The profit share rate, wages and employment in collective bargaining

The profit share rate, wages and employment in collective bargaining

European Journal of Political Economy 8 (19921 i eyer Schmidt- The joint determination of wages and the profit share rate is considered in a right t...

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European Journal of Political Economy 8 (19921 i

eyer Schmidt-

The joint determination of wages and the profit share rate is considered in a right to manage model of collective bargaining. This model encompasses diCkrent labour marker models. It 7s shown for example that the profit share rate is determmed soleiy by and depends positively on the bargaining power of the union and the union’s concern for the level of uncrcplnyment. i.e. the degree of the union’s concern for unemployment may explain why profit shxing is not mnre common.

1. Introduction

Recently important advances have beet made in the analysis of labour mark&s where wages are predominantly determined by some form of collective bargaining, see McDonald and Solow ( 1981) and Oswald ( 1985). The literature focuses on different models of wage and employment determination, e.g. the monopoly union model, the right to manage model and the seniority model. The purpose of this paper is to extend these models to the case where other items such as the profit share rate are also on the cgenda in collective bargaining. This extension is not only of theoretical interest but also of practical importance both for centralized and local bargaining, as profit sharing has been proposed and discussed recentlqr in a number of countries. Pohjola (1987), Holmlund ( 1988) and Anderson and Devereux (1989) have reached important results in a model framework where the tos ( 1989). Their share rate is endogenous; see also Hart and analysing the im to be extended by, for example, introducing a the degree of the union’s concern for the level of employm Specifically, I consider a setting where the wage rate *This paper constitutes part of my Ph.D. dissertation. E thank two anonymous referees, arck, Manfred Holler and Peder J. Pedersen for very helpfuLal Torben M. Andersen, Ssren comments. An earlier version has been presented at 2 workshcrp at the Aarhus School of Business and at the Fourth Annual Congress of the European Economic Association, Augsburg, 1989. 01X--2680/92/$05.00



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J.B. Schmidt-Sorensen,

Profit share rate and wages in collective


rate are negotiated at discrete intervals, whereas firms continuously and costlessly adjust the number of persons they employ in accordance with their labour demand functions. Hence, I leave out the efficient bargaining model as it is not time-consistent under this sequential decision structure, and consider instead ;n extended right to manage model which includes the monopoly union model and the seniority model as special cases. In the right to manage model, wages and the profit share rate are determined by a process of collective bargaining. Wages and the profit share rate are set unilaterally by .i-‘; union in the monopoly union model. Finally, the seniority model can be seen as a special case c’ i he monopoly union and the right to manage models where the union is partly concerned or not at all concerned with the employment level, since the average union member has a low unemployment risk and is therefore primarily concerned about his take-home pay. In these models the emp!oyed workers (insiders) are less concerned with the interests of the unemployed workers (outsiders). Market power of insiders can be related to turnover costs and seniority. In addition, unionization may help insiders to raise the firms turnover costs, see Lindbeck and Snower (1987). In section 2 I specify the characteristics of firms, the households and the union. The bargaining framework is developed in section 3. The joint determination of wages and the profit share rate is considered in section 4. Section 5 provides few concluding remarks.

Concerning the employers it ‘s assumed that the representative firm seeks to maximize the following profit function Ww,L)=(l



where ,zj+=Q is the short run production function, w is the real wage rate, s is the profit share rate (05~5 l), L is the number of employed workers and a is a productivity shifter (a>O). The focus of the analysis will be on the cases where profit is positive. Consider next a setting with identical households with an indirect utility function specified as

where I is total income per worker


J.B. Schmidr-Sorensen. Profit share rate and wages in cd/ecFi~e bargaining


Note that the production function and the employment level indirectly enter the individual utility functions and not only through the effects on wages as in the case without profit sharing. The household only has a choice between working according to the exogenously determined working time or not working at all. If the person is employed hr obtains a utility level given by V(I) - L&l, w, s, L),

where (E indicates elasticity)

Ev1 (l-s)wL>O,






If the person is unemployed he obtains a utility level given by V(b) = P, where 6 is an indicator of outside opportunities, for instance the real value of unemployment compensation. In the following I am only interested in situations where it is not preferable to be unemployed rather than employed. The union is assumed to have a pay-off function given by

where 6 stands for a seniority parameter or an insider power parameter (6>0). If 6 is equal to zero the pay-off function implies that the union aims at maximizing the utility level of employed members, that is, this corresponds to the pure seniority model. If 6 is equal to one the pay-off function corresponds to the utilitarian union which aims at maximizing the weighted average of the utility obtained by employed and unemployed members, see McDonald and Solow (1981). The union’s willingness to substitute between the net gain to employed members (V- P) and employment (it) is found to be d(l’--V) L -__iv- V s=_-= --& dL i.e. ( -6) measures t

@) ness to substitute between



J.B. Schmidt-Sorensen, Profit


rare and wages in collectioe bargaining

to employed members and employment. Hence, a higher 6 means that the union cares relatively more about employment than the well-being of employed members. A great advantage of the specification of the union pay-off function, eq. (7), is that not only the traditional cases in the literature with the seniority parameter equal to zero or one may be analysed, but i.: - %e many relevant cages where the seniority parameter is between zero ~.ricIrine cr even greater than one.

3. The bargaining framework Centralized bargaining over wages and union and the employers’ federation is to profit share rate firms determine the level profits. The employment level for a given determined by the condition that



the profit share rate between the be analysed. Given wages and the of employment so as to maximize wage rate and profit share rate is

The wage rate and the profit share rate are determined the asymmetric Nash bargaining solution max (S’ -P)(IIP) W.8

(9) by the outcome



where the bargaining power of the union is (1 -p) and that of the employers’ federation p. It is assumed that S and I7 reflect the net gains of the two parties of reaching an agreement. It is seen that the monopoly union model (here defined over wages and the profit share rate) corresponds to the special case of (10) where p is equal to zero. When p equals one the firms dominate the negotiation completely. The first-order conditions to the maximization problem given in (tflj ran be written as

(1 -pW,,+p~,,=0,




J.B. Schmibdorensen,



share rare and wages in collectit!e



Eusr0, S”=l-ijpJ




s l-s

The second-order


(W read

H i.e. it follows that (1 -p) %+p%
4. Employment, wages and the profit share rate From eq. (9) follows that the optimal level of employment is invariant to changes in the profit share rate; compare that a change in the profit share

rate affects revenue and costs equally as the profit share rate parameter, s, acts like a neutral profit tax. The first-order conditions (11) and (12) determining wages and the profit share rate using (4), (5) and (6) can be written as (1








share rare ad



in coktive

Table 1 The profit share rate in different models. ___ _ -... -.----~ p=o: monopoly union __.--._o
pure seniority model









6 = 1: utilitarian mode{










6-+ 5:

exclusive focus on employment


As (IS)


fi.( 1 - P/V)‘




rewritten as

it is easily seen from (18’) and ( 19) that

&l --PI s=s(l -p)+p’ This result is more general than the results in Anderson and Devereux (1989) and Hohnlund (1990).’ In the special case of a seniority parameter of unity the Holmlund and Anderson-Devereux models appear. From (20) an intuitive result follows, namely that the profit share rate can be determined independently of the wage level, which may be explained by the fact that the firms’ employment decisions are independent of the profit share rate but depend on the wage level. It is also seen that the profit share rate is determined exclusively via the bargaining power and by how much the union cares about employment.

From table 1 it is seen to be rsserztial jiir the results how much the union cares about the level of employment and thus the generalization of the ’ Pohjola (1987) and Anderson and Devereux (1989) demonstrate in a corresponding model framework that the wage profit-sharing bargain is equivalent to the efkient bargaining outcome, i.e. prolit-sharing eliminates the ineflkiency arising from the inability to negr4ate over

existing models is of great importance. From (20) the consequences on the profit share rate of a change in the union’s care about employment can be derived to be

i.e. the profit share rate increases (decreases) when the union cares more (less) about the employment level. The effects on wages of a change in the seniority parameter can be derived by total differentiation of the first-order conditions ( 17) and (18)

i.e. it turns out that wages increase (decrease) when the union cares less (more) about the employment level. This result is very intuitive and well known as for example higher employment necessarily requires wages to be reduced. All in all, the profit share rate increase partly offsets the reduction in wage income; compare that the profit share rate does not affect labour demand. 4.2. Bargaining power, p The relationship between the profit share rate and the bargaining power is easily derived from (20) and gives very intuitive results, cf. table 1. The precise relationship between the profit share rate and the bargaining power is found by differentiation of (20): ds




i.e. the profit share rate depends negatively on the bargaining power of the employers* federation. The elasticity of the profit share rate with respect to the bargaining power of the employers’ federation is always less than minus one if the bargaining power of the employers’ federation is greater than l/2. The effects on wages of a change in the bargaining power of th employers’ federation can be derived by total differentiation of the first-order conditions (17) and (18)

d!!!O dp



J.E. Schmidt-Sorensen,

Profit share rate and wages in collectiw


where it should be stressed that the condition for the negative relationship between wages and the bargaining power of the employers’ federation is a sufficient condition.2 4.3. Productivity Changes in the in the parameter relative prices of instead of aj’=Q.

shijts or relative

price shifts

parameter a express productivity shifts. However, changes a could also be interpreted as an indicator of shifts in the the firm if the ploduction function is specified as f=Q The concequences on the profit share rate and wages are

ds z=O,


d% .Ada


Again, from (20) it is concluded that the profit share rate is invariant productivity shifts, whereas the wage effect is ambiguous.


5 Concluding remarks The framework employed in this paper is completely static; the bargaining game is one-shut. This precludes an analysis of the adjustment of wages and the profit share rate over time to changes in underlying conditions (market conditions, preferences, technology). The short-run perspective may introduce a bias toward the favorable implications of profit sharing. The explicit treatment of seniority aspects introduced in the model is shown to be essential for the actual bargaining solution. The seniority aspect contributes to the explanation of why profit sharing is not more common. The median union member may not care much about the employment of others; then income will mainly come from wage income rather than profit sharing income. The analysis could easily be extended to include a discussion of profit sharing when the profit is negative, for example, due to a demand shock. This kind of sharing a negative profit could be constrained to ensure that the employed worke:s in any circumstances get a minimum wage such that it is preferable to be employed rather than unemployed. Such an extended profit 2More


power to the union will probably reduce employment. In Schmidt-Sorensen effect when the union gets more bargaining power giver! work effort effects from total income may very well be the opposite, i.e. an emp!oyment increase. The union may therefore under these circumstances be seen to counteract the unemployment creating forces that are the result of efliciency effects from wage income and profit share income.

(~990) it is shown that the employment


Schmidt-Sorensrn. Profit share me and wages itI coIlectice bargaining


sharing scheme should at firstsight be expected to imply a more stable level of employment over time, which is rather important for example in relation to the hysteresis debate, see for example, Blanchard and Summers (1988). Another subject for further research is asymmeiric information. From the point of view of the workers and the union, wage income is more certain than the possibility of profit sharing income, because a necessary condition for profit sharing income is a positive profit. The firm may be expected to have much better information than the workers and the union concerting the prediction of the profit level, i.e. there is asymmetric information. Riskaverse workers will prefer a certain wage income because profits may vary greatly over the business cycle, which reflects variance of the prediction of the profit. Therefore, the union may choose to give profit sharing income a lower preference than ordinary wage income. On the other hand, if the union is very much in favour of a profit sharing scheme, e.g. if profit sharing is combined with employee shares or if the union assesses that profit sharing is a token of fairness, then the union may decide to giv,. more weight to profit sharing income relative to wage income. References Anderson, S. and M. Devereux. 1989. Profit-sharing and optimal labour contracts, Canadian Journal of Economics 22, 425-433. Blanchard, O.J. and L.H. Summers, 1988, Beyond the natural rate hypothesis, American Economic Review, Papers and Proceedings 78, 182-187. Hart, R.A. and T. Moutos, 1989, Wage and profit sharing compensation under efficient contracts (Department of Economics, University of Stirling). Holmlund. B., 1990, Profit sharing, wage bargaining and unemployment. Economic inquiry 28, 257-268. Lindbeck, A. and 9. Snower, 1987, E!liciency wages versus insiders and outsiders, European Economic Review 3 1, 407-416. McDonald, J.M. and R.M. Solow. 1981, Wage bargaining and employment, American Economic Review 71, 896-908. Oswald, A.J., 1985, The economic ?heory of trade unions: An introductory survey, Scandinavian Journal of Economics 87, 160-193. Pohjola. M., 1987, Profit sharing, coliective bargaining and employment, Journal of Insti!utionaK and Theoretical Economics 143. 334-342. Schmidt-Sorensen, J.B., 1990, Essays on efficiency wages, Ph.D. dissertation, CLntre for Labour Economics, Working Paper 90-3 (Aarhus School of Business).