THE ECONOMIC RECORD, VOL 69, NO. 207. DEC. 1993.428-36

Employment and Length of the Working Week in a Unionized Economy in which Hours of Work

Influence Productivity* ALISON BOOTH Birkbcck CourgC

uninrsity of London, London, England

MARTIN RAVALLION Thc woIidBa&

Warhinglon D.C, USA

Conduions are detived for signing the employment fleets in a unionized economy of a lcgrslated cu1 in horn when productivity dcpcnds on the nwnber of how WOM cach week Aggnsatc data sum that employmnt will gmcml?l incrnrv after a smaU cut in how for the UK but the employment e@ct is ambiguous for A m l i a Dicaggrcgted &a for Ausnalia suggest that the employment effect of a cut in ~ O U K is often posirivc However, any cut in how imposd on a monopoly wion, without a cut in pay, will unambiguousiy lead to a drop in employment

When the hours, the nature of the work done, the physical conditions under which it is done, and the method by which it is remunerated, are such as to cause great wear-and-tear of body or mind or both. . . then the labor has been extravagant from the point of view of society at large,. . In such a case a moderate diminution of the hours of labor would diminish the national dividend only temporarily: for as soon as the improved standard of life had had time to exert its full effect on the efficiency of the workers, their increased energy, intelligence and force of character would enable them to do as much as before in less time.

A. Marshall, Principles of Economics ( 1 890694).

Work on this paper began while both authors were at the Australian National University (Booth as a visitor in the Research School of Social Sciences. Ravallion on the staff of the Research School of Pacific Studies). The views expmsed here are those of the authors, and should not be associated with their employers, including the World Bank. We would like to thank two anonymous referees for their comments on an earlier draft, and Paul Grimes for a helpful discussion about standard hours determination in Australia.

An important factor, too, is the kind of work that is done. Long hours of heavy muscular exertion and mental or nervous strain are much more injurious to efficiency than long hours of mere mild attention . . . in each several industry, for each class of workers there is some length of working day the overstepping of which will be disadvantageous to the national dividend.

A.C. Pigou, The Economics of Welfare

As industry develops, the strain to which work people are exposed probably increases; rest and recreation become more necessary; and thus the output optimum length of day probably falls. If output is to be maintained at the maximum possible, hours ought to be reduced. J.R. Hicks, The Theory of Wages (1932:106).

(1920463-4).

I Introduction With the high levels of unemployment in the

early 1980s and again in the early 1990s. there has been considerable interest in the employment effects of a reduction in the standard working week. The European Trades Union Congress, the International Labor Office (ILO) and the EC are

0 1993. The Economic Society of Australia. ISSN 0013-0249.

42 8

1993 EMPLOYMENT AND HOURS IN A UNIONIZED ECONOMY 429

pressing for hours restriction by legislation, while in Australia there has been discussion of the central imposition of a 35-hour standard working week. While labour organizations argw for a shortening of the working week without a drop in weekly income, business interests generally do not look favourably on a reduction in hours. This is largely because of the increase in labour costs, which business argues will induce firms to reduce production and to cut back theirdemand for labour.

Since the countries in which there is a debate about hours arc strongly unionized, it makes sense to study the employment effects of a cut in hours in the context of a union model. There is a small body of work which does this see Calmfors( 19851, Hoe1 (1986) and Booth and Schiantarelli (1987) amongst others. In this literature, union models of the wage and hours determination process are explicitly embedded in a basic model of production. and the impact of an imposed reduction in the mndard working week is modelled, with generally negative or ambiguous predicted employment effects. However, this literature has been unable to capture the essence of the argument of many Libour organizations, namely that workers will be more productive after a cut in hours: it is claimed that they will be healthier and less tired, and thus absenteeism and accidents will decline (Cuvillier, 1984). The importance of the nexus between daily hours and hourly productivity has long been recognized by economists (as the quotations at the start of the paper indicate). Yet this has not yet been captured in the literature examining the employment impact of an exogenously imposed cut in hours in a unionized economy.

The purpose of this paper is therefore to model the impact on employment of a cut in hours in a unionized economy, in which the worker's hourly efficiency depends on the number of hours worked. The paper postulates a hill-shaped relationship between hourly efficiency and the number of hours worked, following the ideas outlined in the quotations at the start of the paper, and empirical relationships discussed in Section 11 of the paper. The efficiency index has some similarities with Banel ( 1973). who uses an analogous index albeit in a non-unionized framework. Some recent literature examining hours and employment has also utilized the notion of an efficiency hours index (see for example Calmfon and Hocl, 1988; Schmidt-Sorenscn, 199 I ; and Bell and Hart, 1991). However, these papers have not incorporated the efficiency hours index into a model of union wage determination. The novelty of the present paper

is to examine the sensitivity of the employment predictions of the uandard trade union models to the assumptions made about hourfy efficiency.

We use variants of two orthodox models of trade union behaviour. The first is where the union and the firm bargain over wages and hours, while in the second model the union determines wages and hours unilaterally. We term the first model an 'efficient bargaining model'.' and the second is the monopoly union model expanded to include hours. In both models, the firm is assumed to retain the 'right to manage'. that is, to determine employment Having characterized the initial equilibrium for each of these models, we then examine what happens to employment when a small cut in hours is imposed on the union and firm. This approach represents the situation in countries considering industry-wide or economy-wide imposition of standard hours. For example, the Social Charter of the EC has raised the possibility of setting a European Standard for hours, which may affect British industries where wages and hours determination occurs at the industry level. In Australia the mooted imposition of a 35-hour week on sectors where unions and firms negotiate hours deals can be analyzed analogously.

The models also yield predictions in the reverse situation in which hours are initially set at the industry level, and we wish to consider the employment implications of allowing for union- firm negotiation of standard hours. However. in this situation it is necessary to know if legislated hours are less than or greater than optimal hours arising from union-firm negotiation in order 10

predict employment changes. It is not implausible that legislated hours are less than optimal hours in industries where hours have been regulated to reduce negative externalities associated with long hours, as in transport industries.

In the paper, we follow the European and Australian unions' view, and historical precedent. by considering situations in which the cut in hours is not necessarily accompanied by an erosion in real weekly pay.* Thus the cut in hours may force

I Our use of the term 'efficient bargaining model' differs slightly from that in much of the literature where the term refers to union-firm bargaining over wages and employment for a fixed level of hours. See for example Ulph and Ulph (1990).

1 Bienefeld (1972) indicates that reductions in hours historically have been achieved without reductions in real income. On recent union demands in the UK SK Trades Union C o n e (1984) which argues for a cut in hours leaving take-home pay unaffected.

ECONOMIC RECORD DECEMBER 430

an increase in the hourly wage rate. This immediately makes the employment cast in favour of a cut in hours ambiguous; under standard (competitive) assumptions, if the hourly wage is unchanged then employment must increase. but if the wage increases then the case will depend critically on the precise value of the wage elasticity of labour demand.

The remainder of the paper is set out as follows. Section 11 describes our assumption about how hours influence productivity, while Section U1 examines implications for labour demand and the employment effects of a cut in hours. The efficient bargaining union model is developed in Section 1V. A significant finding of the bargaining model under the efficiency hours hypothesis is that a simple empirical test reveals the direction of the comparative static effect on employment of an imposed cut in hours. We carry out this test using relevant empirical evidence for the highly unionized economies of Australia and the UK. The evidence presented in Section V suggests that while the aggregate employment effect of an exogenously imposed cut in hours is likely to be positive for the UK. where unions and firms bargain over wages and hours. for Australia the employment effect is ambiguous. This simple test is not applicable to the monopoly union model, and we explain why in Section V1. The conclusion summarizes our findings.

I1 7 k Relationshy between Hours and PrOdUCtiViry

We assume that a firm's output depends on the number of 'efficiency hours' of labor input, rather than simply the total number of clock hours. Output is given by:

where h denotes the number of hours, N denotes the number of workers, and Hh) represents the efficiency hours index.3 The number of efficiency hours obtained from a given number of clock hours is assumed to be a strictly concave differentiable function Hh) of hours worked for h in [ho. h ~ l , where $e function I$ has a maximum h in (MI) i.e.. +'(b ) - 0. Thus there is a 'warm-up' period, in which 4 is increasing for some h c [ho. h I,

3 This is quite distinct from the & k c y wage hypothcrir (Ltibcnslein. 1957) which postulates that the number of 'efficiency houn' per clock hour varies with the wage ate , not houn of work

followed by a 'fatigue -period'. in which + is decreasing for some hc [h , hi]. Since 4 is assumed to have a unique turning point h . the aggregate output obtainable from a given clock hour input is then also a strictly concave function ofh, reaching a unique maximum at h . Notice also that extra work need not have a positive marginal product in this formulation. Suppose that a firm with a given workforce is considering employing that workforce for an extra hour, and that these workers are willing to supply the extra hour at the going wage rate. With the efficiency hours index, ah) the necessary and sufficient condition for the extra hour to have a positive product at given employment is that dln(+)ldln(h) > - 1. In the following analysis, we will not assume that an extra hour's work always has a positive product. since this is a contentious assumption in work-sharing debates. Instead, we shall determine if this condition holds in the neighbourhood of each particular equilibrium of interest in the two union models.

There is some empirical evidence of the sort of relationship between hours and productivity postulated above. British experience in munitions production during World War I is illustrative. In order to increase wartime production, daily hours were considerably lengthened, and the 'fallacy of such procedures was dramatically revealed (Ghiselli and Brown, 1955. p. 274).4 As a result of this experience, considerable research effort was directed towards investigating the relationship between hourly output and daily hours. For example, see Vernon ( 192 I). the British Industrial Fatigue Research Board Reports, Florence (1924). and the I947 US Bureau of Labor Statistics study and associated analyses of these data.' In the 1980s, an extensive survey in Australia found that a majority of manufacturing firms had obtained or expected gains in worker productivity after a cut in standard working hours (Bureau of Industry Economics, 1984; Whittield. 1987,Chapter 4). Our assumed form for the efficiency index is modelled on the empirical relationship discussed in Vernon (1921) and Brown and Ghiselli (1955). showing that hourly output declines dramatically towards the end of the working day as well as the end of the working week. We have been unable to

For example. when the working week in one munitions plant was reduced. hourly output incrr?sed by 68 per cent and total weekly output by IS per cult (Ghirf i and &om. 1955; Goldmark. Hopkins and Florence. 1920; and Memo No. 21. Health of Munitions Workers Committee. 19 18).

5 Sec for example, Denison ( 1962) and Leveson ( 1967).

1993 EMPLOYMENT' AND HOURS IN A UNIONIZED ECONOMY 43 I

locate any more recent data on this relationship in the work of industrial psychologists and others, and would emphasize that the particular form of the efficiency hours index will vary with the particular type of work, and is a matter for further empirical verification. According to Thierry and Jansen (1984). there has been little recent systematic research by labour and industrial psychologists on this important issue. They also indicate a related issue requiring further investigation, v iz whether a shorter standard week is to be achieved by a four-day week with longer hours each day, or by a five-day week with shorter standard days. In this paper, we assume that our efficiency hours index applies to a working week, since this relates to current hours debates; however, it could equally be applied to a working day.

Ill Thp Dcrived Demand for Labour Since the focus of the paper is on the employment

consequences of a cut in hours in the unionized sector of the economy, we consider the two orthodox models of the trade union, namely the efficient bargaining model where bargaining occurs over wages and hours, and the monopoly union model. In both of these models, employment is decided by the firm, after the union and firm have bargained over wages and hours (efficient bargaining model) or after the union has unilaterally determined wages and hours (monopoly union model). This procedure follows !he stylized facts for Britain and Australia, where adult male wages and weekly hours in the unionized sector are determined by the union and the firm (or employers' association at the industry level), while the firm then decides on the number of workers (see for example Oswald and Turnbull, 1985).6 In the unionized sector, the wage rate is thus a flat rate which applies toall covered workers for the number of standard hours determined by the collective agreement. Therefore workers

In Australia, standard hours have generally been negotiated at the industry level. Applications for reductions in standard hours can either be made by individual unions. or through a national enquiry. as a test case for all Australian indusrry. The last time a national enquiry was held was 1947. Applications by indiwdual unions and/or firms arc heard by the Federal Arbitration Commission, or State commissions. The Arbitration Commission has at various tima refused to allow negotiations over standard bun even when both unions and fvms arc in agreement becarue of concern for possible flow-on effects to other industries.

cannot be thought of as necessarily being on their notional labour supply curves.'

Because of the two-stage decision process described above (whereby employment is determined after wages and hours have been set), we can initially consider labour demand for any given w and h separately from the actual determination of w and h. Thus we can write the competitive firm's profit from employing unionized workers at given w and h as

x (w,h) = maxV(Hh)hM - (s+wh) N] (N) (2)

where s X represents the fixed costs associated with employing each worker. For given w and h, the firm's choice of employment satisfies the first- order condition:

(3 1

Thus the firm employs extra union workers until the weekly value of their marginal product of labour in efficiency units is equal to the cost of labour for the week (or other time period).

Now consider a particular level of employment associated with wand h (which will be determined in the models in Section IV and VI of the paper). Suppose that there is some exogenously given cut in hours below the given equilibrium h*, as would occur for example if the government decided to determine standard hours. What is the effect on employment? We assume that the fixed cost of employing each worker s is unaffected. though w may vary. Implicitly differentiating (3) WXL h and rearranging one obtains:

P [ H h ) W H h ) h - s + wh

' We would emphasize that our work is not to be confused with the small but expanding literature in the United States. which examines an inverted U-shaped relationship between hourty wages and hours worked. in a non-unionized economy where workers' wages are individually negotiated (see for example Biddle and W i n . 1989). In our model. rhe wage level IS negotiated by unions and firms the individual is not nccessanly on his or her labour supply curve. Our model is therefore more appropriate for European-style unionized economics, w h e n a flat rate hourly wage for the standard working week is negotiated for all workers covered by a collective agreement.

ECONOMIC RECORD DECEMBER 432

where

t-- d l n N < 0 d lnw

is the wage elasticity of labour demand (for given 5 and h), and

0 = wh I (s + wh) ( 6 )

is the share of variable labour cost in the wage bill.

By inspection of (4), sufficient conditions for a cut in hours to increase employment are that:

(i) the cut in hours does not increase unit labour cost (dlnwldlnh 1 - l ) , (11) the cut in hours reduces output at given

employment ( d I ndld I nh > - 1 ), and (iii) the absolute wage elasticity of demand for labour is less than the share of variable labour cost in the wage bill (-f < 0).

Condition (iii) is also necessary and sufficient for it to be true that a positive productivity effect of a cut in hours will enhance any positive (or mitigate any negative) impact on employment

To judge the plausibility of these conditions we will have to look more closely at how wages and hours are determined, and some relevant empirical evidence.

IV Union and Firm Bargain over Wages and

We will first characterize an efficiently barg- ained contract between union and firm over hours and wages, and then ask What would happen to employment if a small legislated cut in hours is imposed on both parties?

A n efficient contract maximizes the representative worker's utility subject to the firm achieving at least its reservation profits8 (Equiva- lently, the firm could be modelled as maximizing its proriu subject to the union achieving at least its reservation utility.) Suppose that the utility of a representative union worker can be denoted by

u - v ( w 4 h) ( 7 )

which is continuously twice differentiable and strictly quasi-concave, with first derivatives v, - dv/d(wh) > 0 and vh - dvldh < 0. Union

Howof work

See Ulph and Ulph (1990) for an excellent survey of the standard union models without hours determination.

workers' reservation utility is fixed at vg. Suppose that the union's objective is to maximize the expected utility of a representative union member, given by (NIM) u + (l-N/M)vo where M is the number or union workers (assumed fixed), u > vo and (KN5M.9 An efficient contract maximizes:

N ~ I ~ ( W h h ) - ~ 0 1 + ~ o + X [ f [ @ ( h ) h N I - ( s + w ~ ) N - Q ] (8)

with respect to w, h and the Lagrange multiplier X>O, where the firm's reservation profit is fixed at % It is shown in the Appendix that the first- order conditions for an efficient contract imply that:

(9) - I > - I dlnd -hvh d I nh v, (s+ wh)

Thus an extra hour of work will have a positive product in the neighbourhood of an efficient bargain between union and firm for given employment. It also follows that the cut in hours could not then lead to an increase in unit labour cost. as this would violate the conditions for an efficient contract (see the Appendix).

Thus the first two sufficient conditions identified in the previous section hold when a cut in hours is imposed in a neighbourhood of an efficient bargain over wages and hours. The third condition is not implied by any obviously plausible theoretical assumptions. We therefore examine relevant empirical evidence.

V Some Evidence In the model developed in the previous section,

the local effect on employment of a cut in hours is positive if the absolute wage elasticity of labour demand does not exceed the share of variable labour costs in the wage bill. We term this the 'elasticity-share test', and in Table I summarize aggregate evidence for the UK and Australia. In the UK, the test indicates that employment will increase after a cut in hours in unionized markets in which all mutual gains from bargaining over wages and hours have been realized. However, the result of the elasticity-share test is ambiguous for Australia While Freebairn (1977) in a survey of the Australian empirical literature suggested that the aggregate real wage long-run elasticity of

The first-order conditions of equations (AS)-(A7) are unchanged by assuming instead that the union maximizes a utilitarian objective function,or that it follows rent max- imization in utility terms (for example, "wh h) 401).

1993 EMPLOYMENT AND HOURS IN A UNIONWD ECONOMY 43 3

TABLE 1 Employment Effects of a Cut in Hours in he UK and

A W &

Share of Wage elasticity Employment variable of labour effect of

Country labour demand a cut in cost hours

.80 .63 I i k - a l i a .76 .61-1.07

Sources: Shares of variable labour costs are from Han (1984) for the UK for 1981. Variable labour costs comprise both hourly wages and other payments that vary with hours of work. The figure for Australia is an unweighted mean of the estimates reported in Table 2 from Dixon and Williams (1986). Real wage elasticities of demand for the UK are from Bean, Layard and Nickell (1986) and were calculated using annual data from 1953- 1983. The real wage elasticity of labour demand for Australia was found to be -0.61 by Russcll and Tease (1988). -0.75 by EPAC (1988). varying between 0.75 and -1.07 by Symons (1985). and -0.79 by Pissarides ( 1987).

labour demand was about -0.5, more recent estimates suggest that it vanes between -0.61 and - 1.07. These estimates suggest the employment effect of a cut in hours is likely to be ambiguous. But what do the disaggregated estimates look like for Australia?

Table 2 summarizes our results on the efficiency- share test for Australia at industry level. The results suggest that employment will increase after a cut in hours for seven of the 12 industjes. again assuming that wages and hours have been bargained efficiently. Note that the employment effect will generally be positive in the manufacturing sector where (except for Textiles, Clothing, and Footwear) labour demand is relatively wage inelastic. This industrial variation suggests that hours may be best determined at the disaggregated level when employment effects are of concern.

VI A Caveat The Monopoly Union Model Suppose that there is a single monopoly union

which sets the level of wages and hours unilaterally, given the firm's demand for labour. While this is a popular characterization of unionized labour markets, the resultant quilibrium is not efficient, in that at least one party can be made better off without decreasing the utility of the other (McDonald and Solow, 1981). Thus the union's

choice problem is to maximize the following function with respect to wand h, for some l > O

N

where the first two terms are the union objective function. From the first-order conditions for this problem, it is shown in the Appendix that, in a neighbourhood of an equilibrium,

R Iv(whh) -vol + Yo + 5 [f[&h) hAq Q (h) h-s-wh) ( 10)

( 1 1) dlnh

the sign of which is indeterminant without further assumptions or evidence.

However, the employment effect is unambiguous if the cut in hours is not accompanied by a cut in uni t labour cost. Consider the employment effect of an exogenously imposed cut in hours holding unit labour cost constant, in a neighbourhood of the monopoly union's equilibrium.1° Substitution of ( 1 1 ) into (4) with dlnwldlnh = -1 (that is, with s + wh constant) yields:

- I dlnd- -v,,th vy( (s+wh) c + wh)

(12)

Thus we find that, under these conditions, the proposed reduction in hours must lead to a reduction i n employment. However, the comparative static effect on employment is ambiguous if unit labour cost is also allowed to fall with demands for a cut in hours."

This result provides a strong argument against attempts to introduce work sharing in labour markets dominated by monopoly unions, unless sufficient cuts in unit labour costs can be assured. In practice, gains in employment might still be possible if unit labour cost can also be Cut sufficiently.

As an aside, it may be noted that the models developed in this section. and in Section IV, also yield predictions for the situation where hours are

10 Unit labour cost is given by p w h , where s denotes employment costs which are invariant to hours worked. If unit labour cost is constant as hours are cut, then the hourly rate thereafter increases. 1 1 Unit labour cost is also an increasing function of hours worked in a neighbourhood of the monopoly union's equilibrium; more precisely, it can be shown that

is non-negative.

434 ECONOMIC RECORD DECEMBER

TABLE 2 E t n p l o y n o ~ Effects by l n d w for AILmalicl

Sham of variable Wage elasticity Employment of Industry labour costs of labour a cut in

demand hours

1. Mining 2. Food. Drink, Tobacco 3. Textiles, Clothing. Footwear 4. Metal Products 5 . (Total Manufacturing) 6. Electricity. Gas. Water 7. Construction 8. Commerce 9. Transport Communications

10. Finance and Business Services I I . Public Admin, Comm. Services 12. Recreation. Services

69 .76 .77 .74 .75 .73 .78 .:a .75 .75 .78 79

.25

.25 I .o .25 .3 5 .60

.70 I .3 I .4 2.0 .80

.60

Sources: Share of variable labour cost i s for 1979-80 and is from Dixon and Williams (1986) and is defined .IS : -share of 'on costs' in total labour costs ('on-costs' compriv worker's compensation. supennnuation. payroll lax. leave loadings and time paid tor but not worked). Wage elasticities of labour demand are Keating's (1983) eslimales of the elasticity of employmenr to averase earnings for each industry over the period 1948-80. * Sign reverses using the Dixon. Prentice and Williams (1988) estimate of the sham of variable labour cost for i 968i69.

initially determined exogenously, by (for example) some central authonty. and we wish to consider the employment implications of allowing for the decentnlized negotiation of hours. Suppose that [he exogenously determined working week is less than h*. In the efficient bargaining case. we found that. if the elasticity-share test holds then d N l d h < 0 a change from centralized hours determination to decentralized bargaining will lead to a reduction in employment in sectors where the absolute wage elasticity of labour demand is less than the share of variable labour cost in the wage bill. However, in the monopoly union cast. dNldh > 0. Then a switch to decentralized hours bargaining will increase employment when standard hours are initially set below h*.

Finally. it is of interest to consider how our results compare with the conclusions of union models of hours and wage determination in which productivity is held constant across hours of work. Hoe\ (1984). Calmfors (1985) and Booth and Schiantarelli (1987). in the context of a monopoly union model. each found that the employment effect of a legislated cut in hours was ambiguous

(although Booth and Schiantarelli suggested that the effect would be negative for plausible parameter values). Only Booth and Schiantarelli (1987) examine an efficient bargaining model, and find that employment is likely to fall with a legislated cut in hours. Our results with an efficiency hours index predict negative effects on employment for the monopoly model. but indicate that positive employment effects are possible from a legislated cut in hours in the efficient bargaining union model. O u r model also yields a straightforward empirical test, which indicates positive employment effects in some scctors of the Australian economy.

Vl l Conclusion This paper formalized the 'efficiency hours

hypothesis', whereby the output for a pven labour input depends crucially on the number of hours worked each week. This hypothesis was incorporated into two standard models of union- firm behaviour, namely the efficient bargaining model and the monopoly union model.

435 1993 EMPLOYMENT AND HOURS IN A UNIONIZED ECONOMY

Comparative static predictions were derived to examine the employment prospects from an exogenously imposed cut in hours. A straightforward empirical test was found to be sufficient for determining the employment effects of an exogenously imposed cut in hours, whenever the mutual gains from bargaining over wages and hours have been realized, leaving firms free to choose employment. A cut in hours will increase employment if the absolute wage elasticity of labour demand is less than the share of variable labour costs in the wage bill. This is not me for the monopoly union model; if a reduction in length of the working week is imposed on a monopoly union without sufficient cut in unit labour cost then employment will fall irrespective of the labour demand elasticity.

Using aggregate data for the UK, it was found that employment will increase unambiguously after a cut in hours if the conditions of the efficient bargaining model prevail. Using disaggregated data by industry for Australia, it is found that the employment effect can be either positive or negative, though it is generally positive for the manufacturing sectors. This industrial variation suggests that hours should be determined at the industrial level rather than nationally when employment effects are of concern.

APPENMX This Appendix elaborates on the derivation of some

key results in the text. First, total differentiation of equation (3) in the text w.r.L h and N (holding s fixed. w varies with h) yields:

P&Zh'dN + [ (r&hN+fX&'h+&) - (w'h+w)j dh - 0

and so:

(A I )

(A2)

which can be re-written as equation (4) in the text, using the fact that:

and that

The first-order conditions for a maximum of (8) arc:

w: ; v y - l - o

h:$V,vW'+Vhl + 1 If(.) (&+&'(h)h) - W ] - 0 (A6)

1 : jl . ) - ( s + w ~ ) N-14, 0 (A71

Substituting (AS) into (A6) and rearranging yields:

Vh + V Y f ( . ) [&+&'(h)hl - 0 (A81

Equation (9) is then obtained on using (A4) to eliminate

Maximization of (10) in the text w.r.t. w and h requires rhe first-order conditions:

fc. ).

N M w: - v, - )i - 0

N ' ~ : M / Y , w + v ~ I + X l f ( . ) y 9 ' h + * l ~ + / ( . I * ' h + O l - ~ ) - O (A IO)

which together imply:

%+ Vy K . )+@hr( .)M (@'h+&) - 0 (A1 I )

Again substituting out f and f and multiplying through by hi& one obtains equation ( I I ). To &vain (12) in the text. first note that. with unit

labour cost (s+wh) held constant. the first term in equation (4) is zero. Substitution of ( 10) into (4) then yields:

which is (12) in the text

REFERENCES

Barzel, Y. (1973). 'The Determination of Daily Hours and Wages', Quurterty Jownalof Economics. 220-38.

Bean, C.. Layard, R.. and Nickell. S. (1986). 'The Rise in Unemployment: A Multi-Country Study'. Ebonomiccr 53. SI 622.

Bell D.N. and Hart, R.A. ( 1991 ), 'Effort. Worker Quality. Wage Rates and Firm-specific Training', mimeo. airling University.

Biddle. J.E. and Zarkin. G.A. (1989). 'Choice among Wage-Hours Packages: A n Empirical Investigation of Male Labor Supply', Joumal of Lubor Economics 7(4),415-37.

Bicnefeld. M.A. (1972). Working H o w in Bdish Indusny, Weidcnfcld and Nicolson, London. 1972.

Booth, A.L. and Schiantarelli, F. (1987). 'The Employment Effects of a Shorter Working Week'. E'conomica 54,237-48.

Bureau of Industry Economics ( I 984). 'Reducing Standard Hours of Work: Analysis of Australia's Recent Experience'. Research Report No. IS. AGPS. Canberra.

Calmfors, L (1985). 'Worksharing, Employment and Wags', Ewopnut Economic Review 27,293-309. - and Hocl. M. (1988). 'Worksharing and Overtime'.

ScMdinavion Jownal of Economics !30( I ), 45-62.

436 ECONOMIC RECORD DECEMBER

Chapman, SJ. (1909). 'Hours of Labor'. Tlu Economic

Cuvillicr, R. 11984). h e Reducrion of Working T i e . International Labor Office. Geneva.

Denison. E.F. ( 1962). Thp Sourccs of Eronomic Growth and h e AltcmarivcJ Eeforc Us. Supplementary Paper No. 13. New York. Committee for Economic Development.

Dinon. P.B.. Prcntice. D.A. and Williams. L.S. (1988). 'Wages and On-Costs in Australian Industria: 1968169 to 1985186'. Journal of Itufutrid Rebrion~ 30 (2). 294-3 10.

:)iron. P.B.. and Williams, L.S. 19861. 'Wages and On- Costs in Australian Industries: 1968169 to 1984185'. The Institute of Applied Economic and Social Research. Working Paper No.9/1986. University of Melbourne. Melbourne, Australia.

turopean Trade Union Institute ( 1983). 'The Reduction o i Working Hours in Western Europe'. mimeo. ETCI.

I-PAC (1988)..4rcrtrclliasMediurn Term Gmwrh Potenrul. AGPS Canberra.

Freebairn J.W ( I 977). 'Do Wages Matter?'. .4usrruliun Economic Ruvipw. Third Quarter.

Florence. P.S. ( 192-1). Economics of Futigue and Unrest. trnd the Efflcienncy of Labor in Bnrirh und American /t idun. Allen and Unwin. London.

Chiselli. E.E. and Brown. C.W. (19551. Perwnnel und Ind-1 P~cholqpy. McGraw-Hill. 2nd Edition.

Gddmark. 1.. Hopkins. M.D. and Florence. P.S. 1191-0). '('ompanson of an Eight-Hour and a Ten-Hour Plant'. Public Hrulrh Bullerin 106. US Public Health Service.

1984, 77w Economics of Non- W u p L b o r ('051s. Allen and Unwin, London.

lealth of Munitions Workers Committee 1 19 18). Memo s0.2 I .

locl. 1M. ( 1986). 'Employment and Allocation Effects of Reducing the Length ot' the Workday'. &conomicxI 53.

licks. J.R. f 1932). Tlu 77Wory 01. Wuges. .Macmillan. (.ondon. t in t edition 1963.

Keating, M. ( 1983,. 'Relative Wages and the Chanping Industrial Distribution in Australia'. 7hr Eronomic

L.etbenstcin. H. 1957). Economrc Buckwardnut und

Jou~~uI 19.353-73.

BNSSek.

Part. R.A.

R C C O ~ 59.384-97.

Etonomtr Growh. Wiley. London.

Leveson. 1.F. (1967). 'Reductions in Hours of Work as a Source of Productivity Growth'. Joumal of Political Economy. 199-204.

Marshall. A. ( 1980). h c Q h of Economics, Macmillan, London. 8th edition 1947.

McDonald, I.M. and Solow, R.M. (1981). 'Wage Bargaining and Employment'. AmericM Economic

Oswald AJ. and Turnbull, P. (1985). 'Pay and Employment Determination on Britain: What Arc Labor Contracts Really Like:?', Oxford RNkv of Economic Poluy 1,80-97.

Pissandes C. (1987). 'Real Wages and Unemployment in Australia'. CLE Discussion Paper No. 286. London School of Economics.

Pigou, A.C. (19201, 77w Economics of Wc[farr. Macmillan. London.

Russell W. and Tease, W. ( 1988). 'Employment, Output and Real Wages', Reserve Bank of Ausfralia Discussion Paper No. 8806.

Schmidt-Sorenwn J.B. ( 199 1 ). 'An Efficiency-wage- hours Model and Shorter Working Hours'. Scottih Journal of Political Economv 38. I 13-3 I .

Synons I. ( 1985). 'Employment and the Real Wage in Australia' in P.A. Volkcr (ed.). 77u Sfrucmrc and Duruhon of Unemployment in Ausrraliu.

Thieny. H and Jansen, B. (1984). 'Work and Working Time'. in J.P.D. Drenth. H. Thicrry. PJ. Willems and CJ. de Wolff (eds). Handbook of' Work und Orgun- iaawnal P~rhology. John Wiley and Sons.

Trades Union Congress ( 1984). 'Working Time Objectives and Guidelines for Trade Union Negotiators: 1984-5 Pay Round'.

I'lph D.T. and Ulph. A. (1990). 'Union Bargaining: A survey of Recent Work' in D. Sapsford and Z Tzannatos (cds), Curnnr Issues in Lubor Economm, Macmilbn.

United States Bureau of Labor Statistics (1947). H o r n If Work and Ourput, Bulletin No. 9 17. Government Printing Office. Washington.

Vernon. H.M. (192 1 ), IndustMl F ~ t i p ~ und Effiienq. Routledge and Sons. London.

Whitfield. K. (1987), 7hr Ausmliun Labour Market. tiarper and Row. Sydney.

W 71,896-908.