CHAPTER 4 MEASUREMENT OF CAPACITY UTILIZATION: A THEORATICAL APPRAISAL

Transcription

1 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry CHAPTER 4 MEASUREMENT OF CAPACITY UTILIZATION: A THEORATICAL APPRAISAL A measure o Capacy Ulzaon (CU) s necessary o know he levels o he ulzaon o exsng producon capacy n he producon process. The economc heory also avours he esmaon o CU because an accurae assessmen o a producon uncon requres capal n use no capal n place (Solow, 1957). The laer represens he oal capal sock avalable or use n he producon process, whereas he earler relecs he proporon o he oal avalable capal sock acually ulzed. In he sudes lke ours, where he esmaon o producon uncon s requred o access he echncal ecency and producvy perormance o he Indan sugar ndusry, an esmaon o he ndex o CU s sgncan o adjus he exsng capal sock accordng o he capacy ulzaon level usng he ollowng relaon: Capal n Use=Capal n Place Capacy Ulzaon The capal n place can be obaned by he usng he usual echnques such as perpeual nvenory mehod, ec. However, measurng he rae o capacy ulzaon requres denyng he capacy oupu Y * and hen, he capacy ulzaon rae s dened as he rao o he acual oupu Y 0 o capacy oupu (Krkley e al., 2002).e., Y CU = Y However, he noon o capacy oupu has been dened n wo alernave ways; ) prmalechnology based or engneerng concep; and ) an economc based concep. As per he prmal echnology based engneerng concep, he poenal oupu may be echnologcally derved and hence dened relave o he maxmum possble physcal oupu ha he xed npus are capable o supporng when he varable npus are ully ulzed (Johanson, 1968). Alernavely, ull capacy oupu s ha level o oupu whch he exsng sock o equpmen s nended o produce under normal condons wh respec o he use o varable npus (Smhes, 1957). In conras, economss dene ha ull capacy oupu level s assocaed wh ull compeve equlbrum and or an ndvdual rm hs pon occurs a he mnmum o he average cos curve (Chamberln, 1947). Thus, rom he hndsgh o an economs, he poenal oupu can be dened relave o an economc opmum such as he level o oupu whch mnmzes cos or 0 * Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 90

2 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry maxmzes revenue or pros (Gréboval and Munro, 1998). Fgure 4.1, presens wo noons o capacy oupu elaboraed hrough he engneerng and economcs based denons o capacy. Panel A, explans OY o level o capacy oupu as per he engneerng concep o capacy whereas, OY E s he economc based measure o capacy. As he engneerng measure o capacy s a physcal measure, s esmaon doesn requre normaon regardng npu prces. Alernavely, economc measure enals he normaon regardng he prces o acor npus o esmae a cos-uncon. Thus, he engneerng measure o capacy has ound o be more operaonal han he economss concep (Budn and Paul, 1961). Mos o he managers and echncal expers preer o operae wh he engneerng denon o capacy and ncdenally he same denon s he bass o he capacy denon o cenral sascal organzaon (CSO), Mnsry o Sascs and Program Implemenaon, Inda (Paul, 1974a, 1974b). Furher, emprcal deermnaon o he economss verson o capacy oupu s ndeed dcul especally n he conex o mulproduc rm. However, mos cos curves are L-shaped he economc concep can also be approxmaed by he engneerng concep o capacy (Johanson, 1960). Fgure 4.1: Two Conceps o Capacy Oupu Source: Gréboval, (2002) Dverse measures such as, engneerng measure o capacy, elecrcy consumpon mehod, maxmum acheved oupu approach, survey approach, Wharon or peak o peak ndex o capacy ulzaon, he RBI ndex, me nensy approach, Producon Funcon or cos uncon based approach, and Mnmum Capal Oupu Rao mehods ec., are avalable o quany capacy ulzaon levels. All o hese mehods are dscussed as ollows: Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 91

3 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry 4.2 Measures o CU based on Engneerng Concep Under engneerng measure he cener o he ocus s capal. The level o oupu whch opmze he use o he xed acor o producon.e., capal s he capacy oupu. The ollowng measures are based upon he engneerng concep o CU: Engneerng Measure o Capacy Accordng o engneerng concep, capacy s maxmum poenal oupu aanable rom gven capal equpmen n a gven perod o me, and ulzaon o capacy means he acual ou low o oupu n relaon o echncally possble level o oupu. Thereore, s rao beween acual oupu and maxmum possble oupu. I, Yh s he hourly oupu rom gven equpmen a 100 percen ecency, T s oal hours n a year (.e = 8760 ), hen oal annual maxmum oupu Y ˆ = Yh T. I YA s acual oupu durng he year hen capal ulzaon ( K U ) can be dened as n (4.1), K U Y = (4.1) A Y In pracce, s mpossble or an em o equpmen o operae or 24 hours, o 365 days. Ths s because, some loss o he equpmen s me can occur due o he wasage n process, machne breakdowns, and normal soppages or manenance. Thereore, easble echncally maxmum oupu s more relevan measure o capacy (raed capacy). I s calculaed on he bass o avalable me or he acual use o equpmen. I, acual me avalable or he equpmen s T where T < T ˆ hen echncally easble oupu ( Y ) and ulzaon ( K ) can be dened as n equaon (4.2), Where, K YA Y = = Y Tˆ Yˆ h Y = Y Tˆ h A F (4.2) The mehod gven above s approprae or mcro level sudes. The degree and level o aggregaon permssble n hese measures wll depend upon he ollowng condons: a) Oupu should be homogeneous; and b) echnology and sze o he plans are also homogeneous. Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 92

4 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry Elecrcy Consumpon Mehod Ths mehod has been developed by Foss (1963) and laer used by Jorgenson (1966), Grlches (1967) or U.S.A. and by Heaheld (1972) or U.K. Ths mehod s based on he proposon ha lke oupu and labour, CU s relaed o he low o capal servces. Elecrcy s perecly homogenous produc o unorm qualy, and s easer o aggregae elecrcy consumpon daa whou any aggregaon problem. The elecrc moor ulzaon rae s he rao o acual consumpon o elecrcy (khw) o he echncally possble consumpon by nsalled elecrc moors. The echncally possble consumpon o elecrcy measured on he bass o 24 hours use o elecrcy or 365 days, adjused or he energy loss o 10 percen due o dsspaon n he orm o hea. I plan n he h ndusry, AE s acual consumpon o elecrcy by he moors n he R s he raed capacy o he elecrc moors, 8760 are he oal hours n a year, and.90 s he ecency o elecrc moors hen elecrcy based measure o ulzaon o capal ( M ) can be wren as n equaon (4.3), M AE = ( R ) Ths mehod s more useul where elecrcy s he man source o energy; wll be beer proxy or he nensy wh whch he machnes are beng drven by elecrc moors. (4.3) I s however el ha hs measure underesmaes he level o capal ulzaon n case o underdeveloped counres, because n hese counres due o shorages n he supply o elecrcy, plans may be operaed by oher prme movers such as seam engne, urbnes and gasolne engnes. I s also an mporan ac ha some o he equpmens may need npu o elecrcy no only as prme movers, bu also o use o generae hea and coldness. Under hese condons, we use hs mehod, would end o undersae he exen o ulzaon. I does no ake no accoun me o repar, manenance and adjusmens. I does no have proper sysem o weghs when deren secons o plans operae a deren raes hs resul n he downward bas n he measuremen o ulzaon raes Producon Funcon Approach The mehod o esmang capacy by Producon Funcon s an engneerng esmae o capacy or a rm or ndusry. In hs approach several npus can be mplcly ncluded n a capacy ulzaon ndex by combnng hem n Producon Funcon. I has been developed and Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 93

5 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry used by he emnen auhors vz., Ball and Smolensky (1961), Klen and Preson (1967), Brscoe e al. (1970), and Harrs and Taylor (1985). In her semnal work Klen and Preson (1967) esmaed capacy hrough Producon Funcon or 30 U.S. manuacurng ndusres or The esmaed Producon Funcon capures he long-run relaonshp beween he npus and oupu (e.g., capal sock, labour and oupu). For any perod, he gures o acual oupu are compared o he capacy oupu esmaed a ull employmen o resources o deermne capacy ulzaon seres. Thus he noon o capacy used s he economss noon o maxmum oupu correspondng o all acors o producon, ncludng capal sock and esmaon echnque s an analycal one based on Producon Funcon. Suppose he relaonshp beween oupu and npus a any perod can be saed as ollows: Y ( L, K,, ε ) = φ (4.4) Where, Y denoes real oupu, L denoes labour npu expressed n erms o man-hours, K he low o capal servces, s a proxy or echncal change andε s an error erm. I φ can be speced (e.g. Cobb Douglas) and s parameers are esmaed, hen we can wre he relaonshp or oupu a peak (ull capacy) perods as: (,, ) c Y φ L K = (4.5) Where, L and K reer o ull employmen supply o man-hours and avalable low o capal servces. c The ndex o capacy ulzaon s hen compued as U = Y / Y or any perod. The problems wh hs mehod relae o he measuremen o capal sock seres as well as measuremen o ull employmen levels o man-hours and low o capal servces. The measuremen o he wo npus are nerrelaed and alernave assumpons have been made n esmang assumed ha: L and K. Klen and Preson (1967) relae capal ulzaon o manpower and I he Producon Funcon s Cobb Douglas ype, hen: K K L = (4.6) L Y Y c L = ε L (4.7) Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 94

6 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry Full employmen labour orce s obaned by specyng as a uncon o employed labour orce, nvolunary unemployed labour orce and rconally unemployed labour orce. Full employmen man-hours are hen obaned by an adjusmen acor or acual man-hours used. Thus he rae o unemploymen s drecly relaed o he rae o capacy ulzaon. The ndex o ulzaon s obaned as: ( α β) ( ) LogY LogY = + LogL LogL + Logε (4.8) c The mehod used by Klen and Preson (1967) assumes ha he oupu observed n any me perod s he equlbrum level or he observed raes o ulzaon o he npus. I hs s no an approprae assumpon as poned ou by Brscoe e al. (1970) hen he dvergence o acual oupu rom ull capacy s composed o wo elemens. Frs, here s he dvergence due o nsucen ulzaon o npus by he ndusres and second, here s dvergence due o nsucen producon wh he npus acually observed. Ths would be because labour hoardng s occurrng whn he ndusry or because demand or oupu s lucuang regularly so ha he rms are repeaedly n dsequlbrum wh respec o oupu levels (or employmen levels or npus). I s mporan o dsngush beween hese componens snce hey have deren mplcaons or polces concerned wh he elmnaon o excess capacy. Speccally, we mgh nd npus ully ulzed or an aggregae o ndusry bu oal oupu below he level could aan snce he resources are no correcly allocaed beween he ndusres. Gven a proper unconng o he prce sysem and sucen me, hs suaon wll be correced. On he oher hand, each ndusry could be a s equlbrum oupu level or he opmum allocaon o resources bu resources, as a whole may no be ully employed. To remedy hs suaon may requre a delberae polcy desgned o smulae overall demand, employmen o resources and hence supply o oupu. Brscoe e al. (1970) use he smple dynamc adjusmen mechansm o Koyck o show he nluence o lagged oupu erm on he esmaon o capacy ulzaon. I he Cobb Douglas Producon Funcon s assumed, he equlbrum level o oupu s: β β β Y = Ae L K Z (4.9) * and, Y Y * Y = Y 1 1 η (4.10) Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 95

7 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry wh resrcons: 0< η < 1 and * Y Y Y 1. Here A, β 1, β 2, and β 3 are parameers o be esmaed. * Y s he equlbrum level o oupu or observed acor npus and η s he speed o response whle Z s he error erm. From (4.9) and (4.10) we ge: η η * lny = ln Y + (1 )lny 1 [ ] ( ) = η ln A+ β + β ln L + β ln K + ln Z + 1 η lny Once he parameers are esmaed, hen capacy ulzaon seres s obaned as: (4.11) U = lny lny c (4.12) The approach brngs ou clearly he nluence o lagged oupu on he esmaed capacy. Thus, he Producon Funcon approach s analycally beer han smple sascal consrucs Measure based on Daa Envelopmen Analyss Färe e al. (1994) used he relaonshp beween echncal ecency and capacy ulzaon o develop a DEA based model o quany capacy measure usng he denon o capacy oupu gven by he Johansen (1968): capacy s he maxmum amoun ha can be produced per un o me wh exsng plan and equpmen, provded ha he avalably o varable acor o producon s no resrced. Thus, capacy ulzaon s he degree o whch he DMU s achevng s poenal (capacy) oupu gven s physcal characerscs (.e. xed npus such as xed capal n our case). In conras, echncal ecency s relaed o he derence beween he acual and poenal oupu gven boh xed and varable npu use. A DMU may be operang a below s capacy level due o underulzaon o he xed npus, or he necen use o hese npus, or some combnaon o he wo. The wo conceps are llusraed n Fgure 4.2, n whch a DMU o a gven sze s observed o be producng O o level o oupu as a resul o usng V o levels o npus. I all npus were ully ulzed (.e. usng V c raher han V o varable npus), and he DMU was operang a ull ecency, hen he poenal (capacy) oupu would be O c. Even a he lower level o npu usage, he DMU was operang ecenly would be expeced o produce O e level o oupu. Hence, he derence O c -O e s due o capacy underulzaon; and he derence O e -O o s due o necency. To model capacy measure, he npu vecor s separaed no a sub vecor o xed npus, and a sub vecor o varable npus and a scalar measure o capacy can be obaned or each decson makng un a me perod. The sub vecor o xed npus s bounded by observed Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 96

8 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry values, whle he bounds on he varable npus are allowed o vary, whch essenally consrans producon by he xed acors, conssen wh he Johansen denon. Fgure 4.2: Capacy Ulzaon and Techncal Ecency The mahemacal model o compue capacy measure, proposed by he Färe e al. (1994) can be dened as ollows: Maxmze φ (4.13) { φ λ µ } n,, Subjec o: φ y λ Y, x λ X, m F m m X µ x = λ X, n V n n X λ, µ 0. Where, φ = capacy measure a me or h decson makng un (DMU). Assume here are m xed npus, n varable npus and k oupus, hen x m, x n and y k denoes, respecvely, he xed npu, varable npus and oupu vecors or he h year. Thus, x m s a ( m 1) column vecor, x n s a ( n 1) column vecor and y k s a ( k 1) column vecor. Moreover, X = ( x, x,..., x ) s he ( m T ) marx o xed npus, X = ( x, x,..., x ) s he ( n T ) marx o varable npus and (,,..., ) n 1 2 T Y y y y s he k Toupu marx. Furher, λ s vecor o nensy varable o order = 1 2 T T 1 andµ n represens npu ulzaon rae o varable npu n a me and dened as he rao o he opmal use o each npu o s acual usage. However, capacy ulzaon (CU) generally reers o he proporon o poenal capacy ha s used, and s ypcally measured as he rao o acual oupu o capacy oupu (Krkley and Squres, 1999). Ths rao generally canno exceed m 1 2 m Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 97

9 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry uny. Färe e al. (1989) proposed ha CU be measured as he rao o oupu orened echncal ecency o he capacy measure.e., ( CU ) DEA θ = (4.14) φ Where, θ =Techncal ecency score or he h DMU a me and φ =capacy measure or he h DMU a me. The θ can be dened rom he ollowng model whch s popularly known as oupu-orened CCR model. Maxmze θ (4.15) { φ λ} Subjec o: θ y λ Y, o, x λ X, λ 0. In model (4.15) he oupu consran s same as gven n model (4.13) whereas, he handlng o npu consrans ders o some exen. In model (4.15), each npu acqures same reamen and X x x x becomes a marx no derences exs beween xed and varable npus. Thus, (,,..., ) o order ( ) = 1 2 T m+ n T. I s evden rom relaon (4.14) ha capacy ulzaon and echncal ecency are relaed wh each oher. 4.3 Measure based on Operaonal/Manageral Concep The problem wh he engneerng measure and producon uncon based approaches relaes o he measuremen capal npu and he ull employmen resources o boh labour and capal. Anoher major problem wh hs approach s ha unless he parameers o he Producon Funcon are re-esmaed sucenly requenly, ulzaon raes wll become ncreasngly based. Furhermore, whenever he parameers are re-esmaed, he enre hsorcal seres has o be revsed. Thus, he ollowng aemps have been made o make he measure o CU more operaonal and overcome he weaknesses o engneerng mehods: Survey Approach The mos drec and obvous means o obanng numercal CU levels s o ask rms or her own assessmen o he exen o whch hey are usng avalable capacy. Almos all ndusralzed counres now nclude hs queson n monhly surveys o busness. For Ireland, he IBEC-ESRI Monhly ndusral Survey (MIS) underaken on behal o he EU provdes Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 98

10 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry normaon on capacy ulzaon or a number o ndusral secor and sub-secor classcaon. The wo quesons relang o capacy ulzaon are: ) For he comng year do you consder your presen capacy s: Excessve (+) or Insucen (-); and ) Durng he monh, you were operang a abou wha percen o capacy-please ndcae o he neares 10 percen, 50 percen, 60 percen, 70 percen, ec. Whle he responses o queson () canno yeld exac CU rao, hey provde an overall ndcaon o he drecon o change n CU. The number o negave responses gves an ndcaon o he percenage o rms operang a or above ull capacy. As a resul, he rend n capacy ulzaon can be nerred rom he monh-on-monh change n he balance o posve over negave (or vce-versa). Queson () s orward lookng n s orenaon. On he oher hand queson () s rerospecve n ha reers o he prevous monh operang perod. The responses (b) can also provde a numercal CU rao, whch can be aggregaed o provde ndusry or pecoral measures. Apar rom he normal samplng and measuremen error assocaed wh he any survey here are some oher mporan dcules, whch relae speccally o survey CU. One problem relaes o how ndvdual respondens wll choose o dene he erms capacy n boh quesons. Frms may nerpre n he narrow sense o capal ulzaon or n he broader sense whch ncludes all npus (labour and maerals). Smlarly, respondens may conuse he concep o economc capacy wh her own subjecve or preerred capacy level o operaons. Chrsan (1981) has ound ha surveyed measures end o ndcae a hgher level o excess capacy han do daa based measures. He also noes ha respondens end o nd capacy when demand s srong and lose when demand s weak Maxmum Acheved Oupu Approach Ths approach relaes o oupu acheved o a gven perod o me. The mehods ncluded n hs approach are smple n calculaon as hey are based on he acual observaons o maxmum oupu acheved a a pon o me. The mehods compare acual oupu wh esmaes o maxmum aanable oupu. The mporan o hese mehods are: 1) The Wharon Index o Capacy ulzaon or Trend hrough Peak mehod; and 2) The R.B.I Index o poenal ulzaon. Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 99

11 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry The Wharon Index o Capacy Ulzaon or Peak-o-Peak Mehod Klen and summers (1966) evolved an oupu me seres mehod Know as Wharon Index o capacy ulzaon. I s he smples procedure o generang ndces o capacy ulzaon and s also he mos common one. Under hs mehod seasonally adjused monhly values or each o he sub-dvsons o he Federal Reserve Board Index o Indusral producon are averaged no quarerly gures. The quarerly gures are hen charered and peak n each o he seres are hen chosen by nspecon. Each peak s called capacy and s dened as one where oupu (measured a consan prces) exceeds he level o he mmedaely precedng quarer and he wo succeedng quarers. A sragh lne rom peak o peak descrbes capacy durng he nervenng perod. Aer he lnear nerpolaon beween oupu peaks s made, he ulzaon rae s aken as he raos o acual oupu o pons on hs lne segmen. The pcure o he graph so obaned by jonng he successve peak n a sragh lne s wh several knks. For a perod aer a peak bu beore anoher has been reached, he las sragh lne s exrapolaed wh he same slope unl he curren producon nersecs he exrapolaed lne. Aer nersecon, capacy s aken o be he lne connecng he las peak and he mos recen oupu gure unl a new peak s reached. To arrve a a capacy measure or he manuacurng secor as a whole, he ndvdual ndusres are aggregaed wh he help o value added wegh. Despe o varous advanages o hs mehod, he procedure s sll no ree rom crcsm. Brscoe e al. (1970) Paul (1974a), Bhagwa (1961) and Phllps (1963) are among hose who have dscussed s dsadvanages. I s argued ha: ) hs measure reas oupu as a sngle uncon o me and does no relae oupu o npu; ) he assumpon ha capacy grows a a consan rae s no relable; ) hs procedure consders capacy growh o be smooh beween he wo peaks, rrespecve o he ncrease n labour and capal avalably; and v) does no akes n o accoun he supply consrans and oher rgdes o underdeveloped economes The R.B.I. Index o Poenal Ulzaon The ndex o Poenal ulzaon, whch s esmaed by Reserve Bank o Inda, s moded verson o Wharon School measure o capacy. However, some derences exs beween he wo measures. The mporan ones are: a) The RBI ndex o Poenal ulzaon makes use o monhly oupu; b) No aemps are made here n hs measure o connec successve peaks by lnear nerpolaon; and c) The RBI monhly ndces o oupu are no Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 100

12 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry deseasonlsed. Despe hese derences he RBI Index o poenal Ulzaon s very much n he nellecual radon o he Wharon school procedure. Some pons may be rased abou he RBI Index. Frs o all, s very unlkely ha monhly ndces mee he susanably creron. Secondly, capacy expanson may ake dscree jumps as mpled by he RBI measure whch s perhaps a more ahul descrpon o realy a he ndvdual rm level. Bu hs may no be so when several rms are aggregaed a he ndusry level. Capacy expanson may look lke a smooh curve as suggesed by he Wharon measure. Thrdly, here s no reason o beleve ha seasonaly s conned only o sugar, ea and sal ndusres Tme Inensy Approach The me measure devsed by Wnson (1974), measure he number o hours he capal plan s ulzed n a year as a percenage o 8760 hours (he number o hours avalable n a year) and hen adjusng he me measure o he nensy o use. Ths approach relaes 24 hours a day and 365 days a year wh ull capacy. Mos machnes can be operaed a deren speeds hough here s probably only one opmal speed, whch corresponds o he leas wear ear. Producon managers desred hs rae, when s realzed s sad o operae a 100% and here s no need o adjusu. I, on he oher hand, he acual speed o operaon s only 50% o opmal speed, hen he nensy o use only 50% andu has o be adjused downward by hal. Thereore, here s necessy o have an addonal Tme and nensy measure o capal ulzaon U. The Tme-Inensy measure U survey based approach. The manager o plan s asked o sae he number o operaon hours and he approxmae percenage o oal capal conaned n he secon. In cases, where deren secons o plans have deren producon schedules and hereore capal ulzaon raes, he share o each secon n he oal replacemen value o he plan s used as wegh n calculang he Tme nensy capal ulzaon rae or he plan as whole. The same procedure s or he sample secor as whole. There are ceran advanages n usng hs approach o esmae he level o capal ulzaon and also here doesn arse he problem o measurng he varables used n he oupu-based approach o aggregang Producon Funcon and o specyng he relaonshps beween capal ulzaon and s proxy. Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 101

13 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry 4.4 Economc Measure o Capacy Ulzaon The rae o capacy ulzaon nherenly assumes ha he ndusry s no n a poson o adjus he level o capal o s equlbrum level n he shor-run. Thus n he case o shorall n demand and consequen declne n oupu, he level o capal sock canno be reduced mmedaely. Ths resuls n under-ulzaon o he exsng capacy. Smlarly when ncreased demand warrans expanson o capal sock bu shor-run rgdy does no allow, he ndusry has o manage wh overulzaon o exsng capal sock. Thus CU can be on eher sde o uny, whch s n sharp conras o radonal CU measures whch are always less han uny. Moreover, he problem o CU n hs ramework s essenally a shor-run phenomenon A Cos Funcon Based Approach Klen (1960), Morrson (1985a) and Bernd (1989) among ohers, have he nuvely appealng suggeson ha capacy oupu s nherenly a shor-run concep condonal on he level o quas-xed npu avalable o producers. Capacy oupu can hen be dened as he opmum level o oupu or gven levels o quas-xed acors. In hs conex, he producer s echnology can be represened by he Producon Funcon () below n model (4.16), Y = F ( V, X, ) (4.16) Where, V s n 1 vecor o varable npus and X a j 1 vecor o quas-xed npus. Tme, s ncluded as an argumen n he Producon Funcon o ac as a proxy or echnologcal advance. Subjec o ceran regulary condons (Dewer, 1974), coss are mnmzed wh respec o he varable npus V condonal on he level o oupu (Y) he quas-xed oupu (X), hen here exs a varable or resrced cos uncon ( C ) whch s dual o (4.16) v C v = G( Y, P, X, ) (4.17) v Where, P v s he vecor o prces o varable npus o order (1 n). Thus, he Shor-run average oal cos ( SRAC ) can be dened as he sum o average varable coss and average xed coss n equaon (4.18), Where X C P X = + (4.18) v X SRAC Y Y P s 1 j prce vecor or he quas-xed npus. Capacy oupu, dened as opmal level o oupu or gven level o he quas-xed acors, s ha level o oupu whch mnmzed SRAC. Thus, a pon where acual and capacy oupu are equal,.e. Y=Y*, equaon (4.18) s Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 102

14 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry mnmzed. Derenang (4.18) wh respec o Y and seng equal o zero yelds equaon (4.19), δ SRAC 1 δcv Cv PX X = = δy * Y * δy * Y * Y * (4.19) For many unconal orms orc, an exac analycal soluon can be obaned or Y * rom v (4.16). However, by smple nverson, s clear ha Y * wll depend on he argumen o he varable cos uncon ( Pv, X, ) and he prce vecor o he quas-xed acor as shown n model (4.20), Y* = Y *( P, X, P, ) (4.20) In hs seng, capacy oupu s hereore drecly relaed o varable npu prces, he level o xed acors, he prces o xed acors and sae o echnology. From he soluon o (4.19), he rae o capacy ulzaon can be dened as acual oupu, Y, over capacy oupu, Y *.e., CU = Y. Y * A dagrammac Analyss Ths secon presens a smple dagrammac exposon o above CU measure. We assume, ) a sngle quas-xed acor and (e.g. capal); and ) long run consan reurn o scale. Under long run consan reurn o scale, he rms long run cos uncon s homogeneous o degree one n oupu. As a resul long run average coss don depend on he level o oupu and are represened by he horzonal lne LRAC n Fgure-4.3. We can also dene wo shor run average cos curves ( SRAC 0 andsrac 1) or levels o quas-xed capal sock ( K 0 and K 1 ). For K 1> K 0, SRAC 1 wll le o he rgh o SRAC 0. Snce average xed cos ends o all wh oupu and average varable coss end o rase, boh SRAC 0 and SRAC1 wll be U-Shaped as depced n Fgure 4.3. Capacy oupu (.e., he value o Y whch solves he equaon (4.11)) or deren levels o quas xed capal sock s gven by mnmum pons on he SRAC 0 and SRAC 1. Furhermore, he long run cos uncon s jus he shor run uncon evaluaed a he opmum level o he quas-xed acors and hereore, capacy oupu wll also correspond o he pon o angency beween SRAC v and LRAC. Wh only one quas-xed acor, hs measure o CU srcly corresponds o he narrower concep o CU whch reers o he ulzaon rae o all npus X Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 103

15 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry (labour and maerals). Under hs heorecal ramework, here s no raonal or varaon n he ulzaon raes o he oher acors o producon snce hey wll always adjus nsananeously o her opmal levels. Furhermore, under hs shor run nerpreaon, measure o CU can be eher greaer han equal o or less han one. I he rm has SRAC0 and acual oupu s gven byy, hen shor run CU gven by Y Y0 * s greaer han 1. I such a rm expec oupu o reman a Y would have an ncenve o nves n producve capal n order o lower average coss. Alernavely, he rms shor run cos curve s gven by SRAC 1, hen CU gven by less han one and he rm has an ncenve o dsnves expecs ha oupu reman ay. Fgure 4.3: Dagrammac Measuremen o CU Y Y1 * s Mnmum Capal Oupu Rao Approach The mehod o mnmum capal oupu rao, as suggesed by he Naonal Conerence Board o he Uned Saes, esmae capacy on he bass o capal oupu rao. Fxed capal oupu raos are esmaed n erms o consan prces. A benchmark year s hen seleced on he bass o he observed lowes capal oupu rao. In choosng he benchmark year oher ndependen evdence s also aken no consderaon. The lowes observed capal oupu rao s consdered as capacy oupu. The esmae o capacy s obaned rom real xed capal sock delaed by mnmum capal oupu rao. The ulzaon rae s gven by acual oupu as a proporon o he esmae o capacy. Thus, ( CU ) = 100 T Y Kˆ (4.21) Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 104

16 Techncal Ecency, Capacy Ulzaon and Toal Facor Producvy Growh n Indan Sugar Indusry ˆ K K = Mn K Y Where, ( CU ) s capacy ulzaon by h sae a me, 'Y s gross oupu, ˆK s he T esmae o capacy, K represens real gross xed capal, and K Y represens capal oupu rao. Alhough, hs mehod provdes useul measure o capacy ulzaon, he problems o measuremen o capal are ormdable. Capal s even more dcul o measure han capacy. Needless o say, he useulness o hs mehod depends crcally on accuracy o he measuremen o capal. 4.5 Choce o he Technque or CU Measuremen I s evden rom he prevous chapers ha DEA based non-paramerc mehods are o be appled or ecency and producvy measuremens. Thus, he Producon Froner based daa envelopmen analyss mehod has also been preerred o develop a CU ndex or analyzng he ner-emporal and ner-sae varaons n CU o Indan sugar ndusry. The same ndex (..e, CU DEA ) has also been ulzed o adjus he varable o gross xed capal (.e., a proxy o capal n place) as per he ulzaon o he plan capacy o oban capal n use. The choce o he non-paramerc DEA based measures o CU over he oher producon and cos uncon esmaon based paramerc echnques has been governed by s ably o handle small samples. Furher, does no requre any pre-supposon regardng he echncal naure o producon or cos uncons (.e., Cobb-Douglas, CES or Translog, ec.). However, o check he robusness o he CU resuls, an addonal approach.e., mnmum capal oupu rao mehod has also been ulzed o oban CU measures or Indan sugar ndusry. ********** Measuremen o Capacy Ulzaon: A Theorecal Apprasal Page 105