ECONOMIES OF SCOPE AND SCALE EFFICIENCY GAINS DUE TO DIVERSIFICATION

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1 ECONOMIE OF COPE AN CALE EFFICIENCY GAIN UE TO IVERIFICATION Glenn Helmers eparmen of Agrculural Economcs Unversy of Nebrasa Lncoln, Nebrasa Phone: (402) Fax: (402) Emal: aleem ha eparmen of Agrculural Economcs Msssspp ae Unversy Msssspp ae, Msssspp Phone: (662) Fax: (662) E-mal: eleced Paper prepared for presenaon a he Wesern Agrculural Economcs Assocaon Annual Meeng, enver, Colorado, July 13-16, 2003 Copyrgh 2003 by Helmers and ha. All rghs reserved. Readers may mae verbam copes for noncommercal purposes by any means, provded ha hs copyrgh noce appears on all such copes.

2 Absrac Usng a nonparamerc lnear programmng approach, our conrbuon s o examne f effcency gans n Wesern crop producon are realzed due o dversfcaon and o demonsrae ha he dversfcaon effcency gans realzed are a produc of economes of scope effcency gans and scale effcency gans. The analyss employed croppng secor daa for sx major crops for he perod, Resuls ndcae effcency gans are realzed due o dversfcaon for all he wo-crop combnaons.

3 ECONOMIE OF COPE AN CALE EFFICIENCY GAIN UE TO IVERIFICATION versfcaon of producon uns have been advocaed by susanable agrculural due o s advanages over and above specalzed farmng, bu he echnologcal advances leadng o srucural changes 1 n agrculure nclned more owards specalzaon. pecally he echnologcal advances n farmng secor nclned more owards on-farm specalzaon and he rend n reduced crop dversfcaon has connued bu a much reduced rae. Furher he proporons of farms whou lvesoc has sgnfcanly ncreased. The reasons for hese changes are no clear n ha he economc sudes have shown lle advanage of large specalzed uns over moderae szed uns. Currenly begnnng farmers end o concenrae on crop producon alone and encouner dffcules n assemblng fnancal conrol over adequae szed uns. In general here may well be a lac of undersandng of he exsng advanages of negraed operaons and agrculure secor n parcular.e., dversfcaon and wha enerprses can be negraed for purposes of hgher economc reurn and reduced rs. mlarly n he non-farm secor, he concep of dversfcaon has been fadng more so n he recen mes due o specalzaon of echnologcal advances and manufacurng process. The ncreased effcency n producng specalzed goods has lead o a decreasng rend of dversfcaon n non-farm and farmng secors. 1 ee Hallam (1993), Gardner and Pope (1978), slev and Peerson (1982 and 1996), Huffman and Evenson (1997) for research on srucural changes wh respec o farm sze, farm specalzaon, off-farm wages, npu prce changes, echncal, effcency and producvy.

4 2 Examnaon of he srucural changes due o echnologcal deermnans a he frm or ndusry producng a sngle oupu (more han one oupu) can be denfed wh economes of scale (scope). Consderable leraure [Panzar and Wllg (1981); Eaon and Lemche (1991); and Lawrence and Braunsen (1992)] has been dreced owards examnng economes of scope due o producon of mulple oupus or producs. Economes of scope exs f Cy ( 1, y2) < Cy ( 1, 0) + C( 0, y2) where Cy ( 1, y2 ) s he frm s cos of producng mulple oupus,.e., oupu 1 and 2 gven npu prces. Chrsensen and Greene (1976), and Panzar and Wllg (1977) have addressed he economes of scale due o oupu expanson. The overall scale economes (or ray economes of scale) exs f Cy ( 1, y2)/ yc ( y1, y2) s greaer han one, where C ( y, y ) 1 2 s he margnal cos of producng h oupu. ome ohers [Lawrence (1989), and Cohn e al (1989)] have examned he economes of scale and scope n he dual framewor. An alernave o he economerc esmaon of economes of scope and scale s he use of non-paramerc lnear programmng approach. In recen mes, he programmng approach 2 of measurng effcency n publc and prvae secors has receved renewed aenon. aa Envelopmen Analyss (EA) has ceran advanages, 2 The non-paramerc programmng approach o he sudy of effcency has had a relavely shor hsory n agrculure secor, now famlarly now as aa Envelopmen Analyss (EA). M.J. Farrell (1957) dscussed he emprcal esmaon of effcency for mulple oupus and mulple npus. The applcaon made was o U.. agrculure. Farrell and Feldhouse (1962) publshed anoher analyss usng farm survey daa. In 1966 a he Wesern Farm Managemen Assocaon four papers were presened (Bressler, Boles, ez, and orus) relaed o ssues of dfferen componens of effcency and her measuremen. In 1978 EA was nroduced by Charnes e al and popularzed n a more nformave and easly appled way by Fare e al (1994). Lovell (1993) presened a selecve overvew of he exsng echnques and models o esmae producve effcency.

5 3 n ha does no mpose a pror funconal form, can handle mul-oupus and mulnpus, and compue effcency whou he need of oupu and npu prces. A vas majory of EA models use only quany (quany and prce) daa and calculae drec prmal (ndrec dual) measures. Fare (1986), and Fare and Prmon (1988) have proposed he esmaon of dversfcaon effcency gans denfed wh economes of scope nvong he dualy equvalency beween he subaddvy C( Y, w) C( Y, w) = 1 = 1 of he cos funcon for npu prces ( w) and he superaddvy L( Y ) L( Y ) of he npu requremen se. = 1 = 1 Objecve Exendng he wor of Fare and Prmon, ulzng he dualy equvalency beween he cos funcon and he npu requremen se, and he decomposon of he echncal effcency no pure echncal effcency and scale effcency, we (1) examne f effcency gans are realzed due o dversfcaon and (2) demonsrae he dversfcaon effcency gans realzed s due o economes of scope effcency gans and economes of scale effcency gans employng croppng daa of sx major crops for he perod, The analyss used naonal daa. Thus, he resuls hold for he Wes and he remander of he U.. The resuls for he sx crops repored n hs analyss are wdely grown n he Wes. The dversfcaon analyss employed here s applcable where here s wdespread dversfcaon n croppng acves on ndvdual producng uns. In wesern U.. agrculure here are more crops grown han he sx of hs analyss.

6 4 However, some excluded crops are grown under specalzed producon, parcularly under rrgaon. Hence, crops such as peanus, rce, and coon alhough produced n seleced areas of he Wes, are excluded from consderaon. Also, should be recognzed ha all sx analyss crops are rarely produced n sgnfcan proporons n all areas of he Wes. However, here s suffcen dversfcaon of all or par of he sx crops on farms n he Wes o allow he esmaon of scope and scale economes under dversfcaon. Nonparamerc Programmng Model for cope and cale Gans Le an ndusry wh specalzed frms engage n producon of unque producs over me wh vecor of npus x. Inpu requremen se ransformng I - dmensonal vecor of npus x, R + no a vecor of oupu y R + s represened by npu se for frm : () 1 LY ( ) = { x: zy y, zx x, z 0} = 1 = 1,...,T = 1,...I I where z s a nonnegave and z 0 ndcaes consan reurn o scale assumpon, I and T s he npu vecor and he lengh of he me seres respecvely., The npu se for sum of ndvdual specalzed frms can be represened as: ( 2) LY ( ) { x: zy y =, zx x, z 0} = 1 = 1 = 1 = 1, = 1,...,T = 1,...I = 1,... I

7 5 where I, Tand s he dencal npu vecor n each of he frms, lengh of he me seres, number of specalzed frms engaged n producon of unque producs respecvely, and z 0 ndcaes consan reurn o scale assumpon. Insead of have dencal npu vecor for each of he frms, he dversfed frm produces unque producs wh se of I non-allocable npu vecor. The producon echnology of combned frms (dversfed frm) ulzng he same varables n equaon (2) wh he excepon of npu vecor s represened by an npu se as: () 3 L( Y ) = { x : zy y, zx x, z 0} = 1 = 1 = 1 I = 1,...,T = 1,...I = 1,... where he defnons are smlar o he hose defned for equaon (2) above. The dversfcaon effcency gans s compued by comparng he froners of, ndvdual specalzed frms = 1 LY ( ) and dversfed frm (combned frms) L( Y ) = 1 under consan reurns o scale assumpon as: ( 4) versfcaon Effcency gans = LY ( ) L( Y ) = 1 = 1 where he rao grea (equal o) han one ndcaes effcency (no effcency) gans due o dversfcaon. The concep of npu se can be represened by he npu dsance funcon for frm as:

8 6 1 () 5 ( y, x ) = mn λ { λ:( y, λx ) L( Y)}, λ, z or, mn λ s.. y zy λ, z I = 1 λ x z X = 1,..., I, z 0 or ( z = 1), sum of ndvdual specalzed frms as: 1 ( 6) ( y, x ) = mn λ { λ: ( y, λx ) L( Y )}, λ, z or, mn λ s.. y zy = 1,..., λ, z = 1 = 1 = 1 λ x z X = 1,..., I z 0 or ( z = 1) and dversfed frm as: I, = 1 1 ( 7) ( y, x ) = mn λ { λ: ( y, λ x ) L( Y )} where, λ, z or, mn λ s.. y zy = 1,..., λ, z = 1 I = 1 λ x z X = 1,..., I, = 1 z 0 or ( z = 1) ( ) and ( ) s he npu dsance funcon for specalzed frms and dversfed frm respecvely. The nensy varable z 0 descrbes he consan reurns o scale (CR) echnology and z 0 descrbes he varable reurn o scale (VR) echnology. The scale effcency can be compued for specalzed frms and dversfed

9 7 frm as he rao of npu dsance funcons under he assumpon of consan reurns o scale and varable reurns o scale echnology as: () 8 ( y, x) = ( y, x) = ( y, x ) CR ( y, x ) VR ( y, x ) CR ( y, x ) VR where ( ) and ( ) s he scale effcency for specalzed frms and dversfed frm respecvely. Ulzng he decomposon of echncal effcency no pure echncal effcency and scale effcency by Farrell, he dversfcaon effcency gans can be defned as a produc of economes of scope effcency gans (due o pure echncal effcency) and economes of scale effcency gans (due o scale effcency). The dversfcaon effcency gans defned as a produc of scope and scale can be represened by npu dsance funcons as: ( ) 9 1 LY ( ) ( y, x ) ( y, x ) = CR VR = ( y, x CR ) ( y, x VR ) L( Y ) = 1 ( y, x) ( y, x) versfcaon Effcency gans = cope gans cale gans where s he npu dsance funcon, CR s he consan reurns o scale, VR s varable reurns o scale, s he scale effcency, and superscrp s sum of specalzed frms, s dversfed frm. The frs par on he rgh hand sde represens effcency gans due o scope (as n Fare 1986, 1988) wh he second par ascrbed o

10 8 effcency gans due o scale. Hence, he dversfcaon effcency gans can be arbued o scope and scale effcency gans. The measure of he dversfcaon effcency gans, he scope effcency gans and scale effcency gans s graphcally represened n Fgure (1). In Fgure 1, he frm s CR and VR echnology for specalzed and dversfed echnology s represened as CR and VR and CR and VR respecvely. Based on Fgure 1, he npu based scope effcency gans (frs par of equaon 9) due o dversfcaon can be represened: ( y, x VR ) OX OX OX ( 10) cope Effcency gans = = = ( y, x ) OX OX OX VR The npu based scale effcency gans (second par of equaon 9) due o dversfcaon can be represened as: F OX OX ( y, x) OX OX OX ( 11) cale Effcency gans = = = F ( y, x) OX OX OX OX OX OX OX F F and he npu based dversfcaon effcency gans can be represened as: ( 12) F ( y, x ) CR OX OX OX OX = * F ( y, x ) OX OX OX OX CR F F Cos of Producon aa on U Major Crops To compue economes of scope, effcency gans, scale effcency gans and dversfcaon effcency gans due o crop dversfcaon, cos of producon daa and oupu producon for he sx major crops are employed. The npu daa for each of he crop s avalable on a per acre bass from he cos of producon daa publshed by

11 9 Economc Resource ervce (ER) of Uned aes eparmen of Agrculure (UA). The yeld per acre and harvesed acres for each crop s avalable from Naonal Agrculural ascal ervce (NA). In our curren analyss, he oupu producon (equal o he yeld per acre mes he harvesed acres) n mllon bushels or pound dependng upon he crop used as oupu. The per acre cos of producon daa aggregaed o varable cos, capal cos and he land n acres are used as npus. The varable cos s he sum of he varable cash expenses, general farm overhead, axes and nsurance and unpad labor n dollars per acre. The capal cos ncludes capal replacemen, operang capal and oher nonland capal n dollars per acre. The varable and capal coss are mulpled by he harvesed acres o compue he oal varable cos and he oal capal cos. These wo npus are furher convered no real erms usng he gross domesc produc mplc prce deflaor. A sngle oupu and hree npus are used o compue economes of scope and scale effcency gans due o dversfcaon. Resuls To examne economes of scope effcency gans (equaon 10), scale effcency gans (equaon 11) and dversfcaon effcency gans (equaon 12) due o crop dversfcaon, he npu dsance funcon defned n equaons (6 and 7) s esmaed. Oupu and npu daa of he sx crops for he perod are used o examne he effcency gans due o dversfcaon. Table 1 presens he average of he oupu and npu varables employed n he analyss, he average effcency scores over me, and rae of change n effcency scores over he same me perod for each of he sx major crops

12 10 esmaed ulzng he npu dsance funcon defned n equaon (5). The ndvdual echncal effcency, pure echncal effcency and scale effcency scores of each crop provde he bass for decomposon of he dversfcaon effcency gans no scope effcency gans and scale effcency gans due o crop dversfcaon. Table 2 presens he average dversfcaon, scope and scale effcency gans due o wo-crop dversfcaon alhough s very dffcul o acually observe all he wo-way crop combnaons n pracce. Also he resuls of he null hypohess ha dversfcaon effcency gans, scope effcency gans and scale effcency gans for each of he wocrop combnaon s equal o one are examne employng a -es a 5% level of sgnfcance. However emphass s gven only o hose crop combnaons ha exhb dversfcaon. In Table 3 acreage changes n each of he sx sudy crops are presened for he me perod. These acreages can be vewed n concer wh he esmaed scope and scale relaonshps. Overall Techncal and cale Effcency Overall echncal effcency ( y, x CR) defned as a produc of pure echncal effcency ( y, xvr ) and scale effcency ( y, x) s presened n Table 1 for each crop. Overall effcency s hghes for corn wh moderae effcences observed for whea and oas. For corn hs s caused by large scale effcences whle whea and oas have moderae echncal effcency. Barley, sorghum, and soybeans have low overall effcency. For barley and sorghum hs s caused by low scale effcences (negave for sorghum). oybeans had a low echncal effcency level for he perod.

13 11 Observng changes n crop acreages over he me perod, he effcency causes may be beer undersood by he rae of change n effcences. Hgh gans n overall effcency were observed for corn, soybeans, and gran sorghum and lower gans for barley, oas, and whea. These dfferences follow mehods of producon, row crops vs. small gran producon respecvely. Wh he excepon of sorghum hese changes n effcency mrror changes n acreage. For sorghum, negave scale effcency was observed whch may explan par of he declne. The remander, however, s explaned by he wo-crop dversfcaon relaonshps n he followng secon. cale effcency gans echncal effcency gans for corn and soybeans whle he oppose occurs for barley, sorghum, and whea. For oas he wo effcency gans are roughly equal. cope and cale Effcency Gans ue o Two-Crop versfcaon The addonal nsghs of he poenal nfluence on he srucural changes due o dversfcaon can be carefully concepualzed based on he decomposon of average echncal effcency gans no scope effcency gans and scale effcency gans. The average effcency gans, a produc of effcency gans due o scope and effcency gans due o scale for all wo crop-dversfcaon are presened n Table 2. For he wo-crop analyss, scope effcences are acheved from more effcen use of labor and machnery. Where here are crop roaons pracced, ncreased effcency s also possble due o enhanced crop yelds and reduced use of npus. cale relaonshps for wo-crop relaonshps relae o effcences derved from expandng boh crops smulaneously. Research no scale relaonshps n agrculure has been concenraed on sngle producs. Ths s largely because daa s no readly avalable on resource use and

14 12 produc oupu for mulple produc frms. The mehodology used here, however, enables mulproduc scale relaonshps o be esmaed. Resuls from Table 2 ndcae boh echncal effcency gans and he scope effcency gans have been realzed for all he wo crop-dversfcaon. Only one crop combnaon (barley and sorghum) experenced declnng average scale effcency gans suggesng ha frm canno realze effcency gans by jus ncreasng facors of producon. Average overall dversfcaon gans (a crop n combnaon wh he oher fve crops) are hghes for corn and soybeans wh he lowes observed for barley, oas, and whea. orghum was n an nermedae poson. Beween crops hgh gans were observed for corn (wh sorghum and soybeans) and soybeans (wh barley, corn, and whea. A he oher exreme low overall gans were observed for whea (wh all crops excep soybeans) and oas (wh barley and corn). These relaonshps are agan conssen wh he acreage changes over he me perod where large ncreases were observed for corn and soybeans wh declnes for he remanng crops. I can be observed ha corn-soybean dversfcaon s very hgh and consderably hgher han for corn-sorghum or sorghum-soybeans. Thus, sorghum s dversfcaon poenal wh oher row crops s no as hgh as he oher wo row crops. In general, crop combnaons havng hgh scope dversfcaon effcency had hgh scale dversfcaon effcency. However, some excepons nvolvng sorghum occurred (barley-sorghum, corn-sorghum, and sorghum-soybeans).

15 13 The resuls of he es examnng he null hypohess ha he realzed dversfcaon effcency gans, scope effcency gans and scale effcency gans for each of he wo-crop combnaon s equal o one are presened n Table 2. Based on he es sasc and p value for he es a he 5% level of sgnfcance, hs es ndcaes he mean dversfcaon effcency gans and scope effcency gans are sgnfcanly dfferen from one. However, wh he excepons (oas n combnaon wh barley, corn, and sorghum; barley n combnaon wh sorghum; whea n combnaon wh barley and corn) he mean scale effcency gans are also sgnfcanly dfferen from one. Overall, resuls of he average effcency gan measures and he es ndcae all he wo crop-combnaons experenced dversfcaon effcency gans, a produc of he effcency gans due o economes of scope and scale. Ths demonsraes he mporance of economes of scope and scale gans due o dversfcaon of crops o be able o realze hgher economc reurns and reduced rs. Conclusons Ulzng he non-paramerc lnear programmng approach, heorecally and emprcally we demonsrae -he dversfcaon effcency gans realzed s due o economes of scope effcency gans and he economes of scale effcency gans. The ndvdual crop esmaes of he effcency measures over me ndcae he average echncal effcency across all crops s conrbued by pure echncal and scale effcency. Ths suppors he mporance of pure echncal effcency (scope effcency gans) and he scale effcency (scale effcency gans) n explanng he echncal effcency (dversfcaon effcency gans). In case of wo-crop combnaons, he dversfcaon

16 14 effcency gans realzed s explaned by he effcency gans due o scope and scale effcency gans. Ths ndcaes here s poenal for hgher effcency gans of negraed operaons.e., dversfcaon and wha enerprses can be negraed for purposes of hgher economc reurn and reduced rs. Ths sudy can be useful for furher research o address he ssue of spaal effcency gans ha can be realzed by regonal analyses of dversfcaon, effcency gans due o crop-lvesoc dversfcaon and fnally effcency gans due o vercal dversfcaon. References Boles, J.N Effcency quared - Effcen Compuaon of Effcency Indexes. Prov. W. Farm Econ. Assn Bressler, R.G The Measuremen of Producve Effcency. Proc. W. Farm Econ. Assn Charnes, A., W.W. Cooper, and E. Rhodes Measurng he Effcency of ecson Mang Uns. European Journal of Operaonal Research. 2(6), Chrsensen, Laurs R. and Wllam H. Greene Economes of cale n U.. Elecrc Power Generaon. Journal of Polcal Economy. 84: Cohn, Elchanan, herre L.W. Rhne, and Mara C. anos Insuons of Hgher Educaon as Mul-Produc Frms: Economes of cale and cope. Revew of Economcs and ascs. 71: Eaon, B. Curs and.q. Lemche The Geomery of upply, emand and Compeve Mare rucure wh Economes of cope. Amercan Economc Revew. 81: Fare, Rolf Addon and Effcency. Quarerly Journal of Economcs. 101,

17 15 Fare, Rolf Effcency Gans from Addon of Technologes: A Nonparamerc Approach. In Wolfgang Echhorn and W. Erwn (eds.), Measuremen n Economcs: Theory and Applcaons of Economc Indces. Hedelberg: Physca-Verlag; New Yor: prnger-verlag. Fare, Rolf and anel Prmon Effcency Measures for Mulplan Frms wh Lmed aa. In Wolfgang Echhorn and W. Erwn (eds.), Measuremen n Economcs: Theory and Applcaons of Economc Indces. Hedelberg: Physca-Verlag; New Yor: prnger-verlag. Fare, Rolf,. Grossopf, and C.A.. Lovell Producon Froners. Cambrdge [England]; New Yor, NY, UA: Cambrdge Unversy Press. Farrell, M.J The Measuremen of Producve Effcency. Journal of he Royal ascal ocey, eres A, General 120, Farrell, M.J. and Feldhouse Esmang Effcen Producon Funcons Under Increasng Reurns o cale. Journal of he Royal ascal ocey, eres A, General 125, Par 2, Gardner, B. and R. Pope How s cale and rucure eermned n Agrculure. Amercan Journal of Agrculural Economcs. 60: Huffman, Wallace E. and R.E. Evenson Long Run rucural and Producvy Change n U.. Agrculure: Effecs of Prces and Polces. aff paper. Hallam, Arne Emprcal udes of ze, rucure, and Effcency n Agrculure, n A. Hallam, ed., ze, rucure, and he Changng Face of Amercan Agrculure. Boulder, CO: Wesvew Press, pp slev, Y. and W. Peerson Prces, Technology, and Farm ze. Journal of Polcal Economcs. 90: slev, Y. and W. Peerson Economes of cale n Agrculure: A Reexamnaon of he Evdence. In The Economcs of Agrculure: Papers n Honor of. Gale Johnson, Vol. 2, J.M. Anle and.a. umner, eds., The Unversy of Chcago Press, pp Lawrence, Colln Banng Coss, Generalzed Funconal Forms, and Esmaon of Economes of cale and cope. Journal of Money, Cred, and Banng, 21:

18 16 Lovell, C.A Producon Froners and Producve Effcency n: H. Fred, C.A.. Lovell, and P. chmd, eds., The Measuremen of Producve Effcency: Technques and Applcaons. Oxford Unversy Press Panzar, John C. and Rober. Wllg Economes of cale n Mul-Oupu Producon. Quarerly Journal of Economcs. 91: Panzar, John C. and Rober. Wllg Economes of cope. Amercan Economc Revew. 71: Penrose, E.T The Theory of he Growh of he Frm. Oxford: Basl Bacwell. Pulley, Lawrence B. and Yale M. Braunsen A Compose Cos Funcon for Mulproduc Frms wh an Applcaon o Economes of cope n Banng. Revew of Economcs and ascs. 74: ez, W Effcency Measures for eam-elecrc Generang Plans. Proc. W. Farm Econ. Assn orus, B.L Producve Effcency and Redundan Facors of Producon n Tradonal Agrculural of Underdeveloped Counres: A Noe on Measuremen. Proc. W. Farm Econ. Assn

19 17 Fgure 1. cope and cale Effcency Gans ue o versfcaon Y CR CR VR VR (X,Y) O X F X F X X X X

20 18 Table 1. Average Oupu and Inpu per acre, and Techncal, Pure Techncal and cale Effcency of Major Crops for he perod, Varables Barley Corn Oas orghum oybean Whea Producon per acre Varable ( Ml $ /acre) Capal ( Ml $ / acre) Land (Ml acres) Overall Effcency ( y, x CR) ( y, xvr ) ( y, x) Rae of Change (ROC) ( y, x CR) ( y, xvr ) ( y, x) where ( y, x CR) s he overall echncal effcency compued under he assumpon of consan reurns o scale, ( y, xvr ) s he pure echncal effcency compued under he assumpon of varable reurns o scale, ( y, x) s he scale effcency compued under as he rao ( y, x CR ) over ( y, xvr ), and ROC s he rae of change over he me perod, compued as T X X * = T =1 100

21 19 Table 2. cope Effcency Gans, cale Effcency Gans and versfcaon Effcency Gans due o Two-Crop versfcaon, cope Effcency Gans Corn Oas orghum oybean Whea Barley 1.017* 1.013* 1.031* 1.017* 1.007* Corn 1.011* 1.012* 1.018* 1.014* Oas 1.018* 1.009* 1.006* orghum 1.005* 1.010* oybean 1.024* cale Effcency Gans Corn Oas orghum oybean Whea Barley 1.020* * Corn * 1.038* Oas * 1.009* orghum 1.021* 1.009* oybean 1.018* Overall versfcaon Effcency Gans Corn Oas orghum oybean Whea Barley 1.037* 1.016* 1.024* 1.032* 1.017* Corn 1.019* 1.033* 1.056* 1.019* Oas 1.027* 1.027* 1.015* orghum 1.026* 1.020* oybean 1.043* *Indcaes an oucome beyond 5% level of sgnfcance for he -es examnng he null hypohess ha he dversfcaon effcency gans, scope effcency gans and scale effcency gans for each of he wo-crop combnaons s equal o one.

22 20 Table 3. Acreages (000) of Corn, oybeans, Whea, orghum, Barley, and Oas n he Wes (Norhern Plans, ouhern Plans, Mounan, and Wes) Norhern Plans Corn oybeans Whea orghum Barley Oas