European Economic Review 30 ( 1986) 1197-1205. North-Holland

THE REMUNERATION PACKAGE AND PARETO INEFFICIENCY IN THE LABOUR MARKET*

Eliakim KATZ

Uriel SPIEGEL Bar-Iian Uuiwrcity, Ramar Gas, lsrael

Uiniwrsiry q/‘ Petmsyhwniu, Philadelphia, PA 19104, USA

Adrian ZIDERMAN

Bar-llan Vniwrsity, Ramal Gan. Israel

U~~iwr.si/y q/’ Brirish Colwnhitr. Vancouwr, B.C., Canada V6T I W5

Received April 1985, fmal version received December 1985

This paper argues that a simple wage payment system relating wages to hours of work supplied cannot bring about Pareto eficiency in the labour market and that in its search for efliciency, the labour market has evolved an alternative pricing system that differs from those generally found in other markets. Specifically, it is demonstrated that whereas Pareto efficiency will in general be absent in the labour market when a single price system prevails, a labour reward package consisting both of a fixed payment element unrelated to hours of work supplied and a work-input related wage element is likely IO bring about Pareto efliciency.

1. Introduction

In general, in competitive markets for private goods, a social optimum is achieved on the Contract Curve and allocational efficiency is guaranteed by the market price being given by the slope of the indifference curves at the optimum. This in turn implies that if the price of a private good is determined competitively then this price leads to an eficient allocation of resources. In such circumstances, therefore, a single, non-quantity-dependent price achieves the socially optimal result.

In contrast, the labour market, although apparently competitive, does not seem to be characterized by a single price, even when labour is homo-

*Support was provided by the Economics Research Institute, Bar-Ilan University. We are grateful to an anonymous referee for comments and suggestions.

0014-2921/86/%3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)

1198 E. Katz ef trl.. Rrmuneraticm and Parrro itwficiertcy in the lahour market

geneous. Thus, almost invariably, labour receives its reward in two parts; firstly (and mainly) in the form of a wage per unit of time worked and, secondly, in the form of fringe benefits which are not generally related to the units of time worked. The labour market can thus be said to be characterized by a two stage tariff. i.e., a fixed component (the fringe benefit) and a variable one (wages). This paper represents an attempt to explain why this might be so.

There is by now a vast and expanding literature explaining the existence (and growth) of fringe benefits, usually in terms of the outcome of particular institutional arrangements present in modern societies. These include such diverse phenomena as income tax regulations, labour unions, bulk-purchase of goods such as life insurance, or legal requirements such as a paid annual holiday.’ The presumption inherent in these explanations is that in the absence of these institutional factors, fringe benefits would not be present in freely functioning labour markets, and that their existence signifies a departure from the ‘norm’ and perhaps also a departure from efficiency.

In this paper, a very different stance is adopted. It is argued that a simple wage payment system relating wages to hours of work supplied cannot bring about Pareto efficiency and that, in its search for efficiency, the labour market has evolved an alternative pricing system that differs from those generally found in other markets. Specifically, it is demonstrated that whereas Pareto efficiency will in general be absent in the labour market when a single price system prevails. a labour reward package consisting both of a fixed payment element unrelated to hours of work supplied, and a work: Input related wage element is likely to bring about Pareto efftciency.

In section 2, we outline our basic theoretical model, which demonstrates that a single constant wage rate per unit of time will not in general lead to Pareto effciency.’ In section 3 we show how the two-stage tariff provides a solution to this inefficiency. Some comparative statics of the basic model are discussed in section 4 and applications of our findings and conclusions are given in section 5.

2. The model

We begin our analysis by examining the behaviour of employers.3 An employer is assumed to be a profit maximizing firm selling its output competitively at price p per unit of output; the tit-m uses one input only, namely labour. The use of more than one input will modify some of our

‘Woodbury (1983) provides a Ming of the major explanations for the existence and increasing prevalence of fringe benelil payments, supplementing an earlier review by Rice (1966).

‘For a related discussion see the recent paper by Donaldson and Eaton (1984). ‘Our analysis is carried out mainly in diagrammatic form, though mathematical proofs of the

results are obtainable from the authors.

E. Katz er al.. Rentunerafion and Pareto inejficiency in the lahour market 1199

results, but not alter their general direction. The output of each individual worker is given by X, where X is a concave function of the number of hours per day (or perhaps the number of days per week) worked by the individual. This concavity of X in the units of time worked may be attributed to a number of factors of which tiredness is probably the most prominent4

Denote by T* the total time available to an individual and by I his leisure (non-work) time; thus the individual’s working time is T* -I and his output is

X=X(T*-I), (1)

where

ax/al= -X’(T*-I)<O, and

Px/aiz=xfl( T*-f) <o

by the concavity of X. The worker’s total income for a day (or week) is denoted by 1. Hence the

firm’s profits per worker are

n=pX(T*-0-1, (2)

For a given level of profits, II,, therefore, the iso-profit curve is given by

n,=pX(T*-/)-I, (3)

hence

(dI/dl),=,o= -pX’(T*-f)<O, and (41

(5)

and hence the iso-profit curve is concave to the origin. In addition, from (4) it is clear that the slope of all iso-profit curves are the same for a given value of 1, regardless of the value of I7e. This follows directly from the fact that dl/dl is independent of the value of II,.

Given the above properties of the iso-profit curves, they may be plotted as 17°,L’i,172, in fig. 1. Clearly the further to the north east a given iso-profit curve is, the lower are the profits associated with it, since such a curve implies a lower output per $ of worker’s income. Hence, for a sufficiently north easterly ITi, profits will be equal to zero. In fig. 1 this curve is denoted by no, which therefore delineates the feasible set in the (I,I) plane. (Note that on ITo, I must equal T* at I = 0 so as to ensure that profits be equal to zero.)

%ee Ehrenberg and Smith (1982)

1200

INCOME

E. Katz et al., Remuneration and Pareto inejliciency in the labour market

0 1" LEISURE

Fig. I

We turn now to the employee, whose utility, U, is assumed to be defined upon his income I and his leisure time 1 such that

where U(.,.) is a quasi-concave function in 1 and 1. Hence, assuming that both money income and leisure are normal goods, the worker’s indifference curves, denoted by U”, U’ etc., are as plotted in fig. 1. Clearly, the level of worker utility rises as we move upwards, so that U2 is preferred by the worker to U', and so on. Also, of course, the employee will supply no work if the resulting utility level is below his zero work utility, U”.

Given that the set defined as lying between Z7’ and U” (the feasible set) is non-empty, the employer’s iso-profit curves and the employees’ indifference curves create a Contract Curve such as CC’ in fig. 1 where all points on the Contract Curve are Pareto efficient.

E. Katz et al., Remuneration and Pareto inejliciency in the labour mark& 1201

Thus far then, nothing unusual has been described. However, it is now argued that in general workers will find it optimal to be off the CC’ curve for a given wage rate, i.e., that the resulting equilibrium is Pareto-inefftcient.

Assume that the wage rate is given by the slope of W*W* in fig. 1, and let us denote this slope by I%‘*. Drawing a line W* W* with a slope ii/* through T* lands the individual in an equilibrium E*, on V*, this being the highest indifference curve he can reach. In general, however, there is no reason for E* to lie on CC’. Hence, since the indifference curve at the equilibrium is tangential to W*W* and since the iso-profit curve at the equilibrium is not, in general, tangential to W*W*, it is evident that the equilibrium will not necessarily be Pareto-efficient. We conclude that using a single price in the labour market will not, in general, yield Pareto-efficiency. Indeed, there is no reason for any single wage rate to yield such an equilibrium within the feasible set. The result, therefore, is not wage rate specific. This result may be summarized as:

Theorem 1. A single, constant wage per unit of time will not, in general, lead to Pareto efficiency in the labour market.

3. The Pareto-efficient solution

What then is the solution to the above inefficiency? We show that the problem may always be solved by a two part reward system, namely, a work related item (wages) and a fixed item, such as fringe benefits. In other words we argue that if a worker’s total earnings are given by

r=(T*-[)W+F, (7)

where F is the fixed component of earnings, then Pareto efficiency can always be reached.

That this is so can be shown using fig. 2. Let us consider a point on the Contract Curve such as El. It is clear that if we draw a line from T* to E’ this line will not have the same slope as V’ or II2 at E’, but will cut both V’ and f12 at this point.

Let us now work backwards. We draw a line tangential to V2 (and U’) at E2( W’W’) and then drop a vertical line to the 1 axis over T*. It follows immediately that an efficient situation can emerge at E2. Denoting the slope of W’W’ by @’ and the distance W’T* by F’, the reward package I%‘i .( T* -II) + F’ will ensure a Pareto efficient situation at E2. It is easy to show that some W. (T* - I) line combined with some vertical F line dropped to T*, will always ensure that Pareto efficiency is reached. This can always be determined by working backwards, as above, and plotting a line tangential to Vj and l7j at the desired Pareto efficient point and then dropping a

1202 E. Katz et al., Remuneration and Pareto inefjiciency in the lahour market

INCOME

w2

0 1” LEISURE

Fig. 2

vertical line to the I axis over T*. Thus for E’, for example, the wage rate is t@Z (slope of W2W2) and the fixed payment is W2T*, the combination of these leading to Pareto efficiency at El.

To summarize this result, we have:

Theorem 2. Workers can be induced to choose Pareto ejjcient points in the leisure-income plane by a combination of a wage rate and a fixed payment element.

As we shall see in the next section, in principle the fixed payment may be positive or negative for efficiency to be reached. In one very important case, namely for a competitive industry in equilibrium, however, it can be shown that the fixed payment must always be positive. To see this, note that in a competitive equilibrium profits are zero. This means that the equilibrium within a competitive industry will be found on 17’ in fig. 2, and that the Pareto efficient equilibrium in the figure will then be a point such as E3,

which, since both 1 and 1 are normal will be to the north west of T*. Since a tangent to any point on I7” (other than I= T*) cuts the 1 axis to the right of T*, it is clear that the fixed payment must be positive. Thus we have:

Theorem 3. !f the industry is competitive so that in equilibrium projits ure zero, the fixed payment required to bring about Pareto-efficiency is strictly positive, provided both money income and leisure are normal goods.

Before concluding this section a few words seem in order regarding a possible alternative way of bringing about efficiency. One such possibility is that the employer may specify both the wage rate and the hours of work. However, such an arrangement is likely to be unworkable since, given the wage rate, it will in general be suboptimal for an individual worker to adhere to it (witness the phenomenon of absenteeism) and, given the nature of labour as an input, employers will often find it unprotitable to enforce it.’

4. Comparative statics

In this section we analyze some comparative statics of the model. We are concerned mainly with the way in which a trade union induced (or other exogenously determined) changes in the minimum level of utility acceptable to employees might be accommodated. Thus when we discuss the effect of an increase in U in the foregoing analysis, it should be interpreted as being exogenously determined. To derive the comparative statics, we use result (4) that for a given value of 1 the slope of the iso-profit curve is constant.

Let us begin by considering the effect of an increase in U on the wage rate W. Using fig. 3 assume that initially the individual worker was at E’ on Il’ and that he has now bargained himself into utility level U2. How does this affect W? We know that if both leisure and money income are normal goods then on indifference curve U2 more will be consumed both of money income and of leisure than on indifference curve U’; the new equilibrium will be at a point such as E2. However, if leisure increases, then the slope of the iso-profit curves (which, it will be recalled, is the same for all iso-profits curves for a given value of 1) touching E2 will be greater than at E’. Thus, it is clear that as U rises, the wage rate will always rise, providing only that leisure and money income are normal goods. We thus have,

5There are several reasons for this: First, labour is costly to hire and lire; thus the firm may lack credibility as to its preparedness IO lire workers over the extent of absenteeism. Second, labour laws give to labour privileges which makes it relatively easy for labour to unilaterally abrogate contracts. Third, a worker can. in general. vary the quality of his work, so as IO render almost meaningless any legally enforceable contractual time oaligation he has agreed to. This he is likely IO do if he is forced to work a number of hours which differ from his optimum.

E. Katz et al.. Remuneration and Parero inefficiency in the lahour market 1204

INCOME

0 LEISURE

Fig. 3 wl

Theorem 4. Given that both leisure and income are normal goods and that the wage is as defined in (7), the Pareto eflcient wage rate will always rise as the level of utility rises.

Turning to the effect of an increase in V on the fixed payment, it may be shown that this effect is indeterminate. This can be seen from fig. 3. If the worker’s time constraint was T*, then it is clear that the movement from E2 to E3 would raise the fixed payment. If, however, the worker’s time constraint was T** then it is seen that the move from EZ to E3 would reduce the fixed payment. Note, however, that the fixed payment element is not necessarily positive; for example, at equilibrium point E’, the fixed payments W2T* and W’T** are negative.

We thus have,

Theorem 5. An exogenous increase in the worker’s utility may raise or iower the fixed sum payable to the worker.

E. Katz et al.. Renumerariort and Parefo incj,lTcienc)~ in the lahour marker 1205

5. Implications and conclusions

In this paper we have attempted to show that a single wage rate will not in general bring about Pareto efficiency in the labour market whereas such a wage rate combined with a fixed payment element can do so. Our model does not specify the particular form of payment that this fixed element should take. Although there may be a presumption that it would be made in terms of current cash payments, such a limitation is not required by our model. These payments thus could be made in various other forms, such as in kind, non-pecuniary, fringe benefits.

It is therefore interesting to note that in most labour markets such a two- stage tariff regime as outlined in our model is indeed present, with the fixed payment element taking on the particular form of non-work-time related fringe benefits. It would seem that whatever the institutional or other forces that have operated in labour markets to bring about the widespread payment of fringe benefits, they have produced a necessary condition for the market to reach a state of Pareto efficiency: the existence within the remuneration-package of a fixed element that is unrelated to the time input of workers.

From a policy standpoint, the model shows which particular level (or value-equivalent) of fringe benefits is required, given the wage rate and number of hours worked, in order to achieve Pareto efficiency in labour markets. Hence, differential tax policy applied to wage-income and fringe benefit receipts respectively could be used as a policy tool to correct inefftciencies in the labour market if fringe benefits are not set at an appropriate level. 6 Indeed, by taxing fringe benefits differently from wages, government policy may well result in the introduction of fringe benefit payments by firms. In view of our results, such government tax policy may be viewed as enhancing efficiency.

‘Of course, the optimal package may vary with several parameters exogenous to our model, e.g., the price of output, Thus any attempt to convert the above analysis into an operational policy would have to incorporate consideration of several factors not considered above.

References

Donaldson, David and B. Curtis Eaton, 1984, Person specific costs of production: Hours of work, rates of pay, labour contracts, Canadian Journal of Economics, Aug.

Ehrenberg, Ronald G. and Robert S. Smith, 1982, Modern labour economics (Glenview, IL). Rice, Robert G., 1966. Skill, earnings and the growth of wage supplements, American Economic

Review Proceedings, May. Woodbury, Stephen A., 1983, Substitution between wage and non wage benefits, American

Economic Review. March.