Development and prediction of the selected population movement indicators in the Czech Republic

Podobné dokumenty
ANALÝZA POPULAČNÍHO VÝVOJE VE VYBRANÝCH REGIONECH ČR # POPULATION MOVEMENT ANALYSIS IN SELECTED REGIONS OF THE CZECH REPUBLIC. PALÁT, Milan.

ANALÝZA DLOUHODOBÉ NEZAMĚSTNANOSTI V ZEMÍCH EU # ANALYSIS OF LONG-TERM UNEMPLOYMENT IN EU COUNTRIES. KLÍMA Jan, PALÁT Milan.

ANALÝZA VÝVOJE ZDRAVOTNÍHO STAVU OBYVATELSTVA NA ZÁKLADĚ UKAZATELŮ ÚMRTNOSTI VE VYBRANÝCH REGIONECH ČR

ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS SBORNÍK MENDELOVY ZEMĚDĚLSKÉ A LESNICKÉ UNIVERZITY V BRNĚ

ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS SBORNÍK MENDELOVY ZEMĚDĚLSKÉ A LESNICKÉ UNIVERZITY V BRNĚ

ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS SBORNÍK MENDELOVY ZEMĚDĚLSKÉ A LESNICKÉ UNIVERZITY V BRNĚ

Karta předmětu prezenční studium

Zemřelí Vydává Ústav zdravotnických informací a statistiky ČR Praha 2, Palackého nám. 4

VÝVOJ PŘIROZENÉHO PŘÍRŮSTKU OBYVATEL V JIHOVÝCHODNÍM REGIONU ČESKÉ REPUBLIKY PODLE KRAJŮ A VELIKOSTNÍCH SKUPIN OBCÍ

Život na venkově a stárnutí Ing. Pavlína Maříková, KHV PEF ČZU ČZU Praha U3V

Introduction to MS Dynamics NAV

Právní formy podnikání v ČR

Zpráva ze zahraniční služební cesty

ROZBOR DYNAMIKY UKAZATELŮ ŽIVOČIŠNÉ VÝROBY V ČESKÉ REPUBLICE

Zdeňka Lipovská. This project is implemented through the CENTRAL EUROPE Programme co-financed by the ERDF.

DLOUHODOBÝ VÝVOJ ČASOVÝCH ŘAD UKAZATELŮ ZAHRANIČNÍHO OBCHODU ČESKÉ REPUBLIKY PODLE TŘÍD SITC

Dobrovolná bezdětnost v evropských zemích Estonsku, Polsku a ČR

POSTAVENÍ ZDRAVOTNICKÝCH SLUŽEB V SOCIÁLNÍM SYSTÉMU ČR Position of health services in the Czech social security system

Dynamic Development of Vocabulary Richness of Text. Miroslav Kubát & Radek Čech University of Ostrava Czech Republic

VYSOKÁ ŠKOLA HOTELOVÁ V PRAZE 8, SPOL. S R. O.

MINIMÁLNÍ MZDA V ČESKÝCH PODNICÍCH

VÝVOJ SŇATEČNOSTI, ROZVODOVOSTI A PORODNOSTI V JIHOMORAVSKÉM KRAJI

KULOVÝ STEREOTEPLOMĚR NOVÝ přístroj pro měření a hodnocení NEROVNOMĚRNÉ TEPELNÉ ZÁTĚŽE

BTS and Development of Confidence Indicators

ANALÝZA ZÁKLADNÍCH CHARAKTERISTIK DEMOGRAFICKÉ DYNAMIKY V KRAJÍCH ČESKÉ REPUBLIKY

HODNOCENÍ INOVAČNÍCH VÝSTUPŮ NA REGIONÁLNÍ ÚROVNI

VÝVOJ A PROJEKCE VÝVOZU VYBRANÝCH ZEMĚDĚLSKÝCH A POTRAVINÁŘSKÝCH KOMODIT Z ČESKÉ REPUBLIKY

2. Sociodemografická struktura České republiky - současný stav a vývoj od roku 1990

Spotřebitelské důchody na počátku krizového vývoje hospodářství

AIC ČESKÁ REPUBLIKA CZECH REPUBLIC

B. Bodečková, E. Maca

ANALÝZA REGIONÁLNÍHO ROZVOJE S VYUŽITÍM VÍCEROZMĚRNÝCH STATISTICKÝCH METOD

Klepnutím lze upravit styl předlohy. nadpisů. nadpisů.

Výuka odborného předmětu z elektrotechniky na SPŠ Strojní a Elektrotechnické

MEDIA RESEARCH RATINGS

Case Study Czech Republic Use of context data for different evaluation activities

MEDIA RESEARCH RATINGS

MAGAZINE ABOUT WOMEN THE WAY THEY REALLY ARE

STÁRNOUCÍ POPULACE OSTRAVY SOUČASNÝ STAV A OČEKÁVANÝ VÝVOJ

Tento materiál byl vytvořen v rámci projektu Operačního programu Vzdělávání pro konkurenceschopnost.

MEDIA RESEARCH RATINGS

MEDIA RESEARCH RATINGS

The Over-Head Cam (OHC) Valve Train Computer Model

DATA SHEET. BC516 PNP Darlington transistor. technický list DISCRETE SEMICONDUCTORS Apr 23. Product specification Supersedes data of 1997 Apr 16

REGIONÁLNÍ ASPEKTY SPORTOVNÍHO DIVÁCTVÍ 1

Uni- and multi-dimensional parametric tests for comparison of sample results

Litosil - application

LIDSKÉ ZDROJE JAKO VÝZNAMNÝ FAKTOR ROZVOJOVÉHO POTENCIÁLU KRAJŮ ČESKÉ REPUBLIKY

MEDIA RESEARCH RATINGS

Ministerstvo školství, mládeže a tělovýchovy Karmelitská 7, Praha 1 tel.: msmt@msmt.cz

Tento materiál byl vytvořen v rámci projektu Operačního programu Vzdělávání pro konkurenceschopnost.

User manual SŘHV Online WEB interface for CUSTOMERS June 2017 version 14 VÍTKOVICE STEEL, a.s. vitkovicesteel.com

WORKSHEET 1: LINEAR EQUATION 1

Co vím o Ázerbájdžánu?

MEDIA RESEARCH RATINGS

MEDIA RESEARCH RATINGS

Základní škola Marjánka

READERS OF MAGAZINE DOMA DNES

Návštěvnost v září 2008

IS THERE NECESSARY TO RECALCULATE VLTAVA CASCADE PURPOSES??

READERS OF MAGAZINE DOMA DNES

GUIDELINES FOR CONNECTION TO FTP SERVER TO TRANSFER PRINTING DATA

KONVERGENČNÍ PROCESY VYBRANÝCH DEMOGRAFICKÝCH UKAZATELŮ V KRAJÍCH ČR

TOP 4 KOMBI READERS OF MAGAZÍN DNES + TV, ONA DNES, DOMA DNES AND PÁTEK LIDOVÉ NOVINY

Fytomineral. Inovace Innovations. Energy News 04/2008

ANALÝZA EKONOMICKÉ AKTIVITY A NEZAMĚSTNANOSTI OBYVATELSTVA JIHOMORAVSKÉHO KRAJE

Číslo projektu: CZ.1.07/1.5.00/ Název projektu: Inovace a individualizace výuky

THE PREDICTION PHYSICAL AND MECHANICAL BEHAVIOR OF FLOWING LIQUID IN THE TECHNICAL ELEMENT

Characterization of soil organic carbon and its fraction labile carbon in ecosystems Ľ. Pospíšilová, V. Petrášová, J. Foukalová, E.

HODNOCENÍ KRAJŮ ČESKÉ REPUBLIKY PODLE DEMOGRAFICKÝCH CHARAKTERISTIK V ROCE 2006

Czech Republic. EDUCAnet. Střední odborná škola Pardubice, s.r.o.

Configuration vs. Conformation. Configuration: Covalent bonds must be broken. Two kinds of isomers to consider

Stojan pro vrtačku plošných spojů

INTEGRATED APPROACH TO THE LANDSCAPE THE INDICATORS OF SUSTAINABLE DEVELOPMENT AS THE TOOL OF THE REGIONAL POLICY OF RURAL SPACE

Just write down your most recent and important education. Remember that sometimes less is more some people may be considered overqualified.

CHOVÁNÍ SPOTŘEBITELŮ NA TRHU VÍNA V ČR

READERS OF MAGAZINE DOMA DNES

Table of contents. 5 Africa poverty reduction. Africa's growth. Africa - productivity. Africa - resources. Africa development

ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS SBORNÍK MENDELOVY ZEMĚDĚLSKÉ A LESNICKÉ UNIVERZITY V BRNĚ

READERS OF MAGAZINE DOMA DNES

TEPELNÁ ZÁTĚŽ, TEPLOTNÍ REKORDY A SDĚLOVACÍ PROSTŘEDKY

kterou se provádí zákon č. 122/2000 Sb., o ochraně sbírek muzejní povahy a o změně některých dalších zákonů

Návrh a implementace algoritmů pro adaptivní řízení průmyslových robotů

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

Počítačové kognitivní technologie ve výuce geometrie

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MAGAZÍN DNES + TV

EXACT DS OFFICE. The best lens for office work

METODOLOGICKÁ VÝCHODISKA ANALÝZ REGIONÁLNÍHO ROZVOJE METHODOLOGICAL STARTING POINTS OF REGIONAL DEVELOPMENT ANALYSES.

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

READERS OF MF DNES, LIDOVÉ NOVINY AND METRO

PLODNOST V ČESKÉ REPUBLICE PODLE VZDĚLÁNÍ A RODINNÉHO STAVU FERTILITY IN THE CZECH REPUBLIC ACCORDING TO EDUCATION LEVEL AND MARITAL STATUS

Invitation to ON-ARRIVAL TRAINING COURSE for EVS volunteers

POTENCIÁLNÍ OHROŽENOST PŮD JIŽNÍ MORAVY VĚTRNOU EROZÍ

TechoLED H A N D B O O K

VÝVOJ VĚKOVÉ STRUKTURY OBYVATEL KRAJŮ ČESKÉ REPUBLIKY JAKO PŘÍLEŽITOST I HROZBA REGIONÁLNÍHO ROZVOJE

Transkript:

Development and prediction of the selected population movement indicators in the Czech Republic Vývoj a predikce vybraných indikátorů pohybu obyvatelstva v České republice M. PALÁT, E. MACA Mendel University of Agriculture and Forestry, Brno, Czech Republic Abstract: The paper is aimed at the presentation of findings obtained in the study of the developmental trends of the population reproduction indicators in the territory of the Czech Republic in the reference period 1993 003. The analysis of selected indicators is also aimed at a short-term extrapolation prediction. Developmental trends are specified of the population composition according to the main age groups, live births and natural increase of population. The population development in the reference period under study demonstrated increasing qualitative changes in the demographic behaviour of population after 1989. A characteristic feature of this stage of social development is the transition to the west-european model of reproduction behaviour intensified in part of the population by negative impacts of the social and economic transformation. A marked decrease in the number of live births and its point prediction for 005 can bring about further irregularities in the age structure of population together with the development in the number of dead and external migration. Methods of regression and correlation analysis and development trends were applied for the mathematical-statistical analysis. Key words: population, age structure, natality, mortality, natural increase, trend, prediction Abstrakt: Příspěvek prezentuje dílčí poznatky získané při studiu vývojových tendencí demografických indikátorů populační reprodukce na území České republiky v referenčním období let 1993 až 003. Předmětná analýza demografické dynamiky je vedle hodnocení indexních řad zkoumaných jevů a vývojových tendencí směrována i na extrapolační bodovou predikci vybraných ukazatelů. Populační vývoj v posuzovaném referenčním období prokázal prohlubující se kvalitativní změny demografického chování obyvatelstva po roce 1989. Charakteristickým znakem této etapy společenského vývoje je přechod k západoevropskému modelu reprodukčního chování, zintenzívněného u části populace negativními dopady sociální a ekonomické transformace. Výrazný pokles počtu živě narozených a jeho bodová predikce na rok 005 může vyvolat další nepravidelnosti ve věkové struktuře populace a spolu s vývojem počtu zemřelých a zahraniční migrací ovlivnit jak počet obyvatelstva, tak i indikátor jeho stárnutí. Pro statistickou analýzu daného materiálu byly použito vývojových trendů a metod regresní a korelační analýzy. Klíčová slova: obyvatelstvo, věková struktura, natalita, mortalita, přirozený přírůstek, trend, predikce Specific position of demographic analysis represented by the achieved level of characteristics of the population movement and its reproduction as one of the important material conditions of social and economic development requires not only exact evaluation of the main developmental trends of the given phenomena in the past but also prediction of their future probabilistic development. The conception of the presented study is oriented to the quantification of changes in the development of natality and mortality in the Czech Republic in the period 1993 to 003. Within the reference period, time series were also analysed of the population number structure according to main age groups, live births and indicator of the death rate (mortality). The changes in the natality rate, mortality and age structure of the population as quantitative and qualitative changes of the characteristics of the population reproduction becomes more and more social process and not only biological process. The period that started in the Czech Supported by the Ministry of Education, Youth and Sports of the Czech Repiblic, Project MSM 615648904. AGRIC. ECON. CZECH, 51, 005 (6): 35 39 35

Republic at the turn of the 80 s and 90 s is the period of transformation from the central planned economy to the market economy and is very complicated from both social and economic aspects. It is not possible to eliminate the impact of the economic changes that slow down the positive factor of population reproduction, the net reproduction rate. An important role is played by the postponement of concluded marriages which causes a distinctive decrease of the natality. The expected further development of the fertility rate in the Czech Republic and the derived consequences in demographic, social and economic sphere must serve as an initial base for competent approach to the assessing of the purpose, aim and tools of the population policy. Theoretical aspects and interpretation of the results of analical activities in the sphere of the study of demographic events and processes have been dealt with by the number of authors. The following papers can be considered to be fundamental from the aspect of the conception of examination proper: Dufek (1999, 003), Kretschmerová (001), Maca, Palát (004), Palát, Maca (004), Roubíček (1996), Srb (001), Fiala (00) and Kaňáková (00). Methodological procedures of processing the factual data of analysed time series are based on the methods of descriptive statistics presented in the papers of Cyhelský et al. (1979) and Minařík (000). MATERIAL AND METHODS Basic materials necessary for the implementation of the determined objectives of the analysis of time series of studied events were obtained from the database of the Czech Statistical Office. Methodological procedures of processing and evaluating the studied indicators of demographic dynamics were aimed according to the set objectives of the analysis at the evaluation of dynamics and trends of assessed phenomena including their short-term extrapolation prediction. Analysis of the trend of the assessed time series is based on the application of models of developmental tendencies of the following type: t ln t c t a b a t a e b b 1 t t t Informative abilities and accuracy of the applied analical functions were tested by means of correlation indices I. The statistical significance of correlation indices was tested on the significance level P = 0.05 and P = 0.01. Determination indices I were used for verification of the indicators developmental trend models and their short-term extrapolation prediction. Mathematical-statistical processing of the data comes from the methodology given in papers of Minařík (000), Seger et all. (1998), Klíma, Palát (003a, 003b, 004) and Palát, Maca (004). (1) () (3) (4) (5) (6) Table 1. The development trends of selected indicators of the population movement in the Czech Republic in the period 1993 to 003 Indicator Mid-year population Measured unit thousands of person Model type Model parameters of developmental trends I (%) a b c 10 369. 14.6636 91.37 ++ Incl. the age: 0 14 063. 46.4818 99.40 ++ 15 64 thousands of person 1 6 96.4 3.5 96.77 ++ 65 and more 1 343.5 8.318 84.40 ++ Live births per 1000 population 4 8.469 3.134 90.36 ++ Deaths per 1000 population 3 11.864 0.96 0.0177 85.14 ++ Type of the function: (1) linear, (3) quadratic, (4) inverse Determination index I significant on the level: + α = 0.05; ++ α = 0.01 36 AGRIC. ECON. CZECH, 51, 005 (6): 35 39

RESULTS AND DISCUSSION The population development which occurred in the assessed territorial unit and defined time interval confirmed and intensified marked qualitative changes in the demographic behaviour of population appearing after the transition of centrally directed economy to market economy after 1989. The main demographic trends of selected indicators of the population movement in the reference period are presented in Table 1 and Figure 1. There is an enormous annual decrease of the midyear population of the pre-productive population (.99%) and a little increase of the post-productive population (0.58%). Based on the data presented above on the population movement, it is possible to observe a relative increase of the productive population by 0.3% and a total decrease of the mid-year population by 0.14%. The negative direction of the mid-year population development in the reference period is compensated by the number of migrants (105 974 persons). After eliminating them, the trend function of the modified time series would reach the following values: y = 10 36 40.75 15 086.51818 t = 90.50 % ++ and mean annual relative decrease by 0.15%. The most marked feature of the population development was the enormous decrease of marriages and born children and subsequently also the intensity of the processes. The problem of a considerable decrease in natality and its extrapolation prediction in the degree of decrease in 005 as compared with its absolute level in 003 will show consequences in the creation of other irregularities in the age structure of population. Together with the further development of mortality and migration, it will manifest itself in the number of population and its ageing. An overall quantification of the development of time series of the selected indicators of the population movement provides parameters of analical trend functions according to main age groups of mid-year population, live births, deaths and natural increment. A strong relative decrease in the reference period was also proved for the positive component of the population reproduction, presented by the relative rate of general natality (with an average annual relative decrease by 1.99%). When assessing the trend of the relative rate of general mortality as the rate of the number of deaths a year to the mid-year population (per mille) and a negative component of the population reproduction in the reference period, we can see its average annual decrease by 0.79%. Interpreting the indicators of both components of the population reproduction, it is to be stressed that both of the rates natality and mortality are dependent on the age population structure. Results of this stage of analical activities are given in Table. The extrapolate point prediction of the mid-year population for 005 presented in the Table a distinc- A B C D E F 110 105 100 95 % 90 85 80 75 70 1993 1994 1995 1996 1997 1998 1999 000 001 00 003 A Mid-year population B Mid-year population the age 0 14 C Mid-year population the age 15 64 D Mid-year population the age above 64 E Live births per 1000 population F Deaths per 1000 population Figure 1. Dynamics of fitted values of selected indicators of the population movement in the Czech Republic in the period 1993 to 003 AGRIC. ECON. CZECH, 51, 005 (6): 35 39 37

Table. Short-term extrapolation point prediction of the population movement indicators in the Czech Republic compared with selected previous years Indicator Point estimate for 005 Reality in the year 1948 1990 003 Mid-year population (thousands of person) 10 179 8 893 10 363 10 0 Include the age: 0 14 1 459. 3 1 571 15 64 7 68 5 493 6 844 7 11 65 and more 1 45. 1 96 1 40 Live births per 1000 population 8.67. 1.6 9. Deaths per 1000 population 11.00 11.4 1.5 10.9 Natural increment per 1000 population.3 10.8 0.1 1.7 tive increase by 14.3% as against 1948 and indistinctive decreases in the years 1990 (by 1.78%) and 003 (by 0.3%). Decrease in the estimated mid-year preproductive population by 34.3% as against 1990 and decrease in the estimated mid-year pre-productive population by 7.13% as against 003. Decrease of the post-productive population by 1.10% in the prediction year as against 003. There was an enormous decrease in the live-born (by 60.95%) as against 1948 and as against 1990 (by 31.%) and as against 003 (by approximately 5.8%). Decrease in deaths per 1000 inhabitants of the mid-year population by 3.51% as against the 1948 and by 1.0% as against 1990 in the prediction in 005 are also manifested. The same way of interpretation is possible to use for the version assessing the dynamics of natural increases or decreases to the defined unit of measure, which would decrease by 37.06% in 005 as against 003. CONCLUSION The paper is aimed at the presentation of findings obtained in the study of the development of time series of the population movement in the defined territorial unit and time interval 1993 003. In addition to the exact evaluation of the dynamics and trend, the analysis of selected indicators is also aimed at a short-term extrapolation prediction. The population development in the reference period under study demonstrated increasing qualitative changes in the demographic behaviour of population after 1989. A characteristic feature of this stage of a social development is a transition to the west-european model of reproduction behaviour intensified in part of the population by negative impacts of the social and economic transformation. A decrease in the number of both concluded marriages and birth rate, in spite of an extraordinarily favourable age structure, appears to be a serious and negative feature of the population development. A marked decrease in the number of live births and its point prediction for 005 can bring about further irregularities in the age structure of population and together with the development in the number of dead to affect both the number of population and the indicator of its ageing. The changes of the economic and social situation with its social and economic aspects are characterized not only with a continual increase of the expectation of life, but also by the decrease of the natality rate and putting off the marriage to the higher age. Both of these negative assessed processes can lead as far as the depopulation which exists at present in many European countries (from 1995 continuously in Italy, Hungary, Germany, Romania, Russia, Slovenia, Sweden). The expected further development of the fertility rate in the Czech Republic and the derived demographic, economic and social consequences have to motivate competent government authorities to change their approach to the population policy. REFERENCES Cyhelský L., Kaňoková J., Novák I. (1979): Základy teorie statistiky pro ekonomy. SNTL/ALFA, Praha, 365 p. Dufek J. (1999): The reproduction and the migration of the population in the South Moravian region of the Czech Republic in 1993 1997. Acta Universitatis Brunensis, XLVII (): 103 11; ISSN 111-8516 (in Czech). Dufek J. (003): Development of regional unemployment characteristics in the Czech Republic. Agricultural Economics Czech, 49 (1): 571 577. 38 AGRIC. ECON. CZECH, 51, 005 (6): 35 39

Fiala T. (00): Tendencies in marital fertility of the nd and 3 rd orders in the Czech Republic during last fifty years. Demografie, 44: 81 93; ISSN 0011-865. Kaňáková N. (00): Global aspects of migration. Demografie, 44: 119 14; ISSN 0011-865. Klíma J., Maca E. (00): The development of unemployment under conditions of an economic transformation in the Czech Republic. Acta Universitatis Brunensis, L (): 53 64; ISSN 111-8516 (in Czech). Klíma J., Palát M. (003a): Analysis of the development of an external debt of the Czech Republic. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, LI (6): 47 60; ISSN 111-8516. Klíma J., Palát M. (003b): Labour productivity as a factor forming the economic efficiency and competitive ability of the country. Agricultural Economics Czech, 49 (11): 515 519. Klíma J., Palát M. (004): Rates of employment and unemployment in the EU and the associated countries of the EU. Agricultural Economics Czech, 50 (7): 45 5. Kretschmerová T. (001): Development of Population of the Czech Republic in 000. Demografie, 43: 173 186; ISSN 0011-865. Minařík B. (000): Statistika I. MZLU Brno, 107 p.; ISBN 80-7157-47-9. Maca E., Palát M.(004): Obecné a souhrnné míry intenzity reprodukce obyvatelstva České republiky v letech 1945 00. In: Sborník referátů ze 7. mezinárodní konference Firma a konkurenční prostředí, Sekce 4. Kvantitativní metody v hospodářství, pp. 85 91, Brno, 10. 11. března 004; ISBN 80-730-076-9. Palát M., Maca E. (004): Analysis of the development and prediction of the population movement indicators in the Czech Republic. Acta Universitatis Brunensis, LII (3): 17 34; ISSN 111-8516. Roubíček V. (1996): Základní problémy obecné a sociální demografie.vše Praha, 71 p.; ISBN 80-7079-188-8. Seger J., Hindls R., Hronová S. (1998): Statistika v hospodářství. ECT Publishing Praha, 636 p.; ISBN 80-86006-56-5. Srb V.(001): Současný stav demografie na Slovensku. Demografie, 43: 56 57; ISSN 0011-865. Statistical yearbook of the Czech Republic 004. Scientia, ČSÚ Praha, 783 p.; ISBN 80-50-0853-3. Arrived on 5 May 005 Contact address: Prof. Ing. Milan Palát, CSc., Mendelova zemědělská a lesnická univerzita v Brně, Zemědělská 1, 613 00 Brno, Česká republika Doc. Ing. Erich Maca, CSc., Kotlářská 44, 60 00 Brno, Česká republika tel.: +40 545 13 41, e-mail: palat@mendelu.cz AGRIC. ECON. CZECH, 51, 005 (6): 35 39 39