Journal of Financial and Strategic Decisions Volume 13 Number 2 Summer 2000 DOWNSIZING, CAPITAL INTENSITY, AND LABOR PRODUCTIVITY

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1 Joural of Fiacial ad Strategic Decisios Volume 3 Number Summer DOWNSIZING, CPIT INTENSITY, ND OR PRODUCTIVITY Swapa Se * ad Rezeia Farzi ** bstract Recet studies o corporate dowsizig attribute variability i labor employmet to busiess cycle ad the process of techological iovatio Caballero & Hammour, 996, the outsourcig decisio by corporatios Se & Zhu, 996, the lack of flexibility of workers compesatio schemes Gerhart & Milkovich, 99, ad istitutioal factors Nagao, 995. This paper presets a simple model to study employmet variability due to fluctuatios i labor productivity. The study of a productio fuctio demostrates that the firm s use of a factor of productio is iversely related to the productivity of that factor. Further, the variability of employmet of a factor due to its ow productivity fluctuatios is magified by the itesity of employmet of the other factor of productio. INTRODUCTION Corporate dowsizig has led to losses of jobs i millios i large U.S. corporatios Uchitelle & leifield, 996. lthough corporate dowsizig is symptomatic of a recessio, merica firms are layig off more ad more workers i spite of a recoverig ecoomy whe overall uemploymet is at historical lows. This has led to the belief that jobs are chagig rather tha disappearig Greeberg, 996. Dowsizig ad job isecurity have treded up alog with risig labor productivity Filardo, 995. Such empirical observatios would suggest a relatioship betwee dowsizig ad productivity chages. This relatioship, however, is ot discerible i the literature. Explaatios of employmet variability i recet literature appear due to the followig sources: Dowsizig s Result Of Corporate Restructurig ccordig to this view, job reallocatio results from product ad process iovatios. s ew productio processes replace old processes, job creatio i ew processes ad job destructio i old processes becomes ecessary outcomes i a evolvig ecoomy. Caballero & Hammour 996 model this Schumpeteria cocept of creative destructio Schumpeter 94 whereby techological progress is associated with massive factor reallocatio. They show that durig a recessio, job creatio ad job destructio are coupled i a efficiet ecoomy ad de-coupled i a iefficiet ecoomy. Variability i employmet i their model arises as a result of iovative chages i productio processes. I additio, Se & Zhu 996 show that firms outsourcig decisios are complemetary to their decisios to dowsize. Firms seek reductio of fixed costs through outsourcig as the later is used as a meas of reducig headcout i maagerial raks. s a result jobs are reallocated from the origial producer to the outside producer, leadig to employmet variatio i both firms. Dowsizig s Istitutioal Developmet Nagao 995 posits dowsizig as a result of the coflict betwee ecoomic ratioality ad sociopolitical ratioality. Ecoomic ratioality is associated with maximizig output ad log-term profits by the firm. Sociopolitical ratioality etails commitmet to widely accepted societal values, maifested i geeral rules of coduct, regardig fair ad proper treatmet of idividuals employed i the busiess orgaizatio. Nagao poits out *Christopher Newport Uiversity **Michiga Techological Uiversity 73

2 74 Joural of Fiacial ad Strategic Decisios that over log term, large busiess orgaizatios require a balace betwee ecoomic ratioality ad sociopolitical ratioality ad ay sigificat asymmetry causes orgaizatioal dysfuctio icludig loss of employmet. Dowsizig Due To Compesatio Systems Gerhart & Trevor 996 examie orgaizatioal differeces i the impact of compesatio systems o employmet variability ad suggest that a compay s degree of emphasis o variable pay ca determie its employmet variability i several ways. First, the decisio whether or ot to reduce labor costs by egagig i layoffs ca deped upo the extet of flexibility built ito the pay system. ecause performace based labor costs are by defiitio tied to busiess outcomes, layig off flexibly paid employees durig dowturs may be less attractive tha layig off labor who have fixed wages. Secod, the decisio to dowsize ca also deped upo whether a variable pay desig ecourages decisio-makers to emphasize a log-term view of orgaizatioal performace. Decisio-makers ca weigh the short-term labor cost savigs of high employmet variability versus potetial log-term beefits associated with employmet stability. Samplig 5 orgaizatios from the COMPUSTT database, Gerhart & Trevor fid that orgaizatios relyig more heavily o log-term compesatio icetives for maagers exhibited less employmet variability. lso, whe groups of employees were covered by variable pay plas, their employmet variability was observed to be lower. I summary, the studies cited above provide three differet explaatios of dowsizig; iovative processes, istitutioal developmet, ad labor compesatio schemes. I this paper, we develop a simple model of employmet variability ad fid a basic explaatio of employmet variatio i the fluctuatios of factor productivity. This is cosistet with the study of iovative processes as firms elimiate less productive processes ad workers ad retai more productive workers ad products. Sectio II develops a productio fuctio model to study the relatioship betwee factor productivity ad employmet variability ad Sectio III summarizes the results. Defie margial productivity of labor as: Equatio ad average productivity of labor as: Equatio THE MODE The productio fuctio is give by F, where / f/, is the itesive productio fuctio. log the productio fuctio, ay oe factor-ratio ca be expressed i terms of aother. Thus: Equatio 3 where correspods to the factor ratio Multiplyig both sides of by Equatio 4 ad correspods to the factor ratio. we obtai:

3 Dowsizig, Capital Itesity, ad abor Productivity 75 Similarly, equatio, whe multiplied i both sides by, yields: Equatio 5 Utilizig 4 ad 5 we obtai the followig: Equatio 6 The itesive productio fuctio is of the form: Equatio 7 For, the curve is liear. If >, the ad the curve would be covex. If <, the ad the curve would be cocave. Substitutio of equatio 7 i 6 yields: Equatio 8 The firm chooses a factor ratio subject to the itesive productio fuctio. owig that, 8 ca be rewritte as: Equatio 9 Simplifyig the above, we get: Equatio Equatio is a liear differetial equatio of the eroulli type. To solve we let a dummy term v to be equal to: Equatio v For reasos of simplicity we drop subscripts of,.

4 76 Joural of Fiacial ad Strategic Decisios Differetiatig we obtai: Equatio or, dv d Equatio 3 d dv Dividig both sides of by Equatio 4 we get: Substitutio of ad 3 i equatio 4 yields: Equatio 5 v dv d Dividig both sides by Equatio 6 dv d v : 6 is a liear differetial equatio of degree oe. Its solutio takes the followig form: Equatio 7 Pd Pd Pd exp exp d c v exp where P ad. We solve 6 by lettig a dummy variable y be equal to: Equatio 8 e y Itegratig:

5 Dowsizig, Capital Itesity, ad abor Productivity 77 Equatio 9 y l exp ad simplifyig 9: Equatio y Multiplyig both sides of 6 by, we obtai: Equatio v d We summo the terms o the left-had side as a differetial ad simplify the right had side as follows: Equatio v d d Itegratig both sides yields: Equatio 3 c v Dividig both sides by : Equatio 4 c v Substitutig equatio i 4: Equatio 5 c

6 78 Joural of Fiacial ad Strategic Decisios Rewritig 5 ad simplifyig, we get: Equatio 6 c Whe margial ad average productivity of labor are equal: Equatio 7 lim Which gives: Equatio 8 c lim Thus, the average productivity of labor,, ad the margial returs,, edogeously determie the factor ratio, /. Equatio 8 allows derivig the followig propositios: Propositio : Each / o the itesive productio fuctio has a correspodig average factor productivity that displays a iverse relatioship with /. Proof: Whe a firm employs ew labor whose margial productivity is equal to the average productivity of all labor the firm already employs, acquirig this ew labor will ot affect average productivity. Thus, the expressio 8 ca be rewritte with showig the averagig productivity of the factor ratio, /: Equatio 9 Equatio 9 demostrates that average productivity is iversely related to factor itesity /. Recall from microecoomic theory that margial productivity equals average productivity at the maximum of average productivity. The factor ratio obtaied i the limit, whe, such as the factor ratio i 8, is a optimum factor ratio. Propositio : Greater is the variability i the employmet of a factor, greater the itesity of use of the other factor of productio, keepig the other factor costat. Proof: Suppose there are two firms, ad. Firm has high capital itesity ad firm has low capital itesity >>. oth firms maitai the same absolute amout of capital at ay time:

7 Dowsizig, Capital Itesity, ad abor Productivity 79 Firms ad iitially have the same labor/capital ratio: verage productivity of firm ad at time are give by ad t time the labor/capital ratio of the firms are give by expressio 8: Iitially,. The chages i average productivity are represeted by - ad -. chage i average productivity is oly feasible whe -< >. oth firms udergo the same chages i average productivity of labor from time to : - - The labor/capital ratios of both firms at time are give by expressio 6: c c Variability of employmet of firm is show by: c Sice >>, the variability of employmet of firm is reduced to: c >> Similarly, the variability of employmet of Firm : c

8 8 Joural of Fiacial ad Strategic Decisios Sice, the variability of employmet of firm reduces to: Propositio 3: For give chages i, the shift i employmet over time is cotiuous, double differetiable, ad mootoic. Proof: Whe average productivity chages as a liear fuctio of time such as bt, where b is the slope of the fuctio, 9 ca be writte as: let bt c ad <. Equatio 3 c bt This is a polyomial fuctio of degree c>. First ad secod order differetials are: t t bc bt It shows that c b c c bt c will ot chage sig if bt> ad c >. Thus 3 is a mootoe smooth fuctio. t

9 Dowsizig, Capital Itesity, ad abor Productivity 8 SUMMRY OF RESUTS ND CONCUSIONS This study focused o the variatio of factor employmet ad its relatioship with factor productivity ad preseted three mai results: Variatios of factor employmet exhibit iverse relatioship with factor productivity. arger the capital employed by a firm, higher is its variatio i labor employmet due to productivity chages at a give level of capital. We fid that similar chages i average productivity produces larger variatios i employmet for a firm which has higher capital itesity, i.e., a firm that employs relatively more capital tha labor. This result is symmetric for capital, holdig labor employmet costat. That is, a firm havig higher labor itesity will have higher variatio i capital for a give chage i the productivity of capital. 3 Employmet adjustmets due to productivity fluctuatios are smooth ad mootoic. 4 Whereas the first result adds to the recet literature o employmet variability, the secod result leds itself to iterestig empirical ivestigatio. REFERENCES. Caballero, Richardo J; Mohamad. Hammour, O The Timig ad Efficiecy of Creative Destructio, uarterly Joural of Ecoomics, ugust 996, pp Gerhart arry; Charlie O. Trevor, Employmet Variability Uder Differet Maagerial Compesatio Systems, cademy of Maagemet Joural Vol. 39, No. 6, 996, pp Greeberg, Eric R., Jobs are chagig, ot disappearig, Maagemet Review Vol. 85, No. 8, ugust 996, p Nagao, lvi T., Rigid Istitutios: Wages, Worker oyalty, d The Dowsizig Of Corporate merica, Ph.D. Dissertatio, The Joh Hopkis Uiversity, Filardo, drew J., Has Productivity Tred Steepeed i the 99s? Ecoomic Review, Federal Reserve ak of asas Vol. 8, No. 4, 995, pp Uchitelle ouis; N. R. leifield, O the attlefields of usiess, Millios of Casualties, The New York Times, March 3, 996, p.. 7. Schumpeter, Joseph., Capitalism, Socialism, ad Democracy, New York: Harper & ros Se, Swapa ad Guagxi Zhu, The Optimal Degree of Outsourcig, Joural of Fiacial ad Strategic Decisios Vol. 9, No. 3, Fall 996, pp