MEASURING THE EFFECT OF PRODUCTION FACTORS ON YIELD OF GREENHOUSE TOMATO PRODUCTION USING MULTIVARIATE MODEL

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1 MEASURING THE EFFECT OF PRODUCTION FACTORS ON YIELD OF GREENHOUSE TOMATO PRODUCTION USING MULTIVARIATE MODEL Mrn Nkoll, MSc Ilr Kpj, PhD An Kpj (Mne), Prof. As. Jon Mullr Agrculture Unversty of Trn Alfons Hrzj Ntonl Agences of Exms Abstrct: The m of ths study s effcent use of producton resources mong frmers n grculturl ntensve re n Lushnj regon. Through pplcton of mthemtcl models study ms to nvestgte trends of producton processes nd defne the mn pths tht chrcterzed these processes. To nvestgte the relton between tomto yeld of producton (dependent vrble) nd severl producton fctors t s used the multvrte model. Collecton of dt s done by utlzng fce to fce questonnre nd the study re nvolved 16 communes n Lushnj regon where the trget group were frmers engged n greenhouse tomto producton (dt re referrng to the yer 2011). After the dscusson wth experts the most mportnt fctors ffectng the yeld of tomto producton were dentfed lke, orgnc mnure, fertlzer, lqud fertlzer, pestcdes nd rrgton. The nlyss revels tht the overll effect of these fctors on yeld of greenhouse tomto producton ws 56%, whle the mpct of the other producton fctors ws mnor. The correlton mtrx between yeld of tomto producton nd ech ndependent fctor reveled the followng fgures: fertlzer (0.369), orgnc mnure (0.149), lqud fertlzer (0.096) nd rrgton (0.189). Agn, by usng sttstcl multvrte model the mxmum nd potentl yeld ws clculted consderng the effcent use of producton resources. The dfference between theoretcl mxmum yeld nd current yeld of producton results n mxmum potentl for 93

2 mprovement n terms of resource use effcency. The multvrte model ws used lso for other purpose, the potentl for cost reducton wthout get rd of ctul yeld. Bsed on these results the polcy mkers (extenson servce) nd frmers cn develop the most pproprte model n terms of resource use effcency. Keywords: Tomto, Yeld, Multvrte model, Lushnj regon, Prmeters 1. Introducton: Sustnble grculture requres not only ncrese producton for ech entty, but lso ncreses ther economc effcency. One of the bsc ndctors for grculturl productvty growth s the recognton nd effectve use of nternl reserves grculturl frms. Usng mthemtcl models n fnncl nd economc nlyss of the mpct of producton fctors on grculturl productvty growth s prorty n contemporry developments n the grculturl sector. Recognton nd the use of mthemtcl models s mportnt becuse: Assst n developng economc development progrm nd defne lmts for output growth gven mount of producton fctors. Provde optml levels of use of producton fctors, n order to get mxmum vlue resultndex (yeld) or mnmum vlue (cost). Determne the degree of substtuton of producton fctors wth ech other. Provde producton levels t certn moments of tme. Provde nformton of generl nture, necessry to determne the degree of use of producton fctors. Serve s bss for prognoss of development of ndvdul brnches of the economy nd grculturl producton. Type of model to be used subject to the dt collected, nd therefore mde detled study of the dt collected to conclude on the pproprte lnk. The mn purpose of ths pper s the use of mthemtcl models n order to ncrese the effcency of grculturl producton. As the object of study s the greenhouse tomto producton n 16 communes of dstrct Lushnj (Albn). 94

3 2. The study methodology: In order to cheve the objectves of the study followed the followng procedure: 1. Identfcton of key fctors nfluencng the yeld of tomto. Such fctors were consdered: mnure, fertlzer, lqud crystllne fertlzers, pestcdes (kv/dyn) nd rrgton (m 3 /dyn) 2. Defne Tretment mthemtcl model tht wll pply. Locl seres technques were used. 3. Anlyss of the model prmeters n order to ensure mxmum effectveness of selected producton fctors n the model. 4. Determnton of optml level of productvty of tomto n ech muncplty. 5. Clculton of unused nternl resources of ech muncplty, obtned s result of ncresng effcency nd reducng the cost of producton. 6. Clculton of fctor substtuton rtes (n quntty nd vlue). 7. The selecton of the most rtonl possble vrnts. 8. Processng nd clcultons were mde wth the computer progrm Mcrosoft Excel. The nformton gthered from the surveys ws remeded nd underwent regressve nd correltve sttstcl nlyss. Correltve lnks between the yeld of crop nd the fctors tht nfluence ts growth, show the mportnce of knowledge, reserch nd determne the most pproprte lterntves to effectvely use ther quntttve use n chevng the ultmte gol. Mkng nlyss showed tht the mpct of these fctors s bout 56%.The mpct of other fctors of producton s very smll. Correltve nlyss on the mpct of ech fctor n the producton of tomto, rnked n order of mportnce: fertlzer (0369), mnure (0.149), wter (0189), mnure lqud crystllne (0.096). Below s the full tble of ths nlyss. To nlyze the performnce wth other mnufcturers tke on the study, nlyzed nd ppled mthemtcl model Multvrte: 1 0x y x x x x where x j for j = 1,2,3,4,5 re producton fctors. Whle re the prmeters of the model ( = 1, 2, 3, 4, 5). These prmeters reflect the effectveness of the use of the relevnt fctors. Mxmum vlues of the prmeters were clculted ccordng to the formul: 95

4 yk log 0 p mx k log xk, r yx p, 5 1 r yx y, j= x j From clcultons mde bsed on the bove mthemtcl formuls (clcultons re done wth the computer progrm Excel) s well s the ctul vlues of the fctors of producton, re tkng the followng vlues: p 1 = p 2 = p 3 = p 4 = p 5 = = p Hs bult n uxlry tble to clculte the model prmeters where re set rtes. In ech column re selected ther mxmum vlues nd re bsed on mthemtcl formuls for clcultng of prmeters. From these clcultons ws obtned the followng vlues: 1 = , 2 = , 3 = , 4 = , 5 = Wth these prmeters Multvrte model hs the followng ppernce: Y= x x x x x Drwng on ctul levels of producton fctors used by ech muncplty, t ws estmted the mxmum yeld tht cn be cheved on the bss of more rtonl use of fctors. Dfferences between mxmum yeld nd ctul yeld gve mxmum untpped reserves. On the bss of the results obtned, were clculted for ech muncplty n the dstrct of Lushnj mxmum untpped reserves. But, they represent level extremely nd vrtully full use of them cnnot be cheved. In ddton to clcultng the mxmum reserves were estmted reserves of ech muncplty bsed on muncpltes wth the best results. Muncpltes wth better results were clled muncpltes wth hgher thn verge yeld. Use of these resources s vlble to greter extent becuse ther clculton s bsed not on the hghest score of muncplty, but n few muncpltes. In ths cse the clculton of prmeters 96

5 performed wth the formul: k p mes yk log 0 where mes log xk yk log 0 lrger thn the overll verge. These reports fulfll the condton: log x y log log x k 0 k y log log x k 0 k The results obtned for ech fctor of the model re: = = = = = Wth these prmeters Multvrte model hs the followng ppernce: Y = x 1 x 2 x x x 5 p p yk log 0 s verge of rtes log xk On the bss of ths model were clculted for ech muncplty untpped domestc reserves. These reserves compred to the frst model re smller, but lso more lkely (reserves for both models re presented n Tble 2). Above models cn be used to clculte reserves on cost reducton, s dfference between the ctul cost of producton fctors of ech muncplty, wth the mnmum possble cost. Mnmum cost nd mnmum potentl ws clculted wth the formul z mn n 1 dhe y c x mx z n c x mund 1 ymund Were c re prces of fctors x,(all/kv). In Tble 2, re presented (Annex) re throwng ll the results clculted ccordng to the two models mentoned bove. The dt n the tble we fnd tht productvty growth stocks tomtoes re sgnfcnt n muncpltes: Dvjke, Tërbuf, Golem, Hyzgjokj. Reserves for reducng the cost of tomto producton re sgnfcnt n muncpltes: Dvjke, Kolonje, Tërbuf Golem, Hyzgjokj. 97

6 An mportnt spect n the clculton of nternl resources s to estblsh the correct rtos quntttve fctors tht ffect the growth yeld of crop. The sme yeld, but wth lower costs cn be cheved by relyng on the blty to hve dfferent fctors to replce to some extent, ech other. So fertlzer cn be replced wth orgnc fertlzer or vce vers, but snce ther prces re dfferent between them cn be plced such reports wthout reducng productvty, reduced producton costs,.e. the lower the cost per unt. For ths t s necessry to clculte replcement rtes mutul producton fctors. If x fctor reduced or ncresed on verge wth unt, then t cn be replced wth n ncrese or decrese of Dx j unt of x j fctor. Ths mount s clled the rte replcement of x fctor t wth x j fctor. D xj x j x j 1 x D xj x j x j 1 x 1 x verge level of the -fctor, x verge level of the j-fctor, j, j - the coeffcents of the relevnt fctors So, f you reduce the mount of mnure (x 1 ) wth unt, ths reducton cn be compensted by the ddton of chemcl fertlzer (x 2 ) D x21 = kv/dyn unt to obtn the sme yeld But, 1 kv mnure costs 1700 ALL, nd kv/dyn fertlzer cost 37 lek, so ths replcement s of nterest from the economc pont of vew. Mxmum rtes of substtuton of fctors dscussed bove, expressed n nturl mesurement unt nd vlue, re gven n Tble 1 (see Annex). 3. Concluson: The bove nlyss showed tht the reserves to ncrese tomto yelds were consderble. Averge yeld cn grow wth 17 kv/dyn or 30%, whle n the ndvdul muncpltes, s the Golem bout 38%, Tërbuf bout 33% nd n Dvjkë bout 32%. Even n terms of the cost of tomto producton, to reduce ts reserves were substntl, bout 21%, whle n seprte muncplty reserves for reducng the cost of tomtoes hve been even greter s: Dvjkë 31%, 24% Kolonje, Tërbuf 33%. 98

7 Replcement rtes help n the desgn of rtonl lterntves to the use of producton fctors. Bsed crter derved from these rtes nd tht serves to develop these vrnts s: frst used wholly benefcl fctors, nd other fctors to be used s complement, but wth the requrement to mntn the mnmum rtos between fctors. Bsed on the dt n tble 2 nd 3 cn be constructed vrnts pproprte, economclly vble, the use of producton fctors n order to cheve the mxmum possble performnce. Knowledge of domestc reserves helps grculturl frms n crop yeld scentfc plnnng nd cost per unt. The sme model cn be used effcently to mke such nlyss for other crops n the grculturl sector but lso n frmng. Through Multvrte mthemtcl model bult bove, recognzng tht grculturl economy qunttes for ech fctor n the plnnng perod, cn be clculted mxmum yeld, nd he most lkely. Obtned results re good bss for the fnl desgn performnce pln nd tomto crop cost for ech muncplty n the dstrct of Lushnj. References: Rgsdle, C. T. Spredsheet Modelng nd Decson Anlyss, 5th Edton Revsed South- Western, Thomson, (2008) Spredsheet Modelng nd Decson Anlyss, 5 th Edton. AGEC5403 syllbus (1993) Rgsdle, C. T Spredsheet Modelng nd Decson Anlyss. Anderson, J. R, J. L. Dllon nd B. Hrdker. Agrculturl Decson Anlyss. Iow Stte Press, (1977) Luptck,M (2004). Mthemtcl Optmzcon nd Economc Anlyss Vn Loon nd Luptck. M (1991) Optmzton, dynmcs nd economc nlyss Alln, R. G. D (1968). Mthemtcl Anlyss for Economsts Slberberg,E (1990). The Structure of Economc: A Mthemtcl Anlyss Dvd L. Debertn (1986). Agrculturl Producton Economcs Myslym Osmn, (2005). Metodt e Ekonometrsë Johnston, J. (1984). Econometrc Method Pnzr, J. C. R. Wllng (1991). Economes of Scle n Mult-Output Producton 99

8 ANNEX Tble 1. Dt on tomto yeld nd use of fctors n Lushnj dstrct Muncpltes Actul Yeld (kv/dyn) Mnure (kv/dyn) Fertlzer lqud crystllne fertlzers Pestcdes (kv/dyn) K Y X 1 X 2 X 3 X 4 X 5 Bshk Lushnjë Bshk Dvjkë Krbunr Fershegn Allkj Krutje Bubullmë Kolonjë Grdsht Rems Tërbuf Dushk Golem Grbn Hyzgjokj Bllgt Averges Totl Irrgton 100

9 Europen Scentfc Journl October edton vol. 8, No.27 ISSN: (Prnt) e - ISSN Tble 2. Fctors substtuton rtes (quntty nd vlue) X 1 X 2 X 3 X 4 X 5 N V N V N V N V N V N _ X 1 X 2 X 3 X 4 V _ N _ V _ N _ V _ N V X 5 N _ 101

10 Tble 3. Dt on potentl yeld nd producton costs tomtoes n greenhouses, n the Dstrct of Lushnj. Actul Yeld yeld mx possble yeld most lkely Reserves n kv / dyn Mx Actul cost Mn cost Most lkely cost Most lkely Muncpltes kv/dyn (Y mx ) (Y mm ) (R mx ) (R mm ) (Z) (Z mn ) (Z mm ) M =2-1 5= Bshk Lushnjë Bshk Dvjkë Krbunre Fershegn Allkj Krutje Bubullmë Kolonjë Grdsht Rems Terbuf Dushk Golem Grbn Hyzgjokj Bllgt Averges Totl

11 Europen Scentfc Journl October edton vol. 8, No.27 ISSN: (Prnt) e - ISSN