PROCESSES AND STRUCTURES IN ECONOMIC AND SPATIAL ANALYSIS

 

The overall aim of this paper is to show how the market mechanism may act under limited source mobility conditions by employing of the integration of economic and spatial analysis approaches. The paper deals with problems, how a limited (re)source(s) mobility determines creation of basic economic structures, how economic activities of individual competitors influence not only one another but also how the very market structures influence one another at another dimension and at another level, and how within these structures exchange processes take place.

 

1. Introductory remarks

A spatial and economic analysis disparity as well as coherence can be expressed by means of a distinction of the so-called thing scheme and the so-called situation scheme [see Körner (1970)]. In my opinion, a unification of both approaches can be achieved through an explicit modification of theoretic points of departure of perfection competition patterns applied to analyses of a market economy.

These models assume perfection mobility of goods, services and sources (often in an unexpressed way). The spatial (regional) analysis suggests, firstly, imperfection mobility of sources and differentiation of costs towards transportation of individual sources [see Nowotny (1971); Ponsard (1992)]. Secondly, from a point of view of the economic analysis it is, however, necessary to take into account costs of a market performance, costs connected with transfer of property rights towards sources themselves, as the case may be, costs related to combination and search for these sources, i.e. transaction costs.

Among these sorts of costs it is possible to include costs which are necessary to expend in order to transfer property rights towards sources only through an exchange.

2. Source(s) mobility

Perfection mobility of (re)source means that this source ceases to be a localisation factor, at least within the space which this mobility concerns. On the contrary, this source becomes such a source (in a degree of approximation to this situation) that makes possible a disparate sources allocation (at certain space-time points). These sources are necessary for the one or the other production (demanded at the one or the other locality or a certain time and at the one or the other structure [Wang (1990)].

Thinking of market interactions at a specific space and time in itself suggests a change of cost and production structure of their individual partners (agents) and of an individual structure of expenditures and production (goods, services and sources). The locally conditioned structure of expenditures, techniques and productions results in such a situation the same piece of information (as well as a price piece of information) has a different importance for different market partners.

On the one hand, it makes for a lower and especially various scale of source(s) engagement in a transformation process. On the other hand, it increases a propensity of producers to pay possessors for the employment of these sources a higher price in dependence on a degree of immobility of the one or the other source. The higher price producer pays for a source(s) employment, the more tendency of a source possessor is reduced as far as property and spatial changes of its/their employment are concerned. On the contrary, any kind of a source price-cut (=an allowance for its employment) evokes a tendency of possessors of sources to search for the use of these sources in an alternative way (in particular with a relatively higher degree of mobility).

However, from a point of view of producer this fluctuation of one of more combined used sources can threaten efficiency of a particular transformation process because productivity of other remaining sources will decrease in a considerable way which resulted in a growth of costs on one production unit. [(Levinson (1992)]

The specific (property) mobility of sources Mo1 and their specific dislocation is resulting in a certain level of an exercise of direct and indirect costs on an implementation of appropriate transaction among possessors of these sources. This mobility allows for the output level Q1. At the same time, the marginal degree of the mobility MMMo1 does not enable to abstract from expenditures on their transportation beyond an explicit frontier, determined through the distance Ds1. Endeavours of individual producers (firms) at this decision-making point D1 to enhance or maintain this mobility evoke investment processes. This increase in the output dQ in a form of investment conducts partly an equilibrium between cost and prices on the side of producers, partly it conducts the appropriate quantity of the output Q2 = Q1 + dQ.. This moment transfers an economic system on the level of the equilibrium E2. This equilibrium level decreases a demand for these sources, in dependence on a degree of effectiveness of previous investment in source(s) mobility. The conversion of the economy on this level presents its suboptimal situation in respect of the marginal degree of mobility, which enables to diffuse an economic space for expansion of individual firms by a reduction of transportation and transaction costs. These moments motivate firms now at the decision-making point D2 considering a reduction of the price level on P2, and at the same time a modified reduction of the budget limitation B3 to enlarge the production quantity on Q3.

This selfacting dynamics of an output creation, however, under the optimal economic equilibrium E3 approximating to the production possibility frontier between the property source(s) mobility Mo3 and the output level Q3 meets the movable source deficiency immediately. Consequently, sources with a lower marginal mobility degree are drawn, too.

The marginal mobility degree reduction on MMMo3 results in an enhancement of transportation and transaction costs and at the same time in a shift of the decision-making point of firms on D3. In case of an increased demand for all sources, it results in an enhancement of the price level on P3. This price motion hardens the budget limitation of all subjects (persons, firms and institutions) on B1. It leads to the production quantity reduction on Q1. This process decreases to claim to source(s) mobility on Mo1 and Ds1 because possibilities of its (their) effective exploitation from a point of view of possessors of these sources are diminished, with regard to a production possibility frontier. The equilibrium stabilises inside of (about) the initiative point E1 repeatedly.

These processes are leading both households and firms under other things equal to situation when their decision always have the negative impact on price mechanism (see Řeznik,1994a), even in spite of entirely rational expectations of all market partners (agents, participants) and on the terms of the permanent clearing up of all the markets the perfect assessment of their working in future and the perfect price elasticity,

A mobility level change will figure towards individual market subjects as random exogenous failures (disturbances, shocks) in the course of market transactions and their effects, as unexpected fluctuations with regard to a supply and demand for concrete goods and services.

Even on the assumption - that the market demands and offers the same volume and the same quality of goods, services and sources, the spatial and property spread and decomposition of supply and demand are moving day-and-night. The spatial and property diversification of the investment and the consumption shift here and there as well as off and on as well as every now and again. The source(s) mobility marginal degree always will act as a modifying factor. It will determine both the position of these sources on a "source map"[see Řezník (1997)]., and their combination inside of a transformation of a certain input quantity into a certain output quantity (production function). The fluctuation of the mobility marginal degree individualises these sources one another. During this process a qualitative differentiation of these sources takes place and can be noticed.

From a quantitative point of view the position on this source map is identified entirely by the transportation and transaction costs, both direct, as well as indirect. These position are necessary with regard to their involvement in a concrete transformation process, transportation costs are direct proportional to a growing distance between a place of creation and an employment of sources, and transaction costs are direct proportional to their property immobility. The substitution of these sources is determined by their marginal degree of mobility. The aggregation of these transformation costs (TfC) and transportation costs (TpC) are so-called communication costs (CoC). They are described by

(1) CoC = f (TfC, TpC)

By means of communication costs on their acquirement, conservation and exploitation by a consumer (or a producer as a consumer of sources), the marginal degree of source mobility is expressed. It the same time, it is possible to describe transportation costs as costs linked up with bridging over the certain physical distance, and transformation costs can be comprehended as costs related to mastery (overstressing, overcoming, surmount) of a social distance (spacing). [Klaassen, (1969)]

3. Source(s) structure

If it is possible to assume perfect mobility of all sources, it will be concerned (it can be spoken about) one and the same source then from an economic viewpoint; all sources will have an identical (absolute) substitution degree. Only in consequence of their specific mobility individual sources (and at an identical degree of their presence), reflected e.g. in their dislocation and in a (limited) degree of their mutual substitution, play and can play a different importance both in their mutual function, and in their proper exploitation.

Intuitively (on the strength of contemporary historic and theoretic evaluations), it can be showed that an output level is determined by natural conditions, labour, production funds, knowledge and social conditions. The general (complete) production function can be introduced [similarly see Siebert (1970)]:

(2) Q=f (Nc, Lb, Pf, Kn, Sc)

From a viewpoint of this present aggregation approach a level of an output (Q) depends on the above-mentioned real sources which are natural conditions Nc, labour Lb, production funds Pf, knowledge Kn and social conditions Sc.

The property mobility as well as a spatial one of these fundamental factors are complemented, conditioned and changed one another. It is possible to express an assumption that the degree of their mobility increases, from natural conditions through labour, production funds, knowledge to social conditions. Videlicet, these individual factors create a sequential progression: higher degree immobility is proper to natural conditions than labour that is again a less mobile than production funds. The very funds have a higher degree of immobility then knowledge that, for a change, is more immobile then social conditions.

This marginal degree of source mobility determines both communication costs on a source involvement in the transformation process (as if a consumer standpoint), and communication costs on the employment of this source (as if a producer standpoint). In this respect these sources figure vis-à-vis (towards themselves) firstly as determined from a viewpoint of costs on their involvement, secondly as determining (from a viewpoint of costs on a source employment). It means that the above-mentioned production function /2/ is given in a form of a square and symmetrical matrix [see Řezník (1997)] in which mutual interactions of fundamental factors seem to determine parameters of derived factors of a lower order.

(3) Q = f [ (Nc, Lb, Pf, Kn, Sc),(Nc, Lb, Pf, Kn, Sc) ]

The very production (the very transformation process) and its location is predetermined by a mobility of the one or the other fundamental factor. Considering the acquisition of every unit of utility from a given output quantity it is necessary to expend all the above-mentioned sources, hence one can explicate a left-hand side of equality in such a way that Q=1. Thus the function /3/ can be expressed as follows:

(4) 1 = (Nc, Lb, Pf, Kn, Sc) x (Nc, Lb, Pf, Kn, Sc)

Communication costs can be decomposed into transaction and transportation costs, both considering their role of determining agents, and considering their role of determined agents, therefore, each combination of the determining and determined agent puts together a relatively independent form of a concrete factor that is defined by four residual magnitudes. Their total extent has, however, a specific (stable) proportion in relation to the other concrete factors. In dependence on it an absolute and relative importance of individual fundamental and concrete factors changes; this importance increases in connection with the addition to the general marginal degree of source mobility, and it shifts thereby a production possibility frontier too.

From this position an output level is a result of the integral working of the complex of the concrete factors. Every concrete source is characterised by its indigenous spatial and property (social) mobility, its exploitation requires in itself an exercise of specific transportation and transaction costs. The "sum" (the vector) of these costs determines a mobility marginal degree of the one or the other concrete source, of its concrete form.

One can observe working of the labour towards natural conditions in natural environmental stress, working of the labour towards (on) production funds is possible to notice as a technical development. On the contrary, the production funds from a viewpoint of the labour represent for example a certain degree of its automatisation and mechanisation, with respect to the natural conditions they obtain a quantifiable (viewable) form of production capacities. A similar correlation can be found on an "intersection" of a mutual interaction of the above-mentioned fundamental factors.

Thanks to this mutual interaction these fundamental factors decompose into dimensionally fixed concrete sources which are possible to define by a marginal degree of mobility. It can be transferred this whole complex (mutual working) system of fundamental and concrete factors into a matrix table [see Řezník (1997)]. Only this level "of things"(defined in a quantitative way) allows to talk about a scarcity degree of the one or the other concrete source, about its relative deficiency or surplus, both from a individual view, and spatial one, too.

In matrix table lines as a specific multigraph are figured these forms of fundamental factors as determining factors in which they influence other fundamental factors. In matrix table columns are figured these fundamental factors as determined factors, that is to say, their size and potency are given by a sum of elements of concrete factors in a column. Knowledge significance (for a production function) is a function of experience, know-how, skill, education system and science. The position of social conditions in this function is identified by demographic structure, employment, division of labour, arts and society preferences (purposes, needs, interests and human relations).

Individual changes of concrete factors (in concrete factors) are realised thanks to existence of (horizontal and vertical) feedback, they radiate and spread in this structure in connection with shifts (changes) of a marginal mobility degree (of course, through the mediation of human activities). These flows reflect motions of communication (transportation and transaction) costs that are necessary to expend on a production unit. The higher these costs, the worse source(s) availability for these participants (partners), and the greater numbers of theirs are debarred from competition for a success on a market in advance. At the same time the very numbers of buyers and sellers determine not only the size and the extent of a market, its viability, but also at the same time its structure and working of the supply and demand.

4. Market(s) structure

The distance guards a competition against an extraneous supply, a price protects from a demand, but at the same time the other way round, too. The price level and difficulty of the source availability are out of bounds for possible partners of market transactions, they delimitate and enclose a market area under limited mobility of sources. Numbers of these partners both on the supply side, and on the demand side predetermine an appropriate market form, in which the given transaction will be realised.

When numbers of participants in exchange are growing it is possible to observe an increase in possibility of dissonance of individual preferences of these participants. These preferences as a complex cease to be single-peaked preferences. Consequently, it is possible to meet a creation of separate coalitions. Within them individuals reciprocate with services in return (to the detriment of the third side).

What is more, every individual and every group want a certain space, a certain standpoint, a spatial area position for their existence, which results in a fixed configuration (spatial settlement) of interactions among them, in a specific combination of their creation course and their influence course.

If a given phenomenon (impulse) comes out of the only point and if it has an impact on more points, it will be possible to talk about its polarisation. On the contrary, it can be discussed atomisation of a given phenomenon in this case, if impulses coming out of more points fall at one point only. If a given phenomenon comes out of one point and its implementation concerns the only point, if a given phenomenon is observed merely at the only point, then it will be possible to talk about its absolute atomisation (bilateral monopoly situation). If the identical phenomenon comes out of many points and its realisation concerns many points, it is possible to talk about its complete polarisation (perfect competition situation). The point of atomised polarisation (the adjective indicates the direction of course) comes up there where the only buyer buys from many sellers demand monopoly situation), the point of polarised atomisation comes up there where the only seller sells many buyers (supply monopoly situation). Points of partial polarisation come up again there where many sellers sell a few buyers (demand oligopoly situation), or a few sellers sell many buyers (supply oligopoly situation). Points of fractional atomisation can be found again there where the only buyer buys from a few sellers (limited demand monopoly situation), or the only seller sells a few buyers (limited supply monopoly situation).

"A) In the case of the polarised course of the origin: the more mobile the factors, the more so the atomised course of effect is possible, or the more immobile the factors, the greater probability of the polarised course of effect.

B) In the case of the atomised course of the origin: the more immobile the factors, the more so the atomised course of effect is possible, or the more mobile the factors, the more easily the course of effect can obtain the polarised character." [Siebert (1970, p. 23)]

This very face of affairs arises there and then, if each seller tries to find a maximum number of buyers for his goods and if each buyer aspires to compare a supply of many sellers and to buy from many sellers. In case that each of them is reducing supply and demand to a certain share of the market sellers as well as buyers are finding the price and the quantity of goods (which are convenient to regional and industry market). In this case they are coming to an equilibrium point defined quantitatively under monopolistic competition conditions.

The limited source(s) mobility has impacts not only on source(s) structure and market one from a point of view of numbers of the possible partners of the market. The degree of mobility has impacts both on process of exchange of goods between any two individuals as well as on ways and means (uses) of goods (sources) sharing by these individuals. Of course, these individuals behave towards the above-mentioned concrete sources as towards goods. These goods give chances of the satisfaction of their personal needs to these individuals.

If two various supply and demand curves of this sort come into a contact in this market structure, their positions shift in a figure (not for their shapes, on principle) because any way it offered and demanded a certain sum of goods for a certain price [see Řezník (1997)].

5. Good(s) structure

Thanks to limited source(s) mobility as well as thanks to burden of communication costs on the side of sellers and of buyers, supply and demand curves obtain a backward-bending shape. It means a supply begins to decrease beyond a certain border again, even when a price is growing and vice versa, a demand begins again to increase beyond a certain border again, even when a price is growing. From a nature of backward-bending curves it follows that

  1. These curves are intersecting at two points;

2) The site of this one can be both vertical, and well as horizontal; a difference of their site indicates different preferences of individuals, coming out of their different initial positions;

3) The (vertical and horizontal) supply and demand curves are intersecting in extraneous figure borders (in corners of this figure). At the same time, an extremely high supply (demand) of individual i is meeting an extremely low supply (demand) of individual k in two opposite corners. All goods behave as collective goods.

It is obvious any economic system must know how to compare goods not only with normal supply and demand curves. Nevertheless, it must manage a supply and a demand of goods characterised by backward-bending horizontal supply (SSH) and demand (DDH) curves as well backward-bending vertical supply (SSV) and demand (DDv) curves. Strictly speaking, it must manage a demand curve and a supply one of individual i, (offering a good j and demanding a good l) and a demand curve and a supply one of individual k (offering a good l and demanding a good j).

On the condition, that the two individuals can achieve their purposes by common sharing goods, services and sources too, i.e. for the two individuals it will be effective to create to this purpose a certain coalition. It is possible to convert the given situation into a position "the individual" and "the rest of the world" very easily.

The backward-bending shape of supply and demand curves means merely the fact that neither supply, nor demand can increase (decrease) continually but an effective comparison and exchange of goods thanks to their below-mentioned characteristics are possible only in certain quanta, jumps, proportions and volumes.

This backward-bending shape of supply and demand curves can be regarded as typical for a product-life-cycle model. It must create and generate its partial market gradually. A relatively high supply and a relatively low demand stand at the beginning of this cycle "face-to-face" from a point of view of a demand and a supply (gradually converging). At its conclusion, a relatively high supply and relatively low demand stand again (however, gradually distancing each other).All goods require a fixed level of a supply and of a demand under conditions of limited source(s) mobility (a threshold of a good). It follows from four latent attributes of every good that it is produced in a society and for a society in a specific time and in a specific space. This fact conditions not only a character of goods, but also a character of preferences of individuals, and it demonstrates cumulatively through following features of these goods during their consumption:

  1. They can be non-rival in consumption.. Consumption of those goods by one individual need not decrease an available quantity of good of the same kind for other individuals. Their grant to one person makes easy their use by other persons at the very least too. These goods themselves can be designated as non-rival goods. It is possible to talk about rival goods otherwise;

  2. They can be nonexclusive in consumption. A grant of a good to individual by producer can mean its grant (exploitation) to (by) other individuals. Their grant can touch other individual very relevantly. A non-rival consumption in itself is only an essential qualification, however, no sufficient one for action of the principle of non-excludability, i.e. for a border determining an area (areas) of public goods. If a good is nonexclusive in consumption, it has not importance to consider any shape of a supply curve and a demand one. Nonexclusive goods are or they are not at disposal. "When a good is nonexclusive, the transaction costs of excluding a person from obtaining it are extremely high" [Hyman (1989, p. 666)]. Nonexclusive goods are situated unavoidable out of the figure ([see Řezník (1994b)]);

  3. They can be in a certain sense indivisible. They can be offered only more persons at the same time, or effectiveness of their exploitation for each of them grows when numbers of individuals are increasing as the case may be, and so it is possible to talk about a club good;

  4. Their availability can be limited absolutely either in a natural sense or by a social context. In a certain sense outer points of backward-bending supply and demand curves are defined sharply in a negative way, and so it is possible to talk about positional goods.

The price for non-rival goods figures as a restrictive assumption, the quantity is for the rival good a restrictive assumption with regard to a supply-side, or with regard to a demand-side. The similar situation can be observed as far as club goods and positional ones are concerned.

Both for club goods, and for positional ones it holds that these characteristics of theirs can come forward only when they are shared by an explicit number of consumers, an attribute of congestion (inside of the figure marked by an inscribed circle) is peculiar to them. At the same time, congestion costs are specific for them beyond a strict frontier. The contemporaneous sharing club goods can have (together and at the same time) its frontier in a common utility maximisation. Availability of positional goods is limited in a certain moment solely on a certain constituency of users. The more the possibility of accession to a good as a club good decreases for increasing number of users, the more the supply of this good for these users is limited. If a good is used by one individual as a club good, then it is treated (beyond a certain frontier} by another individual as a positional good and vice versa.

If one of above-mentioned characteristics bears itself as a specific departure of either a backward bending supply curve or a backward bending demand one from an equilibrium point of a private good (from a point of view of one equilibrium factor), then it is possible to talk about mixed goods.

If it is possible to meet characteristics 1) and 2) at the same time, then it can be spoken about public goods. If a given good has all of these four characteristics, it is possible to specify it as a collective good. Concerned individuals can produce (or exploit) this good by a mutual agreement, or they can be forced (compelled) into producing (exploiting) it.

Positive externalities rise there and then, when a horizontal situated supply curve and a demand curve intersect on an equilibrium price level (of a private good). In case that production equilibrium level line (of a private good) is intersecting at two points with a vertically increasing supply curve of an individual i with a good j and with a vertically decreasing demand curve of an individual k for the identical (same) good. It is possible to meet negative externalities.

This aberration from an equilibrium point of a private good will appear only as breaking the property rights of somebody else, or in case of negative externalities as inability to preclude from their undesirable non-rival consumption. An intersection of appropriate supply and demand curves of individuals can be noticed only in the frontier proximity of a social or natural availability of goods, which can be advantageous or a disadvantageous to the third party. Any private good can be both a rival good, and a non-rival one in consumption, this good can be treated as a substitution good, and a complementary one.

To treat any good as a mixed one, firstly, it is necessary for this good to be non-rival to a certain extent regarding consumption, and secondly it must be a positional good with a limited availability. To treat any good as a public one, firstly, it must be non-rival concerning consumption, secondly, it must be a positional good, and thirdly, it must be a club good. To treat any good as an externality, firstly, it must be non-rival with regard to consumption, secondly, it must be a positional good, thirdly, it must be shared as a club good and fourthly, it must be nonexclusive in consumption. Therefore, exchanging of externalities are happening at the expense of the fact that social marginal utilities following from the act of the exchange are not equal to social marginal costs in a positive or a negative sense.

The very presence one of the conditions is not sufficient. Thanks to their features free and collective goods are beyond a decision-making horizon of separate (individual, particular) economic subjects (persons) because they are accessible in a way freely for everybody. If a non-rival consumption is characteristic for public goods, a non-excludability in consumption is regarded as characteristic for collective goods. Positional and club goods' features are peculiar to collective goods as well.

Step by step as follows it is possible to obtain two series of goods (their examples and their basic characteristics) that appear in intersection points of (backward-bending) supply and demand curves [see Řezník (1994b, 1997)]

6. Reserve(s) structure

An economy dilemma under limited source(s) mobility consists in the fact that a certain increase in output requires creation of the one or the other reserves in the one or the other degree at the same time, which is given by the one or the other transaction cost quantity. It means as well, however, that an existing reserve is generated at the expense of this increase, in a certain sense it restricts a quantity of this increase at the same time.

The reserve creation happens according to this quantity of expended transaction costs and according to their impact on the output creation quantity. "Co-ordinates" of this reserve determine what kind of demands are put on sectors of economy and what sort of transaction costs are necessary to expend on the output increase, connected with a necessity to create these reserves in the one or the other degree. In this case, the quantity of this output has to be taken as a sum of its increases ([see Řezník (1997)]). This configuration shows the quantity of transaction costs, connected with drawing the particular reserves (from where), at the same time it shows what sort of demands the recovery of these kinds of reserves puts on the output creation (where).

7. Concluding remarks

If limited (re)source(s) mobility leads to formation of a fundamental economic structure, then not only proper activities of individual market actors influence one other, but also at other level and at other dimension the market structures themselves too. Exchange acts and their aggregates are making inside of these structures and entirely within them.

The economy system under limited (re)source(s) mobility generates non-price data (important for individual subjects' decision-making and for a general equilibrium formation). Structures of reserves, sources, markets (institutions) and goods are a very important origin of a concrete regional historic form of this system.

Under given conditions individual market subjects are endeavouring after it so that their individual decisions may be Pareto effective in a time and a space. At the same time these subjects are endeavouring after it so that every additional following decision may bring at the least the same effect as their previous decision. Simultaneously they are endeavouring after it so that their last decision may not decrease a contribution of decisions acted in the past. In short, they are endeavouring after it so that in a space a marginal effect of every individual action of the market subject localised at one standpoint may be for this subject minimally in equilibrium with effectiveness of individual decisions of other market subjects for themselves, located at other standpoints. If these subjects co-ordinate their decisions somehow, then everybody will endeavour after the same separately, i.e after the maximisation of his marginal effect from every action of this sort.

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