent example see Drrze (1989). 2 Dow (1983, 1986) analyzed competitive LMFs with tradeable membership rights in a multi-period context and showed that they behave exactly as their competitive profit-maximizing twins. For the analysis of WEs in a dynamic context, see also T/itiinc/i (1992a,b).

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(departing) members buy (sell) their membership rights. In general, all members have active and passive (voting) rights and claims to (not necessarily equal) shares of the firm's income. 3 The membership market (i.e. the market for tradeable membership rights) in the above papers was modeled as perfectly competitive. Under these circumstances, Sertel established the equivalence principle that the physical economic behavior of a W E matches identically that of its profit-maximizing twin, although it favors workers in its distribution of welfare. The question remains whether this equivalence principle carries over to an imperfectly competitive membership market: in particular, do WEs employ more or less labor than their profit-maximizing twins when facing an upward-sloping labor supply schedule? It turns out that the equivalence principle generalizes for D W E s but breaks down for N D W E s . In general, facing a rising wage schedule, WEs will employ at least as much labor as their capitalist twins. 4 As we shall see below, the precise results depend on the property rights structure of WEs. Sertel's above-mentioned papers can be interpreted as modeling WEs to be sequentially discriminatory in admitting new members: given m incumbents, the next member, the (m + 1)st, pays the difference between the W E ' s value added per worker and his opportunity wage, but then he also receives a share of the entry fee charged of the (m + 2)nd member, and so on. U n d e r this principle, a new member immediately participates in the entry fees of all further members admitted. Apart from (sequentially) discriminatory workers' enterprises (DWEs), here we regard also (sequentially) non-discriminatory workers' enterprises (NDWEs), where all new members pay the same entry fee. Yet only the initial, say m, incumbents receive a share of the entry fee collected from additionally admitted members. Of course, all new members share the W E ' s value added along with the other members. This property rights structure has been analyzed by Dow (1986) and Fehr (1990a,b), and by Sertel (1985) who compared D W E s with N D W E s . U n d e r perfect competition, both forms of W E employ the same amount of labor as a PM twin, but faced with an upward-sloping labor supply schedule, their behavior differs: while sequential discrimination renders the W E fully efficient 5 the N D W E employs in general an inefficient amount of labor. Although all except the marginal member in the D W E earn strictly more than their opportunity wages, the D W E and its twin discriminatory PM monopsony behave identically in their employment. The N D W E , however, employs more labor than its twin non-discriminatory PM monopsony.

2. The sequentially discriminatory worker's enterprise (DWE) Our D W E here faces a perfectly competitive price p in the output market. Output is given by a twice differentiable, strictly concave, increasing function, q(n), where n denotes the n u m b e r of workers. The inverse supply schedule of labor is given by a strictly increasing function, w(n), of n. The number of initial or 'founding' members of the W E is given as m > 0. For simplicity we 3For a survey, see Fehr (1990b) and Kleindorfer and Sertel (1992). 4Notice that if there is imperfect competition in the output market and perfect competition in the labor market the equivalence principle still holds. Sertel (1990, 1991) showed that in oligopolistic markets with Bertrand, Cournot, free entry Cournot or Stackelberg competition, WEs duplicate the behavior of profit-maximizingfirms. On the equivalence in the case of a monopolistic output market, see Fehr (1990a). 5 In our context efficiency means that the marginal product of labor is equal to the supply price of labor, i.e. the reservation wage. Of course, a non-discriminatory PM monopsony fails to be efficient because it settles where the marginal product of labor exceeds the reservation wage.

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assume that the income of a W E with n partners is distributed equally 6 among all n partners, so that each partner receives (1)

y(n) = p q ( n ) / n .

The hth new member admitted is charged r(m + h) = y ( m + h ) - w ( m + h ) ,

and the proceeds from selling a membership deed at the price r(m + h) are shared by the m + h - 1 incumbent members. Treating, for convenience, the number of workers as a 'continuous' variable, 7 the income of each of the m founding members is given by

z = y(n) =

L

[(y(x) - w(x))/x] d x .

(2)

The second term in (2) represents a founding member's income resulting from selling membership rights to n - m additional workers under the principle of sequential discrimination. Generally, when n - m new members buy in, the income of the kth member is given by

z k = y(n) - r(k) +

[(y(x) - w(x))/x] d x ,

(3)

with r ( k ) = y ( k ) - w ( k ) . The second term in (3) denotes the deed price to be paid by the kth member and the last term again reflects this member's income from selling further membership deeds. [Founding members pay no entry fee, i.e. r(k) = 0 if 1 - k - m, giving (2) as a special case of (3).] To derive the employment choice of the D W E , we determine the marginal contribution of an additional member to the income of an incumbent member: ~Zk/~n = ~z/~n = ( 1 / n ) [ p q ' ( n ) - y ( n ) ] + (1/n)[y(n) - w(n)l

= ( 1 / n ) [ p q ' ( n ) -- w(n)].

(4)

Thus, the marginal contribution of a new admission to the income of all incumbents is the same, whether the incumbent be one of the initial m members or a later adhesion. Hence, regarding the partnership's size or the firm's choice of the employment level, the interests o f all m e m b e r s coincide, because the contribution of an additional member to the W E ' s income is ( p q ' - w) and this amount is shared equally among incumbents. Therefore, they agree u n a n i m o u s l y and, in fact, employ the efficient amount of labor, n*, defined by p q ' ( n * ) = w(n*). The equilibrium of the D W E is depicted in Fig. 1. Are the members of a D W E better off where they are or are they indifferent between working in the W E and choosing their next best alternative? We compute 6Sertel (1982) and Fehr (1990a) consider the implications of an unequal distribution of the value added. 7For simplicity in the rest of the paper we treat n and m as 'continuous' variables, i.e. allow them to be any (non-negative) real number.

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)

pof' (~)

~ vyvy(n)

I I I k n~ Fig. 1. Equilibrium of the DWE.

~,rl

I

z~ - w(k)

= y(n)

= =

- y(k)

+

y ' ( x ) dx +

f/

[(y(x)

-

w(x))/x] ax

[(y(x) - w ( x ) ) / x ] dx

[ ( p q ' ( x ) - w ( x ) ) / x I d x >- O,

(5)

which is strictly positive for k < n and nil for k = n. Thus, except for the last admitted ( ' m a r g i n a l ' ) m e m b e r , each m e m b e r is strictly better off in our D W E than abroad. I m m e d i a t e l y upon becoming the kth m e m b e r , one participates in the income generated by admitting ( n - k) additional members. In Fig. 1 this income is given by the shaded area. As (5) indicates, this income has to be shared with all (k - 1) m e m b e r s who joined before the kth m e m b e r as well as with all sequentially admitted further m e m b e r s k ' with k -< k ' - n - 1. O f course, a perfectly discriminatory PM m o n o p s o n y which pays each hired worker just his reservation wage will also employ the efficient amount of labour, n*. But notice that our D W E is not discriminatory in this sense. As we have shown above, all m e m b e r s but the last admitted earn strictly m o r e than their reservation wages. The charter of our D W E ensures an efficient e m p l o y m e n t choice while its m e m b e r s appropriate and share the firm's entire 'rent', and all this in a m a n n e r rendering the partnership unanimous in decision-making.

3. The sequentially non-discriminating workers' enterprise (NDWE) In contrast to the D W E , in our N D W E new m e m b e r s do not participate in the revenue generated by selling m e m b e r s h i p deeds. They receive y ( n ) , having paid an entry fee r(n) = y ( n ) w ( n ) . H e r e the incumbents admit new m e m b e r s all at once and charge them each the same deed price, r(n), while in the D W E new m e m b e r s were admitted sequentially and each paid a different entry fee, r ( k ) , for m < k -< n. U n d e r the N D W E charter the income of an incumbent m e m b e r is given by

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/ Economics Letters 41 (1993) 121-127

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z ° = y(n) + [y(n) - w(n)J(n - m ) ( 1 / m ) = ( 1 / m ) [ p q ( n ) - w(n)n] + w(n).

(6)

It is obvious that when the labor market is perfectly competitive, so that the W E has to take w as a given constant, the maximization of (6) leads to the same first-order condition as the maximization of profits. But if the W E faces an upward-sloping w(n) schedule, the income of incumbent m e m b e r s is maximized, where

pq'(n) = w(n) + (n - m)w'(n)

(7)

holds. In contrast, a non-discriminatory PM monopsony will hire labor up to where

pq'(n) = w(n) + w'(n)n

(7')

is met. Since m > 0 and w' > 0, the marginal cost of labor for the N D W E , as given by (7), is thus lower than that given by (7') for the PM twin, and so the N D W E will employ m o r e labor than its PM twin. The intuition behind this result is that, while employing an additional worker in a PM m o n o p s o n y raises the wages of all its workers by w', the e m p l o y m e n t of an additional m e m b e r by the W E raises the 'wages' of only (n - m) workers by w'. Put differently, the m founding m e m b e r s of the N D W E do not count the increase in w(n) that accrues to themselves as a cost. Only the newly hired (n - m) m e m b e r s become dearer as membership increases. The e m p l o y m e n t choice is depicted in Fig. 2. All m incumbents unanimously agree to admit (m 1 - m) new m e m b e r s , because at m 1 condition (7) holds. Does m~ therefore represent the equilibrium of the N D W E ? Put differently, does the new group of ma incumbents prefer an e m p l o y m e n t level different from m l? The answer to this question can be inferred from Fig. 2. Given m~ incumbents, the marginal cost of labor schedule is now w(n)+ ( n - m l ) w ' ( n ) , which differs from [ w ( n ) + ( n m)w'(n)] with m incumbents and intersects the marginal productivity curve, pq'(n), at m 2 > m]. Therefore, all m e m b e r s of the new group of m~ > m incumbents unanimously agree to employ (m2-ml) additional members. Defining n* by w ( n * ) = p q ' ( n * ) , the incentive to increase e m p l o y m e n t prevails for all m i < n* (i = 1, 2 . . . . ), which we could construct as above. Given n* incumbent members, however, this incentive vanishes, because here the marginal cost of labor, [w(n) + ( n - n*)w'(n)], hits the marginal productivity schedule at n = n* (see Fig. 2). Thus, the

" I

I

J

J

i

Fig. 2. Stepwise and limiting equilibrium of the NDWE.

,~n

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/ Economics

L e t t e r s 41 ( 1 9 9 3 ) 1 2 1 - 1 2 7

sequence {mi}~ ~ of e m p l o y m e n t levels generated by the above adjustment process in the N D W E will converge to the efficient e m p l o y m e n t level, n*. In this adjustment process each new group of incumbents charges the additionally e m p l o y e d m e m b e r s a uniform entry fee, with no discrimination within each new group admitted. Between newly admitted groups, however, the entry fees differ. In Fig. 2, for example, m e m b e r s of the first group of ( r n ~ - r n ) admissions each pay a fee of r~ = y ( r n ~ ) - w ( m l ) , while the next group of (m 2 --ml) m e m b e r s each pay a fee r 2 = y ( r n 2 ) - w ( m 2 ) < r I. Due to this discrimination across groups of workers, to a certain extent the N D W E resembles the D W E . If the charter of the W E or the law requires that all new m e m b e r s have to be charged the same entry fee, that is, if discrimination across groups of workers is forbidden, the equilibrium condition is given by (7). Notice that according to (7) the N D W E may at times actually end up employing more than n* workers during business cycles. Suppose, for instance, that rn happens to be equal to n~ and that there is a fall in the output from P0 to Pl. Then the efficient e m p l o y m e n t level decreases to, say, n *I. Meanwhile the marginal cost of labor now intersect Plq' below m, inducing the N D W E to decrease n. But since the marginal cost of labor is below w(n) for n < m, at this instant equilibrium e m p l o y m e n t in the N D W E will be higher than n~. (A re-adjustment process can now be traced in the reverse order of that analyzed above.) T h e r e is an interesting similarity between the functioning of a N D W E and the decentralized planning mechanism proposed by Ireland and Law (1978). Ireland and Law invented an 'enterprise incentive fund' to include the Illyrian firm, which is supposed to maximize y, value added per worker, to employ the efficient amount of labor. U n d e r this scheme an Illyrian L M F receives (or pays) a p r e m i u m from (or to) the fund. If we reinterpret the deed p a y m e n t s [ y ( n ) - w ( n ) ] ( n - m) of (6) as payments from an enterprise incentive fund to the incumbent m e m b e r s , we will see that such a fund imitates the membership market. ~ Note that under the Ireland and Law scheme, if there is a m e m b e r s h i p reduction from rn to n < m, the L M F is required to pay (y - w)(rn - n) to the fund; when a deed m a r k e t is operative, this p a y m e n t goes to the departing m e m b e r s of the N D W E .

4. Summary We have examined the e m p l o y m e n t choice of two WEs with different internal property rights structures. While they both employ the efficient amount of labor under perfect competition, their e m p l o y m e n t levels differ if they face an upward-sloping labor supply schedule. Both forms of W E employ more labor than a non-discriminatory PM monopsony. A sequentially discriminatory W E is efficient even if monopsonistic conditions prevail, although all m e m b e r s (except the marginal one) earn strictly more than their reservation wages. In the absence of sequential discrimination, however, e m p l o y m e n t will fall short of the efficient level, although by less than the deficiency observed for the PM twin.

The difference between 'our' fund and the proposal of Ireland and Law is that they design the incentive payments in such a way that all members, i.e. incumbent members plus new members, receive the same income. Under their scheme the incentive fund pays P ~ ( x - w ) ( n - m ) to the LMF and P is shared equally among all n members. Here x represents the income of a member and is defined by x - y ( n ) + ( P / n ) , which gives x = ( 1 / m ) ( p q - w n ) + w . Notice that x coincides with z ° in (6).

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References Domar, E.D., 1966, The Soviet collective farm as a producer cooperative, American Economic Review 56, 734-757. Dow, G., 1983, Labor management in a competitive society, Institute for Social and Policy Studies, Working Paper No. 10008, Yale University, New Haven, CT. Dow, G., 1986, Control rights, competitive markets, and the labor management debate, Journal of Comparative Economics 10, 48-61. Dr6ze, J.H., 1989, Labour management, contracts and capital markets (Basil Blackwell, Oxford). Fehr, E., 1990a, The simple analytics of a membership market in a labour-managed economy, forthcoming in: S. Bowles, H. Gintis and B. Gustafson, eds., Democracy and markets-problems of participation, democracy and efficiency (Cambridge University Press, Cambridge). Fehr, E., 1990b, Labour management, forthcoming in: International handbook of cooperative organizations (Vandenhoek and Ruprecht). Fehr, E. 1992, The workers' partnership-full employment through changing insider interests, forthcoming in: M.R. Sertel, ed., Workers' enterprises - alternative in privatization (North-Holland, Amsterdam, New York, Oxford). Ireland, N.J. and P.J. Law, 1978, An enterprise incentive fund for labour mobility in the cooperative economy, Economica 45, 143-153. Kleindorfer, P.R. and M.R. Sertel, 1992, The economics of workers' enterprises, invited lecture presented at the X World Congress of the International Economic Association, Moscow. Sertel, M.R., 1982, Workers and incentives (North-Holland, Amsterdam, New York, Oxford). Sertel M.R., 1985, Lecture notes in microeconomic theory, Bogazici University, Istanbul (unpublished). Sertel, M.R., 1987, Worker's enterprises are not perverse, European Economic Review 31, 1619-1625. Sertel, M.R., 1990, Workers' enterprises in price competition, Bogaziqi University Research Paper, forthcoming in Managerial and Decision Economics. Sertel, M.R., 1991, Workers' enterprises in imperfect competition, Journal of Comparative Economics 15, 698-710. Tiitiincfi, M.M., 1992a, An infinite horizon workers' enterprise with finitely-lived members of different ages, forthcoming in: M.R. Sertel, ed., Workers' enterprises-alternative in privatization (North-Holland, Amsterdam, New York, Oxford). Tiitiincii, M.M., 1992b, An overlapping generations economy with workers' enterprises, forthcoming in: M.R. Sertel, ed., Workers' enterprises - alternative in privatization (North-Holland, Amsterdam, New York, Oxford). Vanek, J., 1970, The general theory of labor-managed market economies (Cornell University Press, Ithaca, London). Ward, B., 1958, The firm in Illyria: Market syndicalism, American Economic RevieW 48, 566-589.