PRACE NAUKOWE Unwersytetu Ekonomcznego we Wrocławu RESEARCH PAPERS of Wrocław Unversty of Economcs 286 Regonal Economy n Theory and Practce edted by Elżbeta Sobczak Andrze Raszkowsk Publshng House of Wrocław Unversty of Economcs Wrocław 2013
Copy-edtng: Elżbeta Macauley, Tm Macauley, Marcn Orszulak Layout: Barbara Łopusewcz Proof-readng: Barbara Łopusewcz Typesettng: Comp-rat Cover desgn: Beata Dębska Ths publcaton s avalable at www.buk.pl, www.ebscohost.com, and n The Central and Eastern European Onlne Lbrary www.ceeol.com as well as n the annotated bblography of economc ssues of BazEkon http://kangur.uek.krakow.pl/bazy_ae/bazekon/nowy/ndex.php Informaton on submttng and revewng papers s avalable on the Publshng House s webste www.wydawnctwo.ue.wroc.pl All rghts reserved. No part of ths book may be reproduced n any form or n any means wthout the pror wrtten permsson of the Publsher Copyrght by Wrocław Unversty of Economcs Wrocław 2013 ISSN 1899-3192 ISBN 978-83-7695-345-8 The orgnal verson: prnted Prntng: Prntng House TOTEM
Contents Introducton... 9 Part 1. Theoretcal aspects of regonal economy Ryszard Brol: Innovaton vs. regonal development... 13 Ewa Glńska, Anna Kononuk: The concept of regonal strategy of smart specalzaton... 27 Hanna Kruk: Reslence, compettveness and sustanable development of the regon smlartes and dfferences... 35 Andrze Sztando: Regonal nnovaton strategy mplementaton system model coverng the results of the analyss of the Polsh experences... 43 Andrze Raszkowsk: Creatvty n the context of regonal development selected ssues... 52 Yulya Melnyk: Regonal peculartes of the global art market... 62 Elżbeta Załoga, Darusz Mlewsk: The mpact of transport on regonal development... 71 Alna Kulczyk-Dynowska: Dversfed spatal neghbourhood a metropols and a natonal park... 79 Part 2. The results of European regonal space research and analyses Małgorzata Markowska, Danuta Strahl: Polsh regons aganst the background of European regonal space wth regard to smart growth aggregate perspectve... 89 Beata Bal-Domańska: Does smart growth enhance economc coheson? An analyss for the EU regons of new and old accesson countres... 100 Elżbeta Sobczak: Typology of European regons vs. effects of workforce changes by the level of research and development actvtes ntensty... 111 Małgorzata Karczewska: Gross domestc expendtures on research and development n GDP of European Unon countres changes n trends... 121 Marzena Grzesak, Anta Rchert-Kaźmerska: Educatonal engagement of the elderly the experences of selected Baltc Sea Regon countres... 133 Ewa Coll: The classfcaton of EU and Eastern Partnershp countres regardng economc development level a dynamc approach... 144 Anetta Waśnewska: The potental of the populaton n the Baltc Sea Regon n the years 2001 2011... 157 Alla Melnyk: Modernzaton of regonal structural polcy mechansms n Ukrane n the process of ts EU ntegraton... 169
6 Contents Part 3. Selected problems of polsh regons functonng and development Darusz Głuszczuk: Barrers to nnovaton actvtes n ndustral enterprses by Polsh regons n 2004 2006 and 2008 2010... 181 Potr Haduga: Specal economc zones as stmul to regonal development durng a crss... 191 Adam Przybyłowsk: Sustanable transport development prerequstes n selected Polsh regons... 199 Marusz E. Sokołowcz: The mpact of transnatonal corporatons actvty on regonal human captal. Case study of the Łódź metropoltan area... 210 Anna Jasńska-Blczak: Interregonal cooperaton as the stmulaton of pronnovaton actons the casual analyss... 222 Francszek Adamczuk: Cross-border cooperaton of Lower Slesa and Saxony current results and prospects... 230 Agneszka Barczak: Managng the producton process of a group of agrcultural farms of the Pomorze and Mazury Regon and ther economc development... 240 Tomasz Dorożyńsk, Wocech Urbanak: Experences of county employment agences n the use of EU structural funds to promote employment. The case of the Łódź vovodeshp... 249 Małgorzata Golńska-Peszyńska: Contemporary nnovatve practces n a regonal context of the Łódź regon... 260 Streszczena Część 1. Teoretyczne aspekty gospodark regonalne Ryszard Brol: Innowacyność a rozwó regonalny... 26 Ewa Glńska, Anna Kononuk: Koncepca regonalne strateg ntelgentne specalzac... 34 Hanna Kruk: Rezylenca, konkurencyność rozwó zrównoważony regonów podobeństwa różnce... 42 Andrze Sztando: Wdrażane regonalne strateg nnowac model systemu stanowący rezultat analzy polskch dośwadczeń... 51 Andrze Raszkowsk: Kreatywność w kontekśce rozwou regonalnego wybrane zagadnena... 61 Yulya Melnyk: Regonalna specyfka globalnego rynku sztuk... 70 Elżbeta Załoga, Darusz Mlewsk: Wpływ transport na rozwó regonalny... 78 Alna Kulczyk-Dynowska: Zróżncowane sąsedztwo w przestrzen metropole park narodowy... 86
Contents 7 Część 2. Rezultaty badań analz nad europeską przestrzeną regonalną Małgorzata Markowska, Danuta Strahl: Polske regony na tle europeske przestrzen regonalne w kontekśce ntelgentnego rozwou uęce agregatowe... 99 Beata Bal-Domańska: Czy ntelgentny rozwó sprzya spónośc ekonomczne? Analza dla regonów państw Un Europeske nowego starego rozszerzena... 110 Elżbeta Sobczak: Typologa regonów europeskch a efekty zman lczby pracuących według pozomu ntensywnośc prac badawczo-rozwoowych 120 Małgorzata Karczewska: Udzał nakładów na badana rozwó w PKB kraów Un Europeske tendence zman... 132 Marzena Grzesak, Anta Rchert-Kaźmerska: Zaangażowane osób starszych w edukacę dośwadczena wybranych państw regonu Morza Bałtyckego... 143 Ewa Coll: Klasyfkaca państw UE kraów Partnerstwa Wschodnego ze względu na pozom rozwou gospodarczego uęce dynamczne... 156 Anetta Waśnewska: Potencał ludnośc regonu Morza Bałtyckego w latach 2001-2011... 168 Alla Melnyk: Modernzaca mechanzmów regonalne poltyk strukturalne Ukrany w procese ntegrac z Uną Europeską... 177 Część 3. Wybrane problem funkconowana rozwou polskch regonów Darusz Głuszczuk: Przeszkody dzałalnośc nnowacyne przedsęborstw przemysłowych według regonów Polsk w latach 2004 2006 2008 2010. 189 Potr Haduga: Specalne Strefy Ekonomczne ako stymulator rozwou regonalnego w dobe kryzysu... 198 Adam Przybyłowsk: Przesłank zrównoważonego rozwou transportu w wybranych polskch regonach... 209 Marusz E. Sokołowcz: Wpływ korporac transnarodowych na rozwó kaptału ludzkego w regone. Przykład łódzkego obszaru metropoltalnego... 221 Anna Jasńska-Blczak: Współpraca mędzyregonalna stymulantem dzałań pronnowacynych przykład woewództwa opolskego... 229 Francszek Adamczuk: Współpraca transgranczna Dolnego Śląska Sakson aktualne wynk perspektywy... 239 Agneszka Barczak: Zarządzane procesem produkc grupy gospodarstw rolnych regonu Pomorze Mazury z uwzględnenem pozomu rozwou gospodarczego... 248
8 Contents Tomasz Dorożyńsk, Wocech Urbanak: Dośwadczena powatowych urzędów pracy w zakrese wykorzystywana funduszy strukturalnych UE w celu promoc zatrudnena. Przykład woewództwa łódzkego... 259 Małgorzata Golńska-Peszyńska: Współczesne praktyk nnowacyne w kontekśce regonalnym w oparcu o regon łódzk... 267
PRACE NAUKOWE UNIWERSYTETU EKONOMICZNEGO WE WROCŁAWIU RESEARCH PAPERS OF WROCŁAW UNIVERSITY OF ECONOMICS nr 286 2013 Regonal Economy n Theory and Practce ISSN 1899-3192 Agneszka Barczak West Pomeranan Unversty of Technology n Szczecn MANAGING THE PRODUCTION PROCESS OF A GROUP OF AGRICULTURAL FARMS IN THE POMORZE AND MAZURY REGION AND THEIR ECONOMIC DEVELOPMENT Summary: The am of ths artcle s an applcaton of the method whch enables the maxmzaton of the volume of output on agrcultural farms. The research was based on the Pomorze and Mazury regon, whch was selected after the analyss of the level of gross output, fnal output and commodty producton. For the sake of the study, a group of farms specalzng n feld crops was selected, usng data for 20042009, made avalable by the Polsh FADN. The method used for the producton optmzaton s the method of the Lagrange multplers. Keywords: agrcultural farms, economc development, regon. 1. Introducton Economc development s the term whch denotes an ncrease n varous aspects of the standard of human lvng. Some of them are mmeasurable. Ths means that t covers both quanttatve and qualtatve changes, brngng on the regon from a lower to a hgher level of development, whch can be related to the concept of economc growth [see Bartkowak 2003]. It should be noted that optmal producton creates opportuntes for a faster economc growth, and consequently, for regonal development. Due to the ncreasng economc dspartes between dfferent regons of Poland, t s partcularly mportant to fnd the means that lead to optmal economc growth. Algnng these dspartes s the man obectve of the actvtes of the regonal polcy [see Chursk 2005, p. 13]. It should also be noted that the Polsh accesson to the European Unon, as well as trade lberalzaton, forced the growth and development of agrcultural farms. Ths s conducve to enlargng ther productvty and effcency, whch are the
240 Agneszka Barczak condtons of mantanng and mprovng ther compettve poston. The concept of growth should be understood as the change of the scale of producton and the ncurred producton factors expendture of the farms, whereas development s a change of the structure of ths expendture [Czeka, Józwak 2009, p. 29]. The dfferences between the regons can be observed on many levels, and ths artcle concerns a branch of the economy, namely agrculture. Therefore, the obectve of ths study s the applcaton of the method whch enables the maxmzaton of the volume of output on farms. The research s based on the Pomorze and Mazury regon, selected accordng to the analyss of the level of gross output, fnal output and commodty producton. For consecutve study, a group of farms specalzng n feld crops was used, usng data for 20042008, made avalable by the Polsh FADN. The method used for the optmzaton of producton s the method of Lagrange multplers. Broader studes are ncluded n the doctoral dssertaton [Barczak 2011]. 2. Analyss of the Pomorze and Mazury regon For the analyss of the macro-regon, some chosen economc varables based on data from the Central Statstcal Offce for the perod 20042008 were used. These nclude gross output, fnal output and commodty producton. Gross agrcultural output ncludes [Rocznk statystyczny rolnctwa... 2009, p. 49]: crop producton.e. unprocessed products of plant orgn, harvested n a gven year, lvestock producton.e. the producton of anmals for slaughter and unprocessed products of anmal orgn, ncrease n lvestock (lvestock prmary lvestock and current lvestock); the term lvestock covers: cattle, pgs, sheep, horses and poultry, products from own producton, whch have been used for producton purposes, such as feed, seed, manure. CSO data does not nclude agrcultural processng, the value of off-farm servces and nvestment and overhauls of the related servces [Rychlk, Koseradzk 1976, p. 110]. The fnal agrcultural output s defned by the CSO as the sum of commodty producton value, the natural consumpton of agrcultural products from own producton, the ncrease n nventores of plant and anmal products and the ncrease n lvestock (lvestock prmary lvestock and current lvestock). Commodty agrcultural producton s the sum of agrcultural products sales to pont-of-purchase and on the markets. Commodty producton does not nclude sales between partcular legal enttes ranked as the same group of enttes as well as sales of agrcultural products by agrcultural producton cooperatves to the members of these cooperatves [Rocznk statystyczny rolnctwa... 2009, p. 49].
Managng the producton process... 241 Over the entre study perod, gross agrcultural output was the lowest n the Pomorze and Mazury regon. The hghest values were recorded n 20042005 and n 2007 n the regons of Welkopolska and Śląsk and n 2006 and 2008 n the Mazowsze regon and Podlase (see Table 1). Table 1. Gross output, fnal output and commodty producton accordng to varous regons of Poland n 20042008 2004 2005 2006 2007 2008 Pomorze and Mazury Gross output [n mllon PLN]* 11 123 11 857 10 726 12 468 14 355 Fnal output [n mllon PLN] 8 584 8 979 8 466 9 853 11 021 Commodty agrcultural producton [n mllon PLN] 7 453 8 631 8 096 8 882 10 352 Welkopolska and Śląsk Gross output [n mllon PLN] 16 385 18 709 16 240 17 850 20 031 Fnal output [n mllon PLN] 12 427 14 278 13 072 14 238 15 158 Commodty agrcultural producton [n mllon PLN] 10 797 13,199 12,172 12,746 13,538 Mazowsze and Podlase Gross output [n mllon PLN] 14 910 16 295 16 353 17 036 21 883 Fnal output [n mllon PLN] 10 940 12 373 13 175 13 450 16 517 Commodty agrcultural producton [n mloln PLN] 9 565 11 004 11 857 11 590 14 599 Małopolska and Pogórze Gross output [n mllon PLN] 14 464 16 031 14 266 16 462 19 648 Fnal output [n mllon PLN] 10 387 11 709 10 978 12 790 14 447 Commodty agrcultural producton [n mllon PLN] 8 415 9 783 9 726 10 075 12 081 * Gross output, fnal output and commodty producton are gven n current prces. Source: own elaboraton based on the CSO data. The values of fnal output looked smlar. Over the study perod, the fnal output was the lowest n the regon of Pomorze and Mazury. The hghest values were recorded n 20042005 and n 2007 n the regon of Welkopolska and Śląsk and n 2006 and 2008 n the regon of Mazowsze and Podlase. The lowest commodty producton value was recorded n the Pomorze and Mazury regon and ths trend contnued throughout the entre perod under study. The hghest value of ths producton was acheved n 20042007 n the regon of Welkopolska and Śląsk, and n 2008 n the regon of Mazowsze and Podlase. Prelmnary analyss based on data publshed by the Central Statstcal Offce shows that n the regons of Pomorze and Mazury, over the entre study perod, the smallest value of gross output, fnal output and commodty producton, was recorded. Therefore, t seems necessary to analyze producton processes on the farms of the Pomorze and Mazury regon. Due to the lmted sze of ths artcle, ths s lmted to the study of the group of farms specalzng n feld crops.
242 Agneszka Barczak 3. Methodology of the study Due to the use of the method of Lagrange multplers, t should be noted that the non-lnear programmng task s dvded nto two groups: wthout constrants and wth constrants (nequalty constrants). In both cases the methods for searchng for the optmum are teratve numercal methods of solvng the non-lnear programmng task. These methods can be dvded nto [Pogorzelsk 1996, p. 79]: 1) a zero order optmzaton methods (gradent-less),.e. those that only search for results on the bass of the value of obectve functon and constrants f necessary, 2) frst order optmzaton methods (gradent),.e. those n whch n the process of searchng for the optmum value, the value of the frst dervatve of the obectve functon and f necessary constrants are used, 3) second order optmzaton methods, n whch the Hessan matrx value s used (matrx of second dervatves). The method of Lagrange multplers whch s used s ranked as the second order optmzaton method. Another dvson (dentcal as n the case of lnear programmng) s a dvson nto the programs n canoncal form and n standard form. The Lagrange unmarked multplers method can be classfed nto programs n canoncal form. A characterstc feature of canoncal programs s that all the constrants (except for the boundary condtons) are n the form of equatons and when t comes to standard programs all constrants are n the form of nequalty. When the obectve functon s a non-lnear functon and the constrants are lnear functons then the Lagrange functon can be used. Ths s the so called Lagrange unmarked multplers method. The producton functon (obectve functon) of the form Y f 1, 2,, n s maxmzed (where,, 1 2, n are the decson varables) wth the followng constrants: F,, 1 2, n b, 1, 2,,m and 0 1, 2,,n. It s assumed that the functons Y and F are contnuous functons and that they have the frst and second order partal dervatves. Addtonally, the producton functon Y s an ncreasng functon of the varables. It means that f 0, 1, 2,,n. When the balance condtons of the task take the form of equatons, the functon of varables and multplers s created whch s called the Lagrange functon. It takes the form:
Managng the producton process... 243 m where: F 1 m, L f F b, (1) 1 b s a functon of resource expendtures whch characterzes the use of resources and ther constrants. The Lagrange functon has the same values (n the area of feasble solutons) as the obectve functon Y. A necessary condton for the exstence of an extremum s: L 0, 1, 2,, n, (2) or: L 0 m 1, 1, 2,, L f F 0 m s, (3), 1, 2,, n. (4) After determnng dervatves f F m and 1 u F m, 1 1, 2,,n the prncple of equalty of margnal ncrements of the product wth the cost functon s used and more specfcally, wth margnal ncrements of expendture. The prncple means that the condton of optmalty of use of the resource s that the margnal ncrement of the obectve functon, caused by the ncrease of expendture of any of the resource, was equal to the margnal ncrement of the resource expendture functon caused by the ncrease of ths resource. If f u, then t s benefcal to ncrease the expendture of resource, whereas f f u, then t s benefcal to decrease the expendture of resource [Zegar 1974, pp. 124125]. A necessary condton to acheve the optmal soluton s the same margnal ncrement of the obectve functon Y for all resources (per unt of resource expendture). A necessary condton for the exstence of the functon s extremum Y f,, 2, can be determned usng the followng formula: 1 n
244 Agneszka Barczak f f f 1 2 u u u 1 2 n. (5) A suffcent condton for the exstence of a maxmum (mnmum) of the Lagrange functon s fulflled when the second dervatve determned for the values of varables, whch meets the necessary condton of the exstence of the extremum, s less (greater) than zero. 4. Fndngs Accordng to the Lagrange unmarked multplers method, the producton functon, whch s the obectve functon, s maxmzed under the assumpton that the level of ncurred expendture on producton wll not change. Cost functons are the functons of resources expendture whch characterze the degree of ther use and ther constrants. Assumptons concernng the contnuty of the producton functon and ts constrants, as well as the frst and second order partal dervatves, have been met. Due to the fact that although the obtaned results meet all the assumptons, they are not always possble to ntroduce n realty and that s why ths study s lmted only to a short analyss of these results. It should be also kept n mnd that the solutons gven apply to a group of farms whch are dverse nternally, and n the estmates the average values were used. Table 2 presents the Lagrange functons bult for a group of farms specalzng n feld crops, where: 1 labour total labour expendture total expendture of human labour wthn the farm operatonal actvty, expressed n converson unts of labour n people employed on a full-tme bass (2 200 hours/year); 2 land utlzed agrcultural area the total area of land used for agrculture consstng of: land ownershp, land addtonally leased for one year or longer, the land utlzed on the prncple of partcpaton n harvestng wth the owner as well as fallow and uncultvated land, does not nclude mushroom cultvaton area, addtonally leased land for the perod of tme less than 1 year, wooded land and other land, expressed n hectares; 3 captal total assets ncludes only assets owned by the farmer (fxed assets and current assets) n PLN. A non-lnear optmzaton method was used to determne the optmal value of expendture, whch enables the maxmzaton of the value of output. The study of the value of second dervatves, under the adopted assumptons, ndcates that for ths group of farms over the entre perod under study, the maxmum values were obtaned. n
Managng the producton process... 245 Table 2. Lagrange functons for a group of farms specalzng n feld crops Years 2004 2005 2006 2007 2008 Model L 19.83 0.2335 0.4195 0.5455 152176.44 37579.61 1873.41 0.0731 346794.7 L 18.85 0.3251 0.3562 0.5581 133558.80 27183.30 1753.08 0.1227 472245.0 L 54.67 0.3677 0.3443 0.4789 93867.33 36243.51 1983.37 0.0948 607119.0 L 64.15 0.3066 0.4729 0.4403 278931.5185546.74 1018.27 0.2261 598424.0 L 42.28 0.4044 0.4119 0.4704 136702.62 48975.27 2932.32 0.0716 634623.0 Source: own elaboraton based on the Polsh FADN data. Fgure 1. The values of producton of the group of farms specalzng n feld crops, actual and determned wth the use of the method of Lagrange unmarked multplers Source: own elaboraton based on the Polsh FADN data. For the group of farms specalzng n feld crops, over the entre perod under study, the Lagrange unmarked multplers method generated values of producton whch are hgher than the actual producton (see Fgure 1). In 2004, n order to acheve a hgher producton by 45.59% (180 786.49 PLN), the method suggests a reducton of labour and land expendture, respectvely, by 10.80% (682 hours/year) and 34.76% (49.67 ha), and at the same tme, an ncrease n captal expendture by 119.29% (1 160 747.17 PLN). In order to acheve producton whch s hgher by 16.09% (83 195.73 PLN), n the consecutve year, the method ndcates the need to ncrease the labour expendture by
246 Agneszka Barczak 94.85% (6,270 hours/year) and captal expendture by 96.27% (1 090 516.64 PLN) and at the same tme reduce land expendture by 47.73% (90.69 ha). A smlar soluton was generated for 2006, n whch a 13.53% (77 825.48 PLN) ncrease n producton could be acheved by ncreasng labour expendture by 49.28% (4,334 hours/year) and captal expendture by 198.66% (2 972 478.06 PLN) and at the same tme reduce land expendture by 54.79% (123.82 ha). In 2007, n order to reach a 4.71% (30 628.23 PLN) of ncrease n producton, the method ndcated a reducton n employment and captal expendture, respectvely by 14.08% (924 hours/year) and 8.60% (131 818.79 PLN) and at the same tme an ncrease n land expendture by 74.89% (143.04 ha). The ncrease n producton by 8.23% (48 230.07 PLN) n 2008, accordng to the obtaned soluton, could be reached after the reducton of land expendture by 53.48% (96.80 ha) and at the same tme an ncrease n labour expendture by 64.99% (4 290 hours/year) and captal expendture by 101.36% (1 982 562.96 PLN). 5. Concluson The analyss relates to the data from a group of farms of one type. Therefore, the conclusons are prelmnary. In order to make them more general, the area of research ought to be expanded to all types of farmng. At the same tme, t should be kept n mnd that the group of farms under study s dverse nternally. In order to make the results more meanngful, they should be dvded nto sub-groups wth smlar characterstcs so that t s possble to mnmze the dfferences. All thngs consdered, t can be sad that the analyss has made t possble to use the method of the Lagrange multplers whch enables the maxmzaton of the volume of output n the group of farms specalzng n feld crops. Its applcaton n practce can be helpful n the optmzaton of producton n agrcultural farms accordng to agrcultural types. The ntroducton of the method wll enable an ncrease, whch s a change n the scale of producton, n ncurred producton factors expendture and development a change of the structure of ncurred expendture. References Barczak A., Wykorzystane metody mnożnków Lagrange a do oceny efektywnośc produkc na przykładze wybranych grup gospodarstw rolnych (PhD dssertaton), IERGŻ PIB, Warszawa 2011. Bartkowak R., Hstora myśl ekonomczne, PWE, Warszawa 2003. Chursk P., Czynnk rozwou regonalnego w śwetle koncepc teoretycznych, [n:] Gospodarka regonu na Jednoltym Rynku Europeskm. Wybrane zagadnena, Zeszyty Naukowe Wyższe Szkoły Humanstyczno-Ekonomczne we Włocławku. Nauk ekonomczne, 2005 T. I. Z. 3, pp. 1330.
Managng the producton process... 247 Czeka T., Józwak W., Barery wzrostu rozwou ndywdualnych gospodarstw rolnych w makroregonach Polsk, Rocznk Nauk Rolnczych 2009, sera G, T. 96, z. 4, pp. 2940. Pogorzelsk W., Teora systemów metody optymalzac, Ofcyna Wydawncza Poltechnk Warszawska, Warszawa 1996. Rocznk statystyczny rolnctwa. Rocznk branżowe, GUS, Warszawa 2009. Rychlk T., Koseradzk M., Podstawowe poęca w ekonomce rolnctwa, PWRL, Warszawa 1976. Zegar J.S., Wybrane zagadnena rachunku ekonomcznego w rolnctwe, Szkoła Główna Planowana Statystyk, Warszawa 1974. ZARZĄDZANIE PROCESEM PRODUKCJI GRUPY GOSPODARSTW ROLNYCH REGIONU POMORZE I MAZURY Z UWZGLĘDNIENIEM POZIOMU ROZWOJU GOSPODARCZEGO Streszczene: Celem nneszego opracowana est zastosowane metody umożlwaące maksymalzowane welkośc produkc w gospodarstwach rolnych. Przeprowadzone badana dotyczą regonu Pomorze Mazury, który został wybrany po dokonanu analzy pozomu produkc globalne, końcowe towarowe. Do badana wybrano grupę gospodarstw rolnych specalzuących sę w uprawach polowych, wykorzystuąc dane za lata 20042009, udostępnone przez Polsk FADN. Metodą wykorzystaną do optymalzac produkc est metoda mnożnków Lagrange a. Słowa kluczowe: gospodarstwa rolne, rozwó gospodarczy, regon.