CC BY
14should first of all pay attention to public goods, which are related to the impact on the life expectancy of a person, his health, knowledge, that is, with human development. Such investments in a person should be considered not only as a "spending" of budget funds, but also as social investments, since they acquire more importance in the structure of national wealth.
References
1. National Report "Sustainable Development Goals: Ukraine". Ministry of Economic Development and Trade of Ukraine, 2017.- 174 p.
2. Official site of the Ministry of Ecology and Natural Resources of Ukraine. - [Electronic resource]. - Access mode: https ://menr. gov.ua/news/31775. html
3. Statistical digest "Environment of Ukraine 2016." - Kyiv, 2017.- 226 p
4. Statistical digest "The Budget of Ukraine 2016". Kyiv, 2017.- 316 p.
5. Statistical digest "The Budget of Ukraine 2015". Kyiv, 2016.- 308 p.
6. Statistical digest "The Budget of Ukraine 2013". Kyiv, 2014. - 244 p.
7. Recommendations of the parliamentary hearings on the topic "On Health Care Reform in Ukraine" : Resolution of the Verkhovna Rada of Ukraine dated April 21, 2016 No. 1338-VIII.- [Electronic resource]. -Access mode: http://za-kon3.rada. gov.ua/laws/show/1338-19
8. National strategy for reforming the health care system for the period 2015-2020. [Electronic resource]. - Access mode: http://uoz.cn.ua/strategiya.pdf
9. The demographic yearbook "The Population of Ukraine for 2016". - Kyiv, 2017.- 102 p.
10. Official site of the Ministry of Health Сare of Ukraine .- [Electronic resource]. - Access mode: http://moz. gov.ua/article/news/
11. The Constitution of Ukraine. [Electronic resource]. - Access mode: http://za-kon2.rada. gov.ua/laws/show/
12. National Accounts of Health Care (NAHC) of Ukraine in 2015. Statistical Bulletin / State Statistics Service of Ukraine. - Kyiv, 2017.- 144 p.
РЕШЕНИЕ ПРОБЛЕМЫ РЕГИОНАЛЬНОГО УСТОЙЧИВОГО
РАЗВИТИЯ
Пшунетлев А.А.
Академия маркетинга и социально - информационных технологий (ИМСИТ), доцент
THE SOLUTION TO THE PROBLEM OF REGIONAL SUSTAINABLE DEVELOPMENT
Pshunetlev A.A.
Academy of marketing and socially - informational technologies (IMSIT), associate professor
АННОТАЦИЯ
Статья расширяет пространство устойчивого развития, приближает гибкие политики, полученные в центральных работах в области устойчивого развития, к рекомендациям, основанным на территориально специфичной информации. Настоящее исследование представляет решение проблемы регионального устойчивого развития (РУР), представляет аналитическую, нормативную рамку с позиции мезо региональной перспективы. Промежуточная панорама позволяет широко взглянуть и целостно управлять различными направлениями этой сложной проблемы, с фокусом на роль межправительственных отношений, в особенности трансфертов, в достижении устойчивости развития, межрегионального равенства, пространственной стабильности, сохранности человеческого капитала, природных ресурсов и состояния окружающей среды. Границы модели охватывают социальные, экономические, энвайронментальные, экологические аспекты, приглашая данные доступные в каждом регионе. С ее помощью, проведено эмпирическое исследование, которое охватило территорию Кубани, в южной части России. Аналитические средства, системный подход, методология системной динамики, равновесный анализ, пороговые значения, позволили сформулировать удовлетворительную политику устойчивого развития, даже в сложной и динамичной среде.
ABSTRACT
The paper's contribution is supposed to be widening the domain of sustainability, bringing closer flexible policies, derived in the field's landmark works, to procedures being grounded on a territory specific information. This study presents the solution to the problem of regional sustainable development (RSD). It extends an analytical normative framework, from a meso regional perspective. The intermediate panorama allows for a broad consideration and cohesive handling of various ramifications of this complex issue, with a specific emphasis on the role of intergovernmental relations, particularly transfers in achieving sustainability, interregional equity, spatial stability and preservation of human capital, natural resources or environmental quality. The comprehensive model encompasses social, economic, environmental, ecological aspects, inviting data available nearly in every region. By means of this model, an empirical study is carried out for the Kuban area in southern Russia. Analytical tools, a
systems approach, the systems dynamics methodology, the equilibrium analyses, the use of threshold values seemed to bring a satisfactory sustainability policy even in a complex and dynamic environment.
Ключевые слова: региональное устойчивое развитие, ресурсная обеспеченность, качество окружающей среды, критическая граница несущей способности, мезо региональная перспектива
Keywords: regional sustainable development, resource availability, environmental quality, critical frontier of carrying capacity, meso regional perspective.
1 INTRODUCTION
The integrated treatment of issues concerning environmental quality and economic wellbeing in the regional policy has so far not received very much focused attention from either environmental or regional economics. This paper aims to narrow the lacuna by presenting a normative dynamic framework allowing for a coherent management of environmental, economic and social aspects of the problem of sustainable development from a meso regional perspective.
Such a view conveys information about how people live in different regions, probably a country, instead of providing a narrow look over some regions, or even group of them. On the one side, it encompasses regional, interregional processes and on the other side is open to the inclusion of "center-region" relations, a supposedly important ingredient in achieving intertemporal, interregional equity and spatial stability. Before a constructing effort, a review is given of economic approaches and policies relevant to this study.
The concerns about the industrialized society's future are old, but it was not until the 70's when they received a systematic treatment. The complex and dynamic nature of environmental-economy interactions has become a good rationale for applying system dynamics methodology [19, 40]. These contributions have attracted a lot of attention and inspired much debate among development theorists, with some defying them, pointing to the lack of inherent economic processes, e.g. the market price mechanism, a consumer or producer behavior, the growing productivity or opportunities arising from trade [42].
Various provisions for economic growth have been considered in the conventional neoclassical framework [16, 29, 50, 51]. Studies in this flavor mainly focused on opportunities stemming from technological improvements or substitution of human made capital for exhaustible resource stock. A specific attention has been devoted to the issue of sustainability, commonly regarded as restraining to the concept of op-timality [6, 24, 43].
Different contributions to the endogenous growth theory focus on the role of externalities related to technological progress, knowledge accumulation and trade in achieving sustainability [26, 25] or examine the impacts of environmental policy on economic performance [e.g. 12]. Alternative approaches to the relation between environmental quality and economic development observe its disequilibrium nature [27] or account for the endogenous technological change in climate policy analysis [21], or deal with an empirical analysis of innovation and diffusion in energy technologies [55].
Being multirelational in nature, the problem of sustainable development appeals to a cooperative treatment. To facilitate a collaboration in addressing various environmental topics, a number of game frameworks
have been suggested. The work by Batabyal [8], stresses the need for employing game models in environmental policy, with the latter being elaborated in the study by Barret [7] to the strategy of environmental treaty-making. Carraro et al. [13] argue the important role of transfers in encouraging participation in environment cooperation, and at the same time, Finus et al. [17] investigate the formation and stability of coalitions to form international environmental agreements. Of specific notion, the relevance of the level for climate control, which is discussed in more detail by Asheim et al. [4], while considering regional cooperation against global treaty. Anger [3], from his side, assesses the economic impacts of linking the EU emissions trading scheme to emerging schemes beyond Europe.
The problem of regional sustainable development engages increasing fascination of academicians and policy makers. Such an interest emerges naturally with the growing understanding of the important role regions play in ensuring high quality of life, and consequently, calls for the need of employing concepts and applied tools that enable the study of conditions for sustainable development in the regional context. As a result of the burgeoning attention, a bulk of literature emerged, discussing separately or in a combination various ramifications of this composite issue.
Since occurrence, the problem of 'regional sustainable development', mirrored limitations of concepts and approaches, appeared in the sustainability debate on a broad scale, and assumed an account for indigenous economic, social, ecological conditions [20, 54].
Having been defined as 'a balanced development policy for all resources in a region concerned', RSD is considered as a program harmoniously engaging the whole range of endowments present in a region. Even so, it aims at achieving 'a maximum level of welfare', as such, one should regard it as an optimal time path, taking into consideration 'environmental, social and economic objectives or constraints', and 'the impact of exogenous circumstances' as well [41].
Stressing 'the normative nature of sustainability', they advocate for 'a framework of analysis and of expert judgment which should be able to test actual and future states of the economy and ecology against a set of reference values'. Pointing to 'the complex interacting patterns of regional development', Batabyal and Nijkamp [9] argue for 'a balanced regional perspective' in the form of 'a comprehensive impact model' facilitating 'thorough investigation of environmental, resource, climatological conditions responsible for sustainable development'.
Moreover, one may readily suggest highly contradictory nature of the concept, as 'putting more emphasis on a higher availability of the one category tends to reduce the availability or usability of either of the other ones'. Such a concept may be regarded, from one side,
as to be resonating with the previously attained consensus on sustainability as 'an interaction among three systems: the biological and resource system, the economic system'. However, from the other side, it may be viewed as a prominent step in clarifying objectives and constraints of the problem, generally acknowledged as to be 'extremely difficult, if not impossible, to define in any analytically rigorous way' [5].
In a spatial context particularly, sustainability has been addressed from various approaches, some of which constitute the methodological basis of the present study. Treating a region as an open system in either economic or environmental respect is a common technique when dependence of regional processes on outside forces is assumed [e.g. 53]. In this case regional economic changes are presented as externally motivated, in the Keynesian way, with an elastic supply and consequently fixed prices.
An additional approach is to present spatial processes explicitly. The common line of attack is to consider regional economies to be 'synergy-laden systems of physical and relational assets', or in a more general sense, to view 'a regional development in the context of a close locked in system, called a region', where a sustainable path emerges 'as a result of a complex inter play of economic, social, environmental, institutional forces' [48].
From this interpretation, a number of theoretical frameworks have been applied. Keynesian and neoclassical multiregional growth models [2] have an apparent economic orientation and provide a very narrow view on the problem of environmentally sustainable development. The interregional perspective [52] incorporates explicitly environment dimension to examine its effects with endogenous technological change and trade or evaluate governance and policy for interregional sustainability [36]. Another information is available from the spatial general equilibrium perspective, which has been applied in recent studies with a particular focus on either internalizing time delays [1, 15] or environmental taxes [10].
Applied research efforts on issues concerning regional sustainability fall into several strands: regional economic development, natural resources, environmental quality and regulation. The study of such a complex problem requires us 'to pay adequate attention to regional and to interregional linkages in production, consumption, transportation, and to ecological interactions' [9]. In agreement with this, a work by Gutman [28], where by resorting to a broad spatial perspective, the author explains the emergence and persistent presence of 'a new rural urban compact'. A work by Verhoef and Nijkamp [56] leads to the conjecture that 'a spatial price equilibrium approach' is a relevant way of examining trans boundary externalities from interregional perspective. An analysis by Hosoe and Naito [31] being addressed to the other side of the same problem, reports that trans regional environmental externalities have an autonomous regional agglomeration effect, and cannot be excluded from consideration.
On a separate note, works on natural resource use. Although many important issues in this regard have
been addressed, including deforestation, water provision there is still a good deal of questions awaiting for an adequate response, and among them, one may note urgently signaling: what impact does an exogenously determined rate of extraction of natural resources have on regional sustainability? Given improving transportation, an expanding external demand for natural inputs, and consequently the disruption of feedbacks between a regional output and an actual depletion pace, what should be done to mitigate unpleasant outcomes arising from depletion of essential to regional output resources? Is the existing transportation network able of delivering resources in a backward direction?
With respect to this, a work by Blatter [11] provides a relevant proposal of integrating regional transportation systems, and still more contributions are emerging in this area of research. Indeed, the regional impacts of natural resource extraction are of the considerable research interest in the related, increasingly expanding literature [18, 37]. Keeping in mind these questions, it seems natural to propose considering the problem of resource availability from a broader, meso perspective, allowing a researcher evaluation of the impact of regional transformations on meso stability, as well as the influence of exogenous constraints on regional performance.
With respect to the environmental policy, there is an apparent move from the 'command and control' type of decision making to a more flexible, allowing for a wider variety of playing actors, regulating style of policy-making. The recent studies explore essential aspects of the environmental management and convincingly show the increasingly growing role of the intergovernmental relations in attaining regional sustainability [33, 34, 35].
Notwithstanding this, there still are critical questions awaiting for a satisfactory reply. The one is how intergovernmental transfers affect the environment. The obvious consequence is that a region, where the product has been created, accumulates pollution of production and has less consumption from either the direct reduction of income in a producing sector, presumably manufacturing, or indirectly, because of the decline in production and associated emission of pollutants in the service industry.
Thus, there is an apparent trade off between benefits, e.g. goods, services and costs in the form of consumption pollution imposed with transfers and production pollution, associated with additional output of the local economy, motivated with an extra demand, as such, one may expect a kind of equilibrium. Although separate topics of regional sustainability in the context of intergovernmental relations are of growing interest, there also presently is persistent need for an integrating effort.
Overlooking conducted research so far, one may conjecture that many vital problems, with regard to sus-tainability of regional development have been addressed. As a result, on the one hand, environmental quality, resource base have widely been acknowledged as important determinants of whether regional development is sustainable or not. On the other hand, regulation of economic activities deteriorating environmental
well-being, as well as management of natural resources have become to be considered as having close links to properties of the space where such policies are implemented.
Nevertheless, there are persistent and increasingly acute social, economic, environmental, ecological issues, in a regional policy agenda, attention to which might be concentrated around the following questions:
1. What is a solution of the problem of RSD, a comprehensive policy, aiming at wellbeing, liable levels of environmental quality, resource availability and social equity in a group of regions or country?
2. What a role in sustaining regional development in general, and supporting economic welfare, maintaining area inhabitation, protecting environment, resource potential in particular, intergovernmental relations may play?
3. How to save a region's human capital, sustain population stock when interregional income level disparity is widening or barriers to migration are becoming lower, and federal and regional policy makers are concerned?
4. How to sustainably use a regional resource potential if a natural capital price is externally motivated, and what policies should be implemented to mitigate unpleasant influence of a mounting outside demand on regenerative capacity?
5. Ho to protect environment and regional ecosystems, control pollution rate and back assimilating capacity when common tools of internalizing externalities fail and production become predominantly onward oriented?
This paper aims to address above questions by means of inclusion 'center-regions' relations into the two region setting. Such an extension is motivated by opportunities naturally arising from the interregional perspective, allowing for spatial interactions and an important intermediate role of a national regulator in ensuring sustainable paths of regional development.
2 THE MODEL
Obviously, when treating a problem as complex as that described above, one inevitably confronts the trade-off between economic realism and mathematical feasibility. Efforts have been made to keep the model as simple as possible, and at the same time, allowing complexity when it does not seem too limiting, so as practically tractable results can still be derived.
The focus is on two interacting areas. Henceforth points will represent them, thus admitting an equal environmental quality and resource availability across a region. Each region is unhabituated by rational individuals, contributing labor, capital, natural resources to a region output and exposing preferences through utility function. The latter is controlled by variations of the levels of consumption and environment amenities, while the former comprises homogenous commodity and service. An equilibrium is supposed to instantly occur in all markets.
Prs
Transportation costs are allowed to be zero, and consequently, they trade a commodity at the same price, which in turn serves as a nominator. Output of a competitive sector, rent for natural resource are considered as exogenous. The description of the model starts with introducing an average consumer's utility function, reflecting a representative citizen standard of living:
0,gTi = 1| (i)
ür=-
where £r, Lr, Cr, Sr - environmental quality, labor stock, commodity, and service consumption respectively. Subscript index r refers to region.
First order conditions for constrained optimization bring volumes of consumption:
(2)
Cr = Tcconsr Tsconsr
Sr =
PrS
(3)
Denoting regulator transfer, rate of return on natural resource as NTr,rent respectively, the aggregate consumption in a region may be expressed as:
consr =
^ wrjLrj + ^ irjKrj + rent resr + Tr ) (4)
Vi=1 i=1 J
The utilization of natural resources is worth of specific notion. Although Hoteling's rule [32, p. 137] keeps analysis simple, having provided a necessary condition for an efficient path in the field's landmark works, however, on regional level, one may doubt its underlying assumptions.
For one, future markets do not present perfect foresight for all natural resources, or if even so, there are local factors exerting impact on price. For two, the assumption of the zero extraction marginal cost seems quite dubious. Instead, one may suggest reserve dependence of the cost of extraction, introducing 7C(res, flfS), linking extraction cost TC with the rate of extraction res and available stock of natural resources flfS. Such a mapping is expected to have next properties [14, p.81]:
< 0 < > 0 and may be cast as
TC {res, = ^ ,q, >1
(5)
RES„
(6)
Supposing a competitive industry brings the equation for the rate of the extraction:
qr-i
= rent (7)
qr resr
fi£Srqr
Now, recalling that perfect competition requires the marginal cost to be equal the price, and taking into account localization of service consumption let one write:
a Y •
rs Arj
wrj- = ■
^r/ PrjßjYrj
L
(8)
(9)
r/
1=1
2
2
Y = 5
By substituting (7), (8), (9), (10) in (4) one gets:
consr = ■
Yc + qr1-qr(rentfi£5r)qr-i + 7r Tc
i qr
Cr = Yc + qr1-qr(rentfl£,5r)qr"1 + 7r
T, '
Prs^c
Yc + qr1-qr (rent R£5r)qr-1 + 7r
(10)
(11)
(12) (13)
Preliminary results need some comment. While the equation for commodity consumption (12) looks quite predictable, the value of service production (13) is not trivial. Actually, under extant premises the utility function (1) attains the most value with and only with the right choice of the level of service's utilization, for which (13) presents a clear formulation.
Lr Ur ( Ts \Tc-1
"^f—) -Yc
Cr \prsTc'
1 qr
qr1-qr(rentflC5r)qr-1
(14)
Since equations of state equilibrium have being derived, it is time to formulate the law of evolution of Substituting (12), (13) for Cr, 5r in (1), finally the two-region system:
brings a national regulator transfer's time path:
2/
I LA e -1 ,
Li = fcA ( 1- l1) + m —-/(L1,L2) + M1
RES1 = r1RES1
i*
L1
i _. RES1
2/
e +1
RES
C1 = e^ (l- |L)- Y1 (rc + - q11-1q!(rent B?1)* 1 (
V C10/ V prsTc/ V
10 J 1
rent RES,
qi A
qi
qi _i
DR,
J
1
.qi-1/ rentra rr1r„
P1STC
P1STC
2C2
F w I 1 LA e /Ui-1 L2 ^M1-^)^ —-
/(L1,L2) + M2
e / + 1
RES = r2RES2
, RES, 1 _-
C2 = e2C2 ( 1 £
(1-CC20)-Y2(7 + 7
+ a1C1
V
t.
RES
20 J
rent RESq2 ^ q2 _1 . q2 j
2l7C + 7S —
20' \ prslc
.)-q21-q2(rentfiq2)q2 1 ('
1
q2-1 / rentra rr2r,
Tfl +7--)
p2sTc ' p2sTc
■DR2 )-
-
L 01 < ^2 / ( Li,L2 ) = ]l2,OI >^2 0,01 = O2
(15)
(16)
(17)
(18)
(19)
(20) (21)
The system deserves a comment. It involves nonlinear equations, and then, a solution existence issue is of independent interest. It may be shown, that it has solution for all negative magnitudes of the system's stocks, and the gradient of the latter is continuous. Thus, thus conditions of the Existence and Uniqueness theorem [27, p. 144] are satisfied and the study dynamic hypothesis is of broad generality1. Further, population stock gets impact from a natural movement and migration.
While the former is described by a common logistic equation (57, 45), the latter is considered to be proportional to the population stock with a coefficient
e /ui-l
^ = m --, which dynamics is presented in figure
e /ui + 1
1. Such an interpretation reflects an assumption that interregional inequality affects the rate of migration. The more the former, the greater the latter. Yet, the marginal rate is diminishing and the migrating population quantity is limited by the region population stock. There is also opportunity to account for a non-economically motivated migration. This part of a population movement may be due to political instability, social adversity or even natural cataclysms. Other reasons for resettlement, for which mechanisms are vague, may share this category. These are collectively presented by comprehensive term M.
1
7
r
1
1 Author welcomes requests for proof, which due to
limitation for space have not been presented
As far as natural resources concerns these are considered broadly, collectively comprising the of the economy natural capital stock. "It includes renewable resources, such as water, terrestrial and aquatic biomass; non-renewable resources, such as land in general, minerals, metals and fossil fuels; and semi-renewable resources, such as soil quality, the assimilative capacity of the environment and ecological life support systems" [6]. The resource bank is affected by natural restoring forces, ensuring, in the absence of anthropogenic activity convergence to an area's carrying capacity [39]. Regardless to a particular process responsible for the limitation of a resource bank, the concept of carrying capacity is easily introduced by increase of the naturally determined rate of depletion, in the form of the logistic equation (14). Besides natural mechanisms, the stock of a region natural endowments diminishes through harvesting due to economic activity or exogenous damage DR (e.g. forest fires).
As concerns the environmental dimension of the regional development, one may confidently argue, that a good deal of work has been done from both theoretical and applied sides of this complicated issue. "Environmental quality is reduced by the discharge of pollutants if the emission flow exceeds the resource's assimilative capacity" [47]. This precise explanation of the cause and condition for an environmental degradation is a starting point to describe environmental dynamics.
Not surprisingly regional environmental studies, due to vast diversity of environmental conditions, tend to explore site-shaped specific aspects of this thought-provoking problem.
However, the very broad spirit of the model encourages the selection of a more general theoretical framework. Such a pattern should meet contradictory constraints. It is assumed to be wide enough to catch common features of various processes accountable for environmental degradation, and at the same time, such a constructive effort is meant to be sufficiently precise, helping actors involved develop and implement robust environmental policies. Keeping this in mind naturally directs one's attention to the concepts of background and assimilative capacity, an endured part of the sus-
tainability debate. As for the former, it represents 'natural' upper bound attained in the absence of anthro-pogenous pollution [47, 38] while the latter can be defined as the ability "to receive a determined level of residues, to degrade them and to convert them in no damaging and even beneficial products" [44]. Putting in a more abstract form, it represents "nature's self-cleansing forces" [47].
Even though there is a quite much consensus on the meaning, the perception of the assimilating capacity's dynamics is a very contentious subject. So far, the four hypotheses have been proposed [19, 49, 46, 6]. Each of the hypotheses is worth of a separate consideration, and can be endorsed in the basic framework according to a region specific self-cleaning processes. Nevertheless, one may note, the similarity on certain intervals of all to the hypothesis assuming a local extreme, therefore, is no surprise to propose this as an actor responsible for absorbing pollution.
The impact function comprises different sources of environmental degradation. To display an independent role of the transfers in the pollution formation, the distinction is made between consumption and production causes of effluence, with the latter being split into pollution associated with manufacturing, service or resource extraction.
When presenting a socio-economic system, which may be a subject of interest to those preferring the verbal or graphical communication, it looks salient to cast a related causal loop diagram. For detailed specification of the system interactions, one is referred to Appendix I. Moreover, the stocks and flows diagram of the model of RSD is presented in Ошибка! Источник ссылки не найден.. So, premises of the model are complete, but how fruitful these are?
3 ANALYSIS
The very first look on the system (15) - (21) is enough for concluding that no equation lives an own life, without being influenced from either another stock or control parameter. It also is obvious that it admits no analytical treatment, and examining solutions involves strengthening premises and numerical handling.
Even so, one may note that no all values of control parameters agree with sustainability. Indeed, equation
(15) has at least one positive equilibrium solution only if
(
M1 < 0&&m <k1 -2 -
k1M l
L
M1 = 0 & &m < k1|| M1 > 0);
meaning the selection of utility levels cannot be random unless policy makers don't care sustainability of a population stock.
Appendix III contains presentation of the equation (15) phase line and bifurcation diagram. Another association providing a motivation for a deliberate regional policy is the equation (16).
Actually, assigning q1 = 2,q2 = 2 is an appropriate way to demonstrate sensitivity of a regional resource base to variations of rent, which is assumed to
be determined on an interregional market, and is subject to regulation.
Indeed, quadratic equation
r,RES,
RESX ) rent RES,2
1 --
RES
+ DR = 0,
10 J
((DR1 < 0&&-
2r
RES
< rent < -
-4DR1 r - r
10
2DR1 RES
has at least one non trivial positive solution only if
)).
2 RFS 2 RES^) || (DR1 > 0&&rent >--2
RES
The inequalities show the range where rent should be to ensure sustainability of a region natural resource stock. The case DR1 > 0 relates to investments in natural bank (e.g. forestation, improving soil quality etc.).
10 10
Figure 2 exhibits the critical frontier of a carrying capacity, going beyond which threatens survivability of natural resources. For each level of carrying capacity, the critical frontier defines the value for rent such that more price would drain the natural resource stock.
Figure 2 - The critical frontier of a carrying capacity
Some remarks with respect to figure 2. For one, given certain exogenous damage to resource base, not all regions can sustain economically motivated extraction of natural reserve, namely regions, whose carrying capacity belongs to the range [0;CC]. For two, there is an apparent threshold level, specifically CC, indicating the edge, that is, regions with carrying capacity exceeding that are liable for resource extraction for some rent. For three, larger regions enjoy more survivability, and finally, carrying capacity exhibits increasing returns,
since Rent > 0.
What are practical implications of the above observation? In fact, these are obvious. Expanding transportation networks, better than ever means of extraction make regional resource base, e.g. crops, forests, water, sand, gravel, energy etc., be very sensitive to external
exposure. As one may see, (16) under certain conditions, a region resource stock disappears in finite time. Such a reflection is a good rationale for national and regional policy makers for a close attention to resource markets and relevant resource price regulation. More information, concerning properties of natural resource dynamics is presented in Appendix IV.
4 CASE STUDY
The examination advances a solution of the above model. Awareness is brought to regions - subjects of the Russian Federation. Krasnodar Krai and the Republic of Adygea occupy the country south part, a historic region, known as Kuban. The motivation of selecting the area as an object of inquiry is an interregional migration, similar structure of the resource base and the presence of common environmental problems. The map of the territory is illustrated in figure 3.
Figure 3 - The map of regions studied and their close environment
The solution plan:
1. Determining the two-region system's trajectory from the initial point, while maintaining the parameters values (base run). It is supposed to help in classifying whether regional development sustainable or not. Equation for utility function (1) is expected to facilitate identification of the standard of living time path. of It's also supposed to be advantageous in detecting development patterns of region's population, resource stock or environmental quality.
Table 1.
2. The calculation of the sustainable development path while varying a control parameter, particularly the level of financial aid. Observing a steady state, an orbit with a constant utility level, reaction of the system stocks, explaining variations. The system state is described by levels of population, renewable resources, non-renewable resources and environment. The starting point of the solution - 01.01.2014. The choice is due to the availability of data on the model-covered areas. The system stocks initial values are presented in
Table 1
Values of the model stocks variables on 01.01.2014
Name of variable Notation Krasnodar Krai the Republic of Adygea
Population 2 L 5.4 x 106 4.5 x 105
Stocks of non-renewable resources, units resnr 100 10
State of the environment,% E 50 50
The estimate for nonrenewable resources based on gases mixture concentration. The other necessary in-
assumption, that these will last for 100 years at the cur- gredient for computation is parameter estimates, which
rent rate of consumption, while environmental quality are presented in Table 2. is assessed relatively to a natural level of particle -
2 Source: Russian statistics service (Rosstat) (22, 23)
Table 2
The model parameters estimation
Name of parameters Notation Krasnodar Krai the Republic of Adygea
1 2 3 4
The elasticity of the utility function by product 0.7 0.7
The elasticity of the utility function for the service Ts 0.3 0.3
Technology coefficient of natural resources extraction 2.695 3.375
Birthrate fcftr 0.13 0.12
Mortality rate krfr 2.4 X 10-5 2.6 X 10-4
Migration3 Mr 57736 18002
The natural level of concentration of harmful substances, mgr / m A 3 ^rO 10 10
Pollution per unit of industrial products4 T ' c 80.5 5.4
Continuation of Table 2
1 2 3 4
Pollution per unit of agricultural products 8.9 0.8
Pollution per unit of non-renewable resources 58.7 2.6
Pollution per unit of service 27.6 1.1
Now, the system is closed and ready to show a way. Figure 4 displays dynamics of life quality level in the two regions. A utility path is projected in a base run, where parameters values are assumed to be fixed at the
Utility, units
starting point. The selection of period is motivated by the interest of spotting development patterns of the nonlinear system. The values are measured relatively to the level of life in Krasnodar Krai, in the reference year.
100 Time, years 1 - Krasnodar Krai, 2 - the Republic of Adygea
Figure 4 - The quality of life path in Krasnodar Krai and the Republic of Adygea in the period 2014-2114
Some remarks are noteworthy with respect to figure 4. The given regions don't develop sustainably, standard of living is diminishing monotonically. Economic forces, combined with environmental, ecological conditions are not strong enough to drive along an increasing or even not declining path. Even so, they struggle to bend the line downward, what seems to be
some sort of a positive sign, reflecting tendency to an equilibrium, a bottom steady state. One way to untwine the complex resulting influence, to distinguish independent impacts is to examine the system's stocks behavior. One of them, the level of population is illustrated in figure 5.
3 Source: Rosstat, population statistics (22, 23)
4 Source: Rosstat, environment statistics (22, 23)
Population, 5,4x10A6 people
o.e
10 zo 3o 40 so 6o 70 bo 90 ioo jjme years
1 - Krasnodar Krai, 2 - the Republic of Adygea
Figure 5 - The population of Krasnodar Krai and the Republic of Adygea in the period 2014-2114
Population stocks are increasing all over the observed period. It gets support from a natural mechanism and migration. Both regions experience significant population influx, due to advantageous climatological conditions, developed social infrastructure, housing market, roads, job opportunities. Additionally, the dif-
Nonrenewable natural
ference in standards of living exerts pressure on interregional migration, moving people to more developed Krasnodar Krai. Growing population, on its ow n. as seen from the equation (1) influence per capita income in a negative way, but being accompanied may be not so noticeable. Figure 6 displays time paths of regions natural stocks.
resources, units
m so to 7s s: i»o soo Time, years
1 - Krasnodar Krai, 2 - the Republic of Adygea
Figure 6 - Non-renewable resources of Krasnodar Krai and the Republic of Adygea in the inten'al 2014-2114
Renewable ones are assumed to be extracted at the rate equal to regenerative capacity, keeping stocks of water, timber, soil, livestock, and other resources intact. While non-renewable resources stocks are declining, being governed by equation (16). Extraction path in
Krasnodar Krai is steeper, due to higher resource potential and favorable technological conditions. Such a change echoes on not only welfare but also level of environmental quality, as might be seen in figure 7, where the state of environment is described.
2
Environmental quality, units aw -
■ ' so so ■ i K: Time, years
1 - Krasnodar Krai, 2 - the Republic of Adygea
Figure 7 - Environmental quality in Krasnodar Krai and the Republic of Adygea in the inten'al 2014-2114
Pollution stocks adjust to anthropogenic activity -related wastes or emissions, specifically in industry, service sector, and field of utilization of natural resources or consumption. It is also noteworthy that considered regions ecosystems might peacefully coexist, keeping in mind mutual interdependence of ecological processes, assumed, by equation (20), Therefore, pollution in the long run has a neutral effect on standard of living and regulation levels to keep sustainable development pace might be activated somewhere else.
Another way to support a regional performance is to engage intergovermnental relations, particularly interregional allocation of a national product. The model explicitly incorporates a control parameter 'transfer'. Utility, units
By assigning values, indicated by equation (14), a regulator brings the territories back on a sustainable development path, as shown in figure 8. Indeed, in every moment the system (15) - (21) lets one identify stocks magnitudes. These C, being integrated with a region industry output and data on consumer preferences, i.e. elasticities of the utility function, may convey information, relating levels of federal government support to secure a targeted standard of living. As it might be readily seen, equation (14) has a unique solution for every non-negative value of variables involved. And this is heartening, because it suggests broad applicability of the procedure or equation either.
0
100
Time, years
10 20 30 40 50 6070 80 90
1 - Krasnodar Krai, 2 - the Republic of Adygea
Figure 8 - The trajectories ofRSD of Krasnodar Krai and the Republic of Adygea in the inten'al 2014-2114
Consequently, the conditions for 'strong' sustain-ability have been identified in regions concerned, over a given period - non-declining welfare is accompanied
with conservation of natural resources and environmental quality. But, what are regulation levels, resources tuning the system's steady state? Figure 9 portrays a transfer volume along a sustainable path.
Balancing transfer, units
Time, years
1 — Krasnodar Krai, 2 — the Republic of Adygea
Figure 9 - The amount offinancial support for sustainable development of Krasnodar Krai and the Republic of
Adygea in the interval 2014-2114
As one can see, to maintain the constant standard of living in both regions requires an increasing amount of financial support. Moreover, the rate of change is diminishing, that might be explained by a declining and positive rate of population growth, a mounting but negative rate of nonrenewable resources extraction, and stable environmental conditions. Furthermore, during the period the volume of financial assistance to the Krasnodar Krai, the Republic of Adygea should increase by 6.4 and 4.9 times, respectively. This relatively greater change of the transfer is explained by faster population growth rates, more rapid decrease in income from non-renewable resource extraction and the lower level of environmental quality.
5 CONCLUSIONS
The problem of regional sustainable development is still a hot topic. A good deal of work has been done with respect to this entangled issue from both theoretical and applied sides. Yet, on a regional scale, there is an apparent need for a further deliberation and clarification of some critical sustainability aspects, concerning resource availability, environmental quality and social equity. Of a specific interest - 'center - regions' context, interregional coordination that tend to play an independent role in determining whether a regional multifaceted performance is sustainably good or not.
To attack this abiding question the present study offers an answer - an integrated policy, explicitly incorporating social, resource, environmental processes with regulation levels, and leading to the following contributions:
1. A solution to the problem of regional sustainable development, a comprehensive regional policy to ensure 'strong' sustainability, a coherent strategy to achieve intergenerational equity, non-decreasing welfare, conserve environmental quality and natural resources.
2. Conditions for a region's human capital preservation. It has been shown, that levels of a regional social policy cannot be arbitrary, since in certain cases, these inflict an irreversible damage to a region's population stock. On contrary, a responsible attitude, particular to issues related territory inhabitation necessarily involves a close care to interregional disparities.
3. A policy for sustainable resource use. The paper demonstrates a need for careful consideration of issues concerning natural resources utilization, particularly rent regulation, 'green' investments and exhibits concerns over a region resource potential vulnerability to an open access.
4. A term 'critical carrying capacity', indicating a threshold value of a region resource potential. The paper argues that for every region there is a critical rent that drains a natural resource stock out and a size of a resource base matters - larger regions are more sustainable in terms of 'resilience' to price changes.
5. An inference that pollution could be analytically split from one side between either industry, service, resource extraction, or from the other side, between production and consumption. Such a distinction helps one examine not only an impact of an economic activity, but also assess an effect of financial aid.
The model is desirably expected to have given more than it has consumed, and at the same time has not been exhausted. Further, the model is open for extensions, and naturally appeals to the introduction of endogenously motivated output in industry or service sectors, division of labor and capital, with engaging a full-scale CGE model. These issues will be addressed in future research.
Appendix I. Specification of reinforcement causalities
Figure 10 displays cumulative causalities of the problem of regional sustainable development.
Figure 10 - Causal loop diagram of the model of regional sustainable development. Positive loops:
+ +
R1+ - Population ^ The rate of growth ^ Population;
+ +
R2+ -Environmental quality ^Assimilative capacity ^ Environmental quality;
+ +
R3+ -Natural resources ^ Resource regeneration rate ^ Natural resources;
+ +
R4+-Environmental quality ^ Environmental quality in other region ^ Environmental quality; Balancing loops:
+
Bl- -Population—> Migration —» Population;
+
B2- -Natural resources —> Depletion rate —> Natural resources.
(3 OLTTPLmNDUSTRYll qOUTPLTTINDUSTRYI
Appendix II. The RSD model variables diagram
T (5TEA1S15FER1
populalionbirthJU—POPULATTONl^ ^ populationdeathl Ct^J^[entR
O \i) J J P ®Vf rentN (3 OLTTPUTRENEWABLEl
-M A/x3 PR1CQNDUSTRY *
LmUTYl ENVI nv dsENVl f( dslevlrfel lS OLFTP UTMOMREMEWABLE1
^ W stock: VC. _ <3 PRICESERVICE1 ~
O O levlH Q - ^volumel ® b-*»—I
volumeZ
O (3 DEATHEC1 ^(3 BJRTHEC1
Oa (i LmUTYl initial O populrett
O SI (3 populationiniü Q envIett dsstock
(3 envinrtl Q
assi milati ri g ca pa cityl ____PQ^ UTK-. pclluticnL
□ uD o
NÎTGCtQ-'ÉttractionM.
* a
(3QN1 (3 9
time
o
(3 MAC
<populationdeathl ( ''
deathi Qrwi:
V
^ £3 MIGRAINEM. ' -0 «6HATI0MEN
Q myl iiik t :>-.'
O i3™ tni
- (3TC1
£
□ o
populaticnfcirthi-^®^™"2
Ievlife2
.¡nitial2 ^ populrel2 W envrel2
o
populationdeath2
stocld □
¿¡J dsENV;
(3 TRANSFER2 (3 OLFTPLmNDUÏTRY22 QOUTPLÎTINDUSTRY2
C*l PRICESERVICEZ ^
w (3 OUTPUTRENEWABLE2 (3 gl DEATH2
(3 background (3 OLFTPLFTNONRENEWABLE2 (3 E1RTH2
(3 OLFTPLFTSERV1CE2 (3 MIGRATIONEN
(3 DEATHEC2 (3 B1RTHEC2
(3QNZ
° f
c>
assimilatingcapacity2 —RQLLUTIOyi2-pollution2
NSTOCK2 EdractionN2
□ O
Figure 11 - The stocks - flows diagram of the RSD model
(3TR2 ..... f3TS2
-- (3 TNZ
Appendix III. Properties of population dynamics The examination of the equation (15) suggests that the choice of the targeted utility levels could not be arbitrary. If the value of migration coefficient passes
kl - 2 -
klM 1
L*1
and Ml is negative, then equilib-
rium solutions disappear. And on the contrary, if m is less the critical value the region's population stock has two equilibrium solutions, the larger, L , and smaller,
L
'low ,
at
L*1
Lup
-kl + ml- ^ kl- m )2 + 1
that
A
2kl
L Lup
Lup
L low
L low
L*1
Uoo
2kl
. Since L (Lup ) < 0 and L^ (L/ow ) > 0, one might
describe L , Llow as the sink and source respectively.
Figure 12 gives the graphical representation of the above solutions.
1
kl-2V(-kllVl 1/L1) ""
Figure 12 - Phase line and bifurcation diagram for population stock in the region with the lower level of life.
Appendix IV Properties of natural resource dynamics
A closer look at equation (16) let one see that not any price on natural resource is appropriate in the context of sustainability. Indeed, if the rent exceeds
-4DRl rl + rl2 RES
l0
2DR1 RES
then resource stock of
l0
first region vanishes in a finite time. Otherwise, the region enjoys equilibrium of its resource stock, and there are two solutions of this kind:
rl +
I
-4DRlrl + rl2RESin -2DRl RES,„ rent
Resup =
VRESl0
2r1 RES
+ rent
l0
ReSlow = *
^-4DRlrl + rl2RES10 -2DRl RES10 rent
_VRESl0_
rl-
2rl
RES
+ rent
l0
, and since Resj'( Resup ) < 0,
Resl (Reslow ) > 0 , these are sink and source respectively. Figure 13 shows the graphical illustration of the above solutions.
ÎES1D)/
Figure 13 - Phase line and bifurcation diagram for a regional natural resource stock.
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