The concept of the production system and the production process. Technological process and technological set. Tutorial consumer behavior theory The convexity of the element technological set means
concept is familiar to every person, since he is born and lives among a set of things that is characteristic of the material culture of his society. Even the entire economic theory begins with a description of the subject set, which he gave in his work, by comparing the number and quantity of objects and the number of professions (technologies), which determined the wealth of a particular state. Another thing is that all previous theories accepted this position axiomatically, but along with the loss of interest in the concept, they understood the meaning of the subject-technological set only in connection with a separate .
Therefore, it is still a discovery that PTM associated with, which can only sometimes coincide with the economy of the state. The phenomenon of subject- technological set turned out to be not as simple as it seemed to economists. In this article about the subject-technological set the reader will find not only description of the subject-technological set like but also a history of recognition PTM as a measure for comparing the development of countries.
subject-technological set
The people themselves are the product of a fairly high standard of living that the steppe hominids have achieved due to the appearance of some stable ones in their flocks. If for primates - gathering, as a way of obtaining resources from the territory of the natural complex, did not require the combined efforts of several individuals, then hunting for large ungulates, which became the main way to ensure the existence of hominids during the development of the steppes, was a complexly organized activity with a division of roles among several participants.
At the same time, the small size of the steppe hominids did not allow them to kill a large animal without hunting tools, even as part of a group. However, in the steppes, stones of a suitable shape are not everywhere and it is difficult to find a pointed stick, so the hominids had to carry hunting tools with them. Along with the clothes that appeared along with upright walking, the result of which was deprivation of hair, and simply - due to the cool climate of the steppes, STAI-TRIBES acquire a certain set, in other words - many- items, the presence of which provides members with a starvation level of existence.
People, on the other hand, appear along with luxury, that is, objects that hominids had no time for before - neither simply appropriate the objects that interested them from Nature, nor make them by labor, since there was neither the need nor the opportunity to constantly carry with them. Luxury goods include all improved tools, after all, for people, as one of the mammalian species, a set of life goods is enough for life, the production of which fully provided the subject set that hominids had in flocks. As a biological being, man already millions of years ago could and lived above the level of hominids with the same set of objects, but people are so strong that people did not stop at the level of hominids, as it should have been for an animal species that reached a level of prosperity. People did not have the opportunity to improve their living conditions in the natural environment, so they begin to create their own artificial environment from the objects of labor.
In the tribes of people, he continued to act, inherited from the hominids, in the flocks of which the first consumer of any luxury (beautiful feathers as an example of "charm") could only be the leader. When the leader had a lot of feathers, he gave them to his close associates - members with a high status. Such gift practice the rest of the tribe gave rise to the belief that the possession of a thing from the everyday life of the leader raises the status of the owner in the hierarchy. Consumption according to status forced high-ranking members of society to demand the most luxurious things.
At the same time, many low-ranking members are ready to sacrifice a lot in order to get things from the everyday life of the hierarchs, since the possession of these things allows them to feel an increase in their status in front of the rest. So things that first appear in the everyday life of hierarchs, in copies, became the subject of consumption of high-status members, and desire from other members with a strong hierarchical instinct led to mass production, which lowered the price, making the thing accessible to any member of the community. This race for prestige has gone on for thousands of years, multiplying the number of items, so that we now live surrounded by millions of items that make people's lives ONLY MUCH MORE COMFORTABLE than the lifestyle of the hominid ancestor.
But biologically man is still the same hominid with a hierarchical instinct, which he realizes in a field called -. Subject-technological set is another difference between man and animals - this is a new artificial habitat that man creates thanks to scientific and technological progress, which is driven by. As you can see, there is nothing sacred in ECONOMIC DEVELOPMENT, only satisfaction is one of the instincts.
We can say that it is familiar to every person, since he is born and lives surrounded by many objects, but the idea of a subject-technological set appeared when they decided compare wealth of different states. And here subject-technological set turned out to be a clear indicator of wealth or the degree of development. In one case, it is possible to compare by assortment - i.e. by the number of different subjects, which makes it possible to characterize the development of the same society over a certain period of time (which is described in the topic of scientific and technological progress). Otherwise, we can say that one society is richer than another, but then it is necessary to add a characteristic of the quality and technological perfection of the compared items to the assortment parameter (this is studied in the topic -). But, as a rule, fundamentally new objects appear in the subject set of a richer society, in the manufacture of which new technologies were used. The connection between more advanced and fundamentally new products and new technologies is quite obvious, therefore, which a certain society has, implies not just a list of items, but also technology set, which allows in the sphere of production of this society to produce these products.
For old economic theories, the unit of the economy is the economy of a sovereign state. It is the population of the state that is considered the community, the subject-technological set of which is determined by the ability of the economy of this state to produce all these items. And the connection with technologies is assumed to be mechanical - literally, if the state has technologies, then nothing prevents the production of products corresponding to them.
However, with the advent of the global system of division of labor, the inaccuracy of identifying the economy of one country with the community of people that has such an attribute as subject-technological set. The fact is that in countries participating in the international division of labor, most of the components, parts and spare parts from which finished products are assembled here can even not produced in the territory of this state and vice versa - only parts are produced, but final products are not produced.
It must be said here that discrepancy THE AVAILABILITY of technology and the POSSIBILITY to produce some products on its basis - there was also BEFORE the international division of labor, but the old economic science discrepancy I didn’t even notice, even more - in the understanding of previous theories - the economies of all states were equal (the difference was accepted only in size - one can be more or less than the other) and as soon as technology is given, the POSSIBILITY to produce anything appears immediately.
The fact that practice refuted these theoretical assumptions did not interfere with the old economics give recipes for developing countries to build production facilities of any technological complexity. A very common example is Romania, which, according to economists, has no barriers to reaching the level of the United States of America, at least in the field of production, although it is clear that in order for Romania's subject-technological set to become as large as in USA, it is necessary to have at least as many people in production. However, if the assortment of the subject-technological set of the United States exceeds the number of a resident of Romania, then it is not clear who on the territory of Romania will be able to produce so many items.
There are objective restrictions for development - and they come down rather not only to the size of the division of labor system that can be created in the country (for example, India, where the population theoretically allows you to create the largest in the world, but from a theoretical possibility - India has not become richer) , and in . For example, Finland is short term managed to take the place of the most advanced country in the production mobile phones. But after all, the manufactured Nokia phones did not all remain within the subject-technological set of Finland, they replenished the subject sets of many countries. Therefore, we must conclude - power of subject technological set specific is determined not so much by the number of people employed in production, but to a greater extent by the size of the market (the number of products depends on it), and most importantly, by the presence of a mass solvent DEMAND for the product.
As you can see now - the concept of subject-technological set not as easy as it seems. First, we now understand that subject-technological set rather associated with a certain system of division of labor, and not with the state (in the sense, although historically subject-technological set we deduce from the subject set , which was the first ). This system can be inside or external supersystem in relation to the population. Second, present subject-technological set we can, if it has a countable assortment - otherwise, the number of different items in it is finite, which implies a countable limited number of people in the community. If we mean by a community having PMT, a system of division of labor, then we must talk about its CLOSENESS, since objects from a multitude are both produced and consumed in this system.
Own scientific value subject-technological set receives with the opening new object in the economy, which is called , which represents closed, in which those items that are produced are also consumed in it. An example of a reproductive complex is in, but the following - such as, and especially - could have a combination of several.
The term subject-technological set used already in the first works on , when he was interested in the interaction of developed and developing countries. That's when I started using term subject-technological set, as a certain characteristic of the systems of division of labor that have developed in different countries. Then it was not very clear what entity it was connected with. PMT, that's why term subject-technological set was used to characterize states when comparing them. Tut followed the founder of political economy, who in his work compared the welfare of countries as a comparison of the number and volume of products that are produced by the labor of citizens.
Eligibility of use PMT concepts to the state - remained, but the reader must remember - subject-technological set characterizes closed system of division of labor, which in some models may mean economy of one independent state.
Another question directly related to the forecast of the present is Can the subject-technological set decrease? The answer is, of course, it can, although it seems to many that scientifically technical progress can only increase power of the subject-technological set, if you look at it as an attribute of the state. It is clear that some objects naturally leave the life of people, others are so improved that they no longer resemble their historical prototype. This natural process is associated with the emergence of new technologies, but, as the history of the Roman Empire has shown - subject-technological set can shrink along with the oblivion of all technological achievements, if the system of division of labor that replaces it is not able to ensure the reproduction PTM in all volume.
At the beginning of our era, a demographic crisis begins in Europe, so that the tribes cannot bud, and the desire to remove the excess population leads to land. On the periphery of the Roman Empire, states begin to turn, and it turns out that Ancient Rome (like Ancient Greece) was a branch of the eastern empire on the European continent. Indigenous Europe comes to a natural state of the period of formation of states, which in Europe, due to the initial small population of its master, has shifted centuries later than it was in the EAST. The Roman Empire did not have a chance to resist the desire of the tribes to expand, and the loss of territories destroyed the existing system of division of labor, the collapse of which led to the disappearance of demand for the former everyday products of the Romans. The collapse of the subject set was so great that many Roman technologists were completely forgotten and they were rediscovered only after a millennium, and the standard of living that existed in the cities of Ancient Rome was re-achieved in Europe only in the 19th century, for example - plumbing in the upper floors of multi-storey buildings.
I outlined the main nuances of the concept subject-technological set, but must lead definition of subject-technological set from the official Glossary of Neoconomics:
THE CONCEPT OF SUBJECT-TECHNOLOGICAL SET (PTM)
it SUBJECT-TECHNOLOGICAL SET consists of items (products, parts, types of raw materials) that actually exist in a certain system of division of labor, that is, they are produced by someone and, accordingly, consumed - sold on the market or distributed. As for the details, they may not be goods, but be part of the goods.
Another part of this set is a set of technologies, that is, methods for the production of goods sold on the market - from and / or with - using the items included in this set. That is, knowledge of the correct sequences of actions with the material elements of the set.
In every period of time we have subject-technological set(PTM) different in power. As the division of labor deepens PTM expands.
The importance of this concept lies in the fact that PTM determines the possibility of scientific and technological progress. When poor PTM new inventions, even if they can be implemented in the form of prototypes, as a rule, do not have a chance to be mass-produced if they require certain products or technologies that are not available in PTM. They just turn out to be too expensive.
Related materials
Only in front of you excerpt from Chapter 8 of The Age of Growth, in which gives description of the subject-technological set:
Let's introduce concept of subject-technological set. This set consists of items (products, parts, types of raw materials) that actually exist, that is, they are produced by someone and, accordingly, are sold on the market. As for the details, they may not be goods, but be part of the goods. The second part of this set is technologies, that is, methods for the production of goods sold on the market from and with the help of items included in this set. That is knowledge of the correct sequences of actions with the material elements of the set.
In each period of time we have a different power subject-technological set (PTM). By the way, it can not only expand. Some items cease to be produced, some technologies are lost. Maybe the drawings and descriptions remain, but in reality, if suddenly necessary, the restoration of elements PTM may be a complex project, in fact - a new invention. They say that when, in our time, they tried to reproduce the Newcomen steam engine, they had to expend great efforts in order to make it at least somehow work. But in the 18th century, hundreds of these machines worked quite successfully.
But, in general, PTM while expanding. Let's highlight two extreme cases of how this expansion can occur. The first is pure innovation, that is, a completely new item created using a previously unknown technology from completely new raw materials. I don’t know, I suspect that in reality this case has never occurred, but let’s assume that it can be so.
The second extreme case is when new set elements are formed as combinations of already existing elements. PTM. Such cases are just not uncommon. Already Schumpeter viewed innovations as new combinations of what already exists. Take the same personal computers. In a sense, it cannot be said that they were "invented". All of their components already existed, and were simply combined in a certain way.
If we can talk about some kind of discovery here, then it lies in the fact that the initial hypothesis: "they will buy this thing" - was completely justified. Although, if you think about it, then it was not at all obvious, and the greatness of the discovery lies precisely in this.
We understand that most of the new elements PTM are a mixed case: closer to the first or second. So, the historical trend, it seems to me, is that the share of inventions close to the first type is declining, while the share of the second type is increasing.
In general, in the light of my story about the devices of the series BUT and device B it is clear why this happens. For more details, see Chapter 8 of the book at the click of a button:
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Ministry of Education and Science of the Russian Federation
Yaroslav the Wise Novgorod State University
Abstract by discipline:
Management
Completed by a student gr.6061 zo
Makarova S.V.
Received by Suchkov A.V.
Velikiy Novgorod
1. PRODUCTION PROCESS AND ITS ELEMENTS.
The basis of the production and economic activity of the enterprise is the production process, which is a set of interrelated labor processes and natural processes aimed at manufacturing certain types of products.
The organization of the production process consists in combining people, tools and objects of labor into a single process for the production of material goods, as well as in ensuring a rational combination in space and time of the main, auxiliary and service processes.
Production processes at enterprises are detailed by content (process, stage, operation, element) and place of implementation (enterprise, redistribution, shop, department, site, unit).
The set of production processes occurring in the enterprise is a total production process. The process of production of each individual type of product of the enterprise is called private production process. In turn, in a private production process, partial production processes can be distinguished as complete and technologically separate elements of a private production process. production process, which are not the primary elements of the production process (it is usually carried out by workers of different specialties using equipment for various purposes).
As a primary element of the production process should be considered technological operation- a technologically homogeneous part of the production process, performed at one workplace. Technologically separate partial processes are stages of the production process.
Partial production processes can be classified according to several criteria:
For the intended purpose;
The nature of the flow in time;
The method of influencing the object of labor;
The nature of the work involved.
Processes are classified according to purpose. main, auxiliary and service.
Main production processes - processes of transformation of raw materials and materials into finished products, which is the main, profile
products for this company. These processes are determined by the manufacturing technology of this type of product (preparation of raw materials, chemical synthesis, mixing of raw materials, packaging and packaging of products).
Auxiliary production processes are aimed at the manufacture of products or the performance of services to ensure the normal flow of the main production processes. Such production processes have their own objects of labor, different from the objects of labor of the main production processes. As a rule, they are carried out in parallel with the main production processes (repair, packaging, tool facilities).
Serving production processes ensure the creation of normal conditions for the flow of the main and auxiliary production processes. They do not have their own object of labor and proceed, as a rule, sequentially with the main and auxiliary processes, interspersed with them (transportation of raw materials and finished products, their storage, quality control).
The main production processes in the main workshops (sections) of the enterprise form its main production. Auxiliary and service production processes, respectively, in auxiliary and service shops - form an auxiliary economy.
The different role of production processes in the overall production process determines the differences in the management mechanisms of various types of production units. At the same time, the classification of partial production processes according to their intended purpose can only be carried out in relation to a specific private process.
Combining the main, auxiliary, service and other processes in a certain sequence forms the structure of the production process.
The main production process represents the process and production of the main products, which includes natural processes, technological and work processes, as well as inter-operational waiting.
Natural process - a process that leads to a change in the properties and composition of the object of labor, but proceeds without human intervention (for example, in the manufacture of certain types of chemical products).
Natural production processes can be considered as necessary technological breaks between operations (cooling, drying, aging, etc.)
Technological the process is a set of processes, as a result of which all the necessary changes occur in the object of labor, i.e. it turns into a finished product.
Auxiliary operations contribute to the implementation of the main operations (transportation, control, sorting of products, etc.).
Work process - a set of all labor processes (main and auxiliary operations).
The structure of the production process changes under the influence of the technology of the equipment used, the division of labor, the organization of production, etc.
Interoperational laying - breaks provided for by the technological process.
According to the nature of the flow in time, they distinguish continuous and periodical production processes. AT continuous processes no interruptions in the production process. Production maintenance operations are carried out simultaneously or in parallel with the main operations. In periodic processes, the execution of basic and maintenance operations occurs sequentially, due to which the main production process is interrupted in time.
According to the method of impact on the object of labor, they distinguish mechanical, physical, chemical, biological and other types of production processes.
According to the nature of the labor used, production processes are classified into automated, mechanized and manual.
The principles of the organization of the production process are the starting points on the basis of which the construction, operation and development of the production process are carried out.
There are the following principles of organization of the production process:
differentiation - the division of the production process into separate parts (processes, operations, stages) and their assignment to the relevant divisions of the enterprise;
combination - the combination of all or part of diverse processes for the manufacture of certain types of products within the same site, workshop or production;
concentration - the concentration of certain production operations for the manufacture of technologically homogeneous products or the performance of functionally homogeneous work at individual workplaces, sites, workshops or production facilities of the enterprise;
specialization - assigning to each workplace and each division a strictly limited range of works, operations, parts and products;
universalization - the manufacture of parts and products of a wide range or the performance of heterogeneous production operations at each workplace or production unit;
proportionality - a combination of individual elements of the production process, which is expressed in their certain quantitative relationship with each other;
parallelism - simultaneous processing of different parts of one batch for a given operation at several workplaces, etc.;
straightness - the implementation of all stages and operations of the production process in the conditions of the shortest path of passage of the object of labor from beginning to end;
Rhythm - repetition through established periods of time of all individual production processes and a single process for the production of a certain type of product.
The above principles of organization of production in practice do not operate in isolation from each other, they are closely intertwined in each production process. The principles of the organization of production develop unevenly - in one period or another, one or another principle comes to the fore or acquires secondary importance.
If the spatial combination of elements of the production process and all its varieties is implemented on the basis of the formation of the production structure of the enterprise and its subdivisions, the organization of production processes in time finds expression in establishing the order of execution of individual logistics operations, the rational combination of execution time various kinds works, determination of calendar and planning standards for the movement of objects of labor.
The basis for building an effective production logistics system is the production schedule, formed on the basis of the task of meeting consumer demand and answering the questions: who, what, where, when and in what quantity will be produced (produced). The production schedule allows you to establish volumetric and temporal characteristics of material flows differentiated for each structural production unit.
The methods used to compile the production schedule depend on the type of production, as well as the characteristics of demand and parameters of orders can be single, small-batch, serial, large-batch, mass.
The characteristic of the type of production is supplemented by the characteristic of the production cycle - this is the period of time between the start and end of the production process in relation to specific products within the logistics system (enterprise).
The production cycle consists of working time and break time in the manufacture of products.
In turn, the working period consists of the main technological time, the time for carrying out transport in control operations and the picking time.
The time of breaks is subdivided into the time of interoperational, inter-sectional and other breaks.
The duration of the production cycle largely depends on the characteristics of the movement material flow, which is serial, parallel, parallel-serial.
In addition, the duration of the production cycle is also influenced by the forms of technological specialization of production units, the organization system of the production processes themselves, the progressiveness of the technology used and the level of unification of products.
The production cycle also includes waiting time - this is the interval from the moment an order is received to the moment it begins to be executed, to minimize which it is important to initially determine the optimal batch of products - a batch at which the cost per product is the minimum value.
To solve the problem of choosing the optimal batch, it is generally accepted that the cost of production consists of direct manufacturing costs, inventory storage costs, and equipment readjustment and downtime costs when changing batches.
In practice, the optimal batch is often determined by direct calculation, but when forming logistics systems, it is more effective to use mathematical programming methods.
In all areas of activity, but especially in production logistics, the system of norms and standards is of paramount importance. It includes both enlarged and detailed norms for the consumption of materials, energy, use of equipment, etc.
2. Methods for solving the transport problem.
Transport problem (classic)- the problem of the optimal plan for the transportation of a homogeneous product from homogeneous points of availability to homogeneous points of consumption on homogeneous vehicles (predetermined quantity) with static data and a linear approach (these are the main conditions of the problem).
For the classical transport task, two types of tasks are distinguished: the cost criterion (achieving a minimum of transportation costs) or distances and the time criterion (minimum time is spent on transportation).
History of the search for solution methods
The problem was first formalized by the French mathematician Gaspard Monge in 1781 year . The main advance was made in the fields during Great Patriotic War Soviet mathematician and economist Leonid Kantorovich . Therefore, sometimes this problem is called transport task Monge - Kantorovich.
It is characterized by variables that take an active part in changing the production function (capital, land, labor, time). Neutral technical progress is determined by such technical changes (autonomous or material form) that do not disturb the balance, that is, they are economically and socially safe for society. Let's present all this in the form of a diagram (see diagram 4.1.).
The main typical models for optimizing the production activity of a company with a linear technological set, statistical and dynamic models for planning production investments, issues of economic and mathematical analysis of economic decisions based on the use of the apparatus of dual estimates are considered. The main approaches to the problem of assessing the quality of industrial investments, as well as methods and indicators for assessing their effectiveness are outlined.
Let us consider the case, which is very important for modeling applications, when the technological set of the production system is a linear convex set , i.e., the production model turns out to be linear.
Comment. Assumptions 2.1 and 2.2 together mean that the technological set is a convex cone. Assumption 2.3, distinguishing linear technologies, means that this cone is a convex polyhedron in the half-space
Can it be argued that in the economic field of a company with a linear technological set, the production function is monotonic How is the definition of the production function related to the optimality criterion in the Kantorovich problem
Relation (3.26) makes it possible to indicate a specific type of production function for a model of a production system with a linear technological set (model (1.1) - (1.6) considered above)
The general technological set of a production element can be obtained as a result of the union of all cost-output vectors admissible from the point of view of conditions (2.1.2) and (2.1.3)
The description of the technological set of a single-product element given in the previous paragraph is the simplest. Taking into account the additional properties of the element technology leads to the need to supplement it with a number of features. We will consider some of them in this paragraph. Of course, the above considerations do not exhaust all the possibilities available in this direction.
Separable convex production model. Accounting for the nonlinearity factor in the model of production constraints described in the previous example leads to a nonlinear separable model of a multi-product element. Nonlinearity is taken into account by introducing non - linear separable production functions . The technological set of a multi-product element with such production functions has the form
In the considered technological models of production elements, the description of the technological set is given by setting the set of allowable costs and the set of allowable outputs for each level of costs. Descriptions of this kind are convenient in problems such as the optimal distribution of resources, in which, for given levels of resource consumption, it is necessary to determine the permissible and most efficient (in the sense of one or another criterion) output levels. At the same time, in practice (especially in a planned economy), there is also a kind of inverse problem, when the level of output of the elements is given by the plan and it is necessary to determine the allowable and minimum levels of costs of the elements. Problems of this kind can be conditionally called problems of optimal execution of the planned output program. In such problems, it is convenient to apply the reverse sequence of describing the technological set of a production element, first set the set U of allowable outputs and g = U, and then for each allowable level of outputs - the set V (u) of allowable costs v E = V (u).
The general technological set Y of the production element in this case has the form
On fig. 3.4 this restriction is satisfied by all points of the technological set located above the EC segment or lying on it.
For the most part, material 4.21 is also original. An assessment of the effectiveness of market mechanisms that ensure the existence of a single equilibrium management was carried out in the works. Material 4.21 is an extension of these works. Consideration of the auction scheme in the market system is carried out according to. famous model, considered as an example in this paragraph, is the market economy model. A detailed discussion of it can be found, for example, in the works. In 4.21 we assumed that a market equilibrium exists. As an examination of the auction scheme in a market system shows, this may not always be the case. Consideration of issues related to the existence of equilibrium in market models is one of the central issues of mathematical economics. In relation to models of a competitive economy, the existence of equilibrium has been established by a number of authors under various assumptions. Usually the proof assumes the convexity of utility functions (or preferences) of consumers and technology sets of producers. In the generalization of the Arrow-Debré model for the case of a continuum of players is given. At the same time, it was possible to abandon the assumptions about the convexity of consumer preference functions.
Each producer (firm) j is characterized by a technological set Y. - a set of technologically admissible l-dimensional vectors of costs - output, their positive components correspond to produced quantities, and negative - spent. It is assumed that the manufacturer chooses the cost-output vector in such a way as to maximize profit. At the same time, he, like the consumer, does not try to influence prices, taking them as given. Thus, his choice is the solution to the following problem
From (16) the weak axiom of revealed preference also follows. Inequality (16) is certainly satisfied if the demand of each of the consumers is strictly monotonous, and no special requirements are imposed on technological sets. An interpretation of the monotonicity condition and a number of related results are given in . For smooth functions of excess demand, the uniqueness of the equilibrium is also ensured by the condition of the dominant diagonal. This condition means that the module of the derivative of demand for each product at the price of this product is greater than the sum of the modules of all derivatives of demand for the same
manufacturer model. When choosing production volumes yj = y k, each firm j e J is limited by its technological set YJ with 1R1. These sets of admissible technologies can be specified, in particular, in the form of (implicit) production functions fj(yj) YJ = UZ e Rl /,(%) > 0 . Another convenient representation (when only one good h is produced) is as an explicit production function y 0.
Technological set and its properties
TECHNOLOGICAL SET - see Production set, Technological way.
Description of one specific type Let us consider a technological set for a production element that consumes several types of costs and produces products of only one type (single-product production element). The state vector of such an element has the form yt-(vtl, viz, . . . , v. x, ut). A well-known method for describing the technological set of a single-product element is based on the concept of a production function and is as follows.
It is usually assumed that the technological set of an element is a convex, closed subset of the Euclidean space Ет containing a zero element of dimension m О Е Y d Em.
The methods of representation of technological sets of production elements considered in the previous paragraph characterize their properties, but do not specify a description in an explicit form. For one-product production elements, an explicit description of the technological set can be given using the concept of production function . In 1.2 we have already touched on this concept and its use, in this section the consideration of these issues will be continued.
Using single-product production functions to describe the technological set of a multi-product element. If a multi-commodity element produces goods types of products, while consuming / gewx types of inputs, then its input and output vectors have the form , itvy), respectively.
It corresponds to a part of the technological set, limited by a curved triangle AB (marked with hatching in Fig. 3.4).
The Arrow-Deb-re-McKnzie decentralized economy model. The general model of a decentralized economy describes production, consumption and decentralized
Let us continue the study of models of balanced economic growth at a more general level and move on to models of economic well-being close to them. The latter, like growth models, are normative models.
Speaking about the welfare economy, they mean such a development when all consumers evenly reach the maximum of their utility. However, in practice, such an ideal situation rarely occurs, since the well-being of some is often achieved at the expense of the deterioration of the condition of others. Therefore, it is more realistic to speak of such a level of distribution of goods, when no consumer can increase his welfare without infringing on the interests of other consumers.
If along the trajectory of equilibrium growth, no consumer, like no producer, can acquire more without additional costs (no profit in equilibrium), then with the development of the economy along the trajectory of such “welfare”, no consumer can become richer without impoverishing while another.
It follows from the previous section that taking into account time factors in mathematical models of the economy helps to reveal a completely logical connection between economic processes and the natural growth of production and consumer opportunities. Under the conditions of linear models, under certain assumptions, the rate of such growth is equal to the percentage of capital, and the corresponding process of economic expansion is characterized by a balanced growth in the output intensities of all products and a balanced decrease in their prices. In this section, we formulate a general dynamic model of production, covering the previously considered linear models as special cases, and study the issues of balanced growth in it.
The generality of the model considered here lies in the fact that the production process is described not by the production function in general, and the linear production function (as in the Leontiev and Neumann models) in particular, but by the so-called technological set.
technological set(we denote it by the symbol ) is the set of such transformations of the economy, when the production of goods at costs is technologically possible if and only if . The couple is called production process, so the set is the set of all production processes possible with this technology. For example, in the Leontief model, the technological set j-th industry has the form 
where - gross output j-th product, and - j-th column of the technological matrix A. Therefore, the technological set in the Leontief model as a whole is 
and in the Neumann model - 
The production process, generally speaking, may contain such products that are both consumed and produced at the same time (for example, fuels and lubricants, flour, meat, etc.). In economic-mathematical models, for greater generality, it is often assumed that each product from can be both spent and produced (for example, in the Leontiev and Neumann models). In this case the vectors x and y have the same dimension and their respective components denote the same products.
Let - the amount spent i-th product, and - its output volume. Then the difference is called net release in the process . Therefore, instead of the production process, the vector of net output is often considered, characterizing this difference as flow(or intensity), i.e. net output per unit of time. At the same time, the technological set is understood as the set of all possible pure outputs. and the vector is called process with thread.
We list some properties of the technological set, which are a reflection of the fundamental laws of production.
Different production processes can be compared both in terms of efficiency and profitability.
A process is said to be more efficient than a process if , . The process is called effective, unless it contains more efficient processes than .
Let be a price vector. They say that the process more profitable than the process if the value is not less than the value .
These two options for in-kind and cost evaluation of processes are actually equivalent.
Theorem 6.1. Let be a technological set. Then a) if for the price vector the process maximizes profit on the set , then it is an efficient process; b) if is convex and is efficient in the process, then there is such a price vector , that the profit reaches a maximum at
Let us determine the structure of the technological set for those models that take into account the time factor. Consider a planning period with discrete points Let the economy be characterized by a stock of goods in a year (i.e. at the beginning of the planning period ) 
In this case, the economy is said to be in state . By the end of the period, the economy reaches a different state, which is predetermined by the previous state. In this case, we say that the production process has been implemented where is a given technological set. Here, the vector is considered as the costs incurred at the beginning of the period , and - as the output corresponding to these costs, produced with a time lag of one year. On the next steps we have production 
etc. In this way it is carried out dynamics of economic development. Such a movement of the economy is self-sustaining, since the products in the system are reproduced without any influx from outside.
A finite sequence of vectors is called acceptable trajectory of the economy(described by the technological set Z) on the time interval , if each pair of its two successive terms belongs to the set Z, i.e. 
Denote by the set of all admissible trajectories on the interval corresponding to the initial state
Let 
The trajectory is called more efficient than if the trajectory is called effective trajectory, if there is no more efficient trajectory than . The trajectory is called more profitable than if 
