Incentives and Labour Supply in Co-Operative Enterprises

Incentives and Labour Supply in Co-Operative EnterprisesAuthor(s): Norman CameronSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 6, No. 1(Feb., 1973), pp. 16-22Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/133859 .

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INCENTIVES AND LABOUR SUPPLY IN CO-OPERATIVE ENTERPRISES*

NORMAN CAMERON University of Manitoba

Les stimulants et l'offre de travail dans les entreprises cooperatives. Dans les entreprises cooperatives du type des fermes collectives sovietiques, les menages ont le choix de repartir leur temps entre le travail pour la cooperative, le travail pour eux-m6mes sur leur propre lot, et le loisir. Michael Bradley a fait une analyse de cette question dans le cas d'une cooperative composee de menages identiques qui cherchent a maximiser leur utilite. L'auteur du present article apporte des corrections a la partie de l'analyse de Bradley dans laquelle il pr6tend que des changements des frais fixes de la cooperative modifient les choix des menages. I1 consacre ensuite son article au cas beaucoup plus interessant et important d'une cooperative composee de menages qui n'ont pas des gouts identiques et qui n'agissent done pas de facon uniforme. Dans cette situation, le rendement marginal du travail 'a la cooperative pour un menage se situe d'autant plus pres du revenu net moyen de la cooperative que le nombre d'autres menages qui se comportent de la meme facon est faible: Cela explique les bas rendements marginaux au debut du fonctionnement d'une cooperative, et peut-etre une certaine partie de l'indifference des fermiers russes a l'egard du travail pour les cooperatives. Notons toutefois que dans cette situation, il est vrai que les changements des frais fixes de la cooperative affectent les decisions des menages.

Dans la derniere section de l'article, l'auteur reprend la question du choix des menages quand il y a des quotas minimums de travail pour la cooperative, en utilisant toutefois la theorie du moindre mal ( second-best ) qui convient a l'etude des choix de ce type. II montre que les conclusions de Bradley sur cette question ne valent que pour un cas special.

In a recent issue of this journal, Michael E. Bradley made a short but useful contribution to the burgeoning literature on the co-operative enterprise.l In the context of a Soviet collective farm, he based labour supply upon utility-maxi- mization by collective farm households. He then assessed the impacts on that labour supply of fixed charges and quotas. Unfortunately his assertions about fixed charges and some of the analysis of the quota are technically incorrect, and a number of important implications are missed which bear directly on the role of and the need for such a quota in the first place.

I / The impact of fixed charges on labour supply

Bradley's model (without quotas) is as follows. Each of the M households on the collective farm is free to distribute its fixed amount of time (t) between the three uses of work on the collective farm (nl), work on the household's private plot (n2), and leisure (1) in such a way as to maximize a utility function u(i,l), where i is income. Income is derived from the return to each type of labour, which in turn consists of the product of the amount of labour and its average net revenue product, i.e.,

'Very helpful comments and suggestions were received from Brian Scarfe, Louis Schulson, and the editor and referees. The author is also indebted to James Seldon and Lawrence Copithorne for useful discussion of an earlier draft. 'Bradley (1971).

Canadian Journal of Economics/Revue canadienne d'Economique, VI, no. 1 February/fevrier 1973. Printed in Canada/Imprime au Canada.

- - , ac-?sh-s--r _ -rsc- bpeaar-iap-eaeses - -- ak - 1 _ rrqqqqqqqqqqqqqqqqq



(1) i= [(PXX-R)/Ni]n + [(P,y-s)/n2]n2,

where P, and P, are the centrally-fixed prices for collective farm output (X) and household plot output (y), R and s are all of the fixed charges borne by collective farms and household plots respectively, and N1 is the total supply of labour to the collective farm from all of the M households. All of the households in Bradley's version of the model have identical tastes, so N1 = nlM in this case. There are also production functions for X and y:

(2) X=X(N1, A),

(3) y=y(n2, a2), where A1 and a2 are fixed amounts of land.2 Diminishing returns to labour are assumed.

To maximize its utility the household will so distribute its available time that

(4) (Ou/Oi) (di/Oni) = (Ou/Oi) (Oi/On2) = Ou/l.

Rearranging this equation and substituting for the derivatives Oi/0nl and Oi/On2 from equations 1-3 yields Bradley's equilibrium condition that

(5) P, (OX/ON) = Py (Oy/On2 ) = (Ou/ll)/ (u/Oi). The household's allocation of its time therefore depends on the output prices and the shapes of the utility and production functions. Nowhere in equation 5 is there any mention of the size of the fixed charges R and s, so that it will not

generally be true, as Bradley claims, either (a) that "the collective's output of X will be affected by changes in the parameters P,, Pv, R, and s" or (b) that "any increase in P$ or s, or a reduction in R or P,, ceteris paribus, results in Oi/On, > Oi/On2 and Oi/9nl > MRS,I."

It is true, as he claims in a footnote, that the average net revenue product (w, in Bradley's model) will increase with increases in P, and decreases in R. It is not true, under Bradley's assumption of identical tastes, that Oi/Onl in equation 4 will increase as wl increases, so there is no necessary connection between the level of R and the value of Oi/0nl. Similar logic applies in the allocation of labour to the household plot, but there the result is even independent of whether all tastes are identical. There is no connection at all between the marginal return to labour on the household plot (Oi/0n2) and the level of fixed charges (s). A household's choice of n2 could be affected by changes in s only for some critical level of s where extra fixed charges cause the household to give up its private plot entirely.

'Brian Scarfe has pointed out that Bradley has implicitly assumed all households to have identical production functions for their identical private plots. Otherwise they will face different opportunity sets, choose different levels of ni, and respond differently to parameter changes, so that Oi/Odn will not be equal to P, OX/OdN and equation 5 will not hold. In that case, analysis of the type used below for the case of non-identical tastes must be used. Also, since the value of Oi/Odn is influenced by the actions of all households, any one household with a large private plot might find itself unable in its available time to lower ai/Onz and Ou/0l to the levels of Oi/On, which were left open to it. A corner solution would result instead of equation 4. 3Bradley (1971, 347). This also invalidates his conclusion on pp. 348 and 350 about the effects of changes in prices for compulsory deliveries, which have the same effects as changes in fixed charges.

Co-operative Enterprises 17



All the above rests on the assumption that (a) tastes, private plots, and production functions are identical for all households, and (b) there is perfect knowledge and certainty. Under these circumstances each household is aware that its every move is accompanied by similar moves by all of the M - 1 other households. These other households act the same way for exactly the same reasons. When one household decides to allocate an extra hour of its available time to work on the collective farm, therefore, it knows that M hours in total will be added to the work on the collective farm (N1), and not just its one hour. As a result, the net effect on that one household's income from collective farming (Oi/Onl) is its marginal revenue product, just as on its own private plot, viz., P, (OX/ONi).

If the assumption of identical tastes is relaxed, the situation changes radically. Any one household such as the Firsovs' now knows that any change in its input into the collective farm will be accompanied by similar changes on the part of

only some fraction of the M households.4 Assume for convenience that fM households have the Firsovs' tastes, and the remaining (1-f)M households have another set of quite different tastes such that they do not alter their inputs at all.

The Firsov household therefore knows that ON1/Odn = fM, i.e., that whenever it adds an hour of nl the total hours worked on the collective farm rise by its one hour and the extra hours of all of the other fM - 1 households which share its tastes.

In this situation the Firsov household's marginal return from its extra hour of work on the collective farm can be derived from equations 1 and 2, using the chain rule, as

Oi/Onl = (PxX - R)IN1 + nl[N2P, (OX/ON1) (ON1/Onl)

- (P,X-R) (ONl/Onl)]/N12, so

(6) Oi/On = [1 - (fMnl/N1)] (P,X - R)/N1 + [fMnI/Ni] P, (OX/ON1).

From this it can be seen that the household's marginal return is a weighted combination - with weights of (1 - fMnl/N1) and fMnI/Nl - of (a) an extra share of the average net revenue product derived from the previous production level [(Pa,X - R)/N1], and (b) a share of the value of the marginal product of this one household's extra input of labour [Ps (OX/ON1) ].

This result has two striking implications. First, the size of R plays a part in the marginal income yield of labour on the collective farm, so half of Bradley's incorrect assertion at least is validated when his assumption about identical tastes is relaxed. Second, if the fraction f of the M households which put in extra work on the collective farm is very small, the weight fMnI/N1 will be very small; the marginal income yield to those households of extra work on the collective farm will therefore depend very heavily on the level of the average net revenue product and very little on the actual value of the marginal product of labour on the land. Conversely, if tastes are identical so that any one house- 4One of the referees has objected that this assumes interdependence of the households' utility functions, rather than just that they are no longer identical. It is still true, however, that each household's utility function depends only on its own income and leisure, and not on that of any other household, which satisfies the usual definition of non-interdependence. Cf. Graaff (1957, 39).

18 NORMAN CAMERON



Co-operative Enterprises

VMP

Li

m Wg- ANRP

//, \ an,

ANRP MVP

Nm

N, (Total Labour Input of Collective Farm) FIGURE 1 The Firsov household's marginal income yields from collective farming. ANRP average net revenue product per man-hour (P.X -- R)Ni; VMP - value of the marginal product ( P,x/ON1); Wg = guaranteed money wage

hold expects all other households to behave as it does, then the fraction f = 1, the weight fMnl/N1 attached to the marginal revenue product, becomes unity, and the other term drops out; this is Bradley's case, and it is clearly an extreme case.5

To illustrate this result, Figure 1 has been drawn for the Firsov household with a value of fMnl/NI of 0.2, which corresponds roughly to the assumption that when the Firsov household thinks about putting in more time on the collective farm it expects 20 per cent of the total M households to do the same.

The curve Oi/Onl in this figure points up two other interesting properties of the co-operative distribution system. First, at levels of labour input beyond N1? the marginal income yield to the Firsovs of additional work on the collective farm land is in fact higher than the value of its marginal product. If the collective farm is already at some point to the right of N1? and households are free to allocate their time between their own plots and the collective farm, they will tend to equalize Oi/On1 and Oi/On2 but not the value of the marginal products of the two types of labour. The collective farm would under these circumstances be using marginal amounts of labour which had a higher revenue productivity elsewhere. Second, exactly the opposite is true, and more dramatically, at the

beginning of each season when the collective farm is of course far to the left of N1?. Here the VMP of labour on the collective farm may be very high, but the

marginal income yield to the household is very low and the Firsovs will be

'To clarify the weights that are being used, N1 is the sum of all nl for all households; N1 = Mnl if all households' inputs nl are of the same size. The fraction f can range from 1/M to 1, taking the value 1/M for any household which does not expect its action to be accompanied by similar actions by any other household. The weight fMnl/N1 will therefore range between nl/Ni if f = 1/M, and 1 if f = 1. It is necessarily assumed that all households which are expecting to act identically in adding time on the collective farm also have identical tastes, production functions, land allotments, and therefore equal levels of ni. If not, fMnl/N1 could exceed 1.

19



correspondingly reluctant to give up leisure or work on the private plot for that use.

There is no reason to assume that the weight fMnl/Ni stays the same all season long, however. If the Firsovs can be led to expect greater and greater participation by other households, then the fraction f and the weight fMnl/N1 rise. Pari passu the curve Oi/Onl moves closer to the VMP curve in Figure 1, and further away from the ANRP curve.

II / Introduction of quotas

The introduction of quotas for collective farm output leads to prescription of minimum work quotas for collective farm work (ni*) for each household. As-

suming the work quota is binding for each household, it can be expressed in any one of four ways.6 (i) nl = nl for each household, leaving the latter free only to choose n2 and 1. This essentially imposes an indivisibility in nl on the household. (ii) Households must settle for less I and deliver more nl than they would have without the quota, i.e., (Ou/Oi) ( Oi/ni) < Ou/Ol. (iii) Households must settle for less n2 and deliver more nl than they would have without the quota, i.e., (Ou/Oi) (Oi/Ori) < (Ou/Oi) (Oi/On2). (iv) Both (ii) and (iii) above.

Bradley chose the first approach, and derived the result that the household maximizes its utility only when (Ou/li) (Oi/n2) = Ou/l1.7

In fact this is not the case, as Smithies has shown in the context of a multi-

input firm faced with a significant indivisibility in one of its inputs.8 Just as that firm will not in general maximize its profit by setting the relative marginal revenue products of the other factors equal to their relative marginal costs in the presence of the indivisibility constraint, so in this case the household which does as Bradley suggests will not in general be maximizing its utility by setting the relative marginal utilities derived from n2 and I equal.

Instead, one of the other forms of constraint should be chosen (depending on how the collective farm household itself perceives the impact of the quota), and a standard second-best approach used.9 The relationships of (Ou/Oi) (Oi/On2) to Ou/Ol which result can be derived from the marginal conditions for each of those second-best utility maxima. For the second type of constraint, where households must give up some I to deliver more nl, the resulting choice of n2 and 1 is such that for normal utility functions (Ou/0i) (Oi/On2) < Ou/Ol. This implies, relative to Bradley's solution, that households give up even more leisure to work more on their private plots. By looking at the two extreme possibilities of reallo- cation of n2 and I in response to the quota it can be deduced further that (Ou/Oi) (OilOn2) > (Ou/Oi) (Oi/Oni).

For the third type of constraint, where households must give up some n2 to deliver more nl, the results are just the opposite. In this case the choices of n2 and 1 are such that (Ou/Oi) (Oi/0n1) < (Ou/Ol) < (Ou/0i) (Oi/On2.) This result

6I am indebted to one of the referees for the third way of looking at the constraint. 7Bradley (1971, 349). sSmithies (1936, 329). "Cf. Lipsey and Lancaster (1956, 15-16) and Smithies (1936).

20 NORMAN CAMERON



suggests, relative to Bradley's solution again, that if households see the quota as

forcing them to give up work on their own plot, they respond by giving up more of it than if they did not see it that way.

For the fourth type of constraint the relationship of (Ou/Oi) (Oi/On2) to Ou/0l is mathematically indeterminate, as one might expect from the results above.

Bradley's result is possible, but it would be a special case.

III / Conclusions and policy implications

The foregoing analysis suggests two important conclusions for a Stalinist policy- maker. First, the system of pooled product and shared residual wages in a collective farm can be expected to hold the incentive to work (Oi/Onl) above the value of the marginal product of labour at high levels of labour input and under the conditions of non-identical tastes (see Figure 1, points to the right of N1?). This is not true of the household plots.

Second, fixed charges on private production have no effect on the marginal incentive to private production except insofar as they cause changes in the

marginal utility of income generated on the private plot. This is not the case for collective production unless identical tastes are assumed, so that in general the

imposition of a fixed charge would disturb household production less than collective production.

There remains the question of why quotas had to be imposed in the first place. If tastes are identical and there is no positive utility attached to either kind of labour per se, then households will voluntarily allocate their time in the absence of quotas such that Oi/dOn = di/On2, or P, OX/ON1 = Py Oy/On2. Since labour is the only variable input, this means that the relative prices of X and y correspond to the relative marginal productivities of labour in producing y and X, or relative

prices are equal to relative marginal costs. The application of a quota to force increases in X beyond that point implies with these assumptions that the state's relative marginal valuations of X and y exceed the ratio of their prices. If that is the case, why not just increase the price of X and leave it to farm households to make the adjustments?

The reasons for the quota presumably lie in one or more of the following three factors. First, the state may be attempting via the quota to influence households' allocation of their time to leisure - an allocation of labour to "unuse" which the state may see as excessive relative to the marginal social benefit of such leisure. Second, it is quite possible that households attach some positive utility to work-

ing on their "own" private plot, which would cause them to put in time on it

beyond the point where the value of the marginal product was equal for both

types of activity; quotas could be a means of redressing the balance in favour of collective farming.

Third, and most important, the fact of non-identical tastes in a residual wages scheme in a co-operative enterprise can cause serious problems at low levels of labour input, especially where the fixed charges on the collective are large. If fixed charges are large, then residual wages will be small or negative to start with even though VMPs may be large. Since the marginal income yield of work on

Co-operative Enterprises 21



the collective farm is a weighted combination of the two under conditions of non- identical tastes, it may be so small at low levels of N, that households would avoid collective farming entirely if they could, even though at higher levels of labour input the marginal income yield may be sufficiently high to induce further

inputs.10 To put the matter from a different angle, it is possible and even likely that at levels of total labour input below N1? the value of P, OX/9N, could be

greater than Py, Oy/n2, the alternative VMP from working on the private plot, while the relative incentives to households (Ou/Oi) (Oil/On) and (Ou/Oi) ( i/On2) could be exactly the inverse.

Some of the post-Stalinist agricultural reforms have attempted to deal with this problem. Higher prices for collective farm output, lower fixed charges via

prices for compulsory deliveries, and experiments with decentralization of some collective farms using the "link" method are all aimed at raising the ANRP and VMP curves in Figure 1. As a result they shift the marginal income yield curve

up as well, but do not change its shape much. The introduction of a guaranteed money wage for collective farmers, however, attacks the problem of household incentive directly by changing the shape of the Oi/On, curve. With a guaranteed money wage Wg all points on Oi/Onl below the level of Wg are automatically raised to that level, without any change in ANRP or VMP curves on the farm.

References

Bradley, Michael E. "Incentives and Labour Supply on Soviet Collective Farms." This JOURNAL 4 (Aug. 1971), 342-52. Graaff, J. de V. Theoretical Welfare Economics (Cambridge, England, 1957). Lipsey, R. G. and Kelvin Lancaster. "The General Theory of the Second-Best." Review of Economic Studies 24, no. 63 (Jan. 1956), 11-32. Smithies, Arthur. "The Boundaries of the Production and Utility Function." Exploration in Economics (London, 1936), 326-36.

1Bradley (1971, 349n.) cites an alleged Soviet source as saying that in fact households would prefer not to work on the collective farm at all in the absence of quotas. This analysis may provide the major reason for such an extreme decision.

22 NORMAN CAMERON



Incentives and Labour Supply in Co-Operative Enterprises

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