Production set and its functions. Technological sets

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Methods for describing technologies.

Manufacturing is the main activity of the company. Firms use production factors, which are also called introduced (input) factors of production. For example, a bakery owner uses inputs such as worker labor, raw materials such as flour and sugar, and capital invested in ovens, stirrers, and other equipment to produce products such as bread, cakes and pastries.

We can subdivide factors of production into large categories - labor, materials and capital, each of which includes more narrow groupings. For example, labor as a production factor through an indicator of labor intensity unites both skilled (carpenters, engineers) and unskilled labor (agricultural workers), as well as the entrepreneurial efforts of company managers. Materials include steel, plastic materials, electricity, water, and any other product that a firm purchases and turns into a finished product. Capital includes buildings, equipment and inventories.

The set of all vectors of net outputs technologically accessible for a given firm is called the production set and is denoted by Y.

PRODUCTION SET- set of admissible technological ways given economic system (X, Y ) , where X - aggregate cost vectors, but Y - aggregate release vectors.

The item of m is characterized by the following features: it closed and convexly(cm. A bunch of), the cost vectors are necessarily nonzero (you cannot produce something without spending anything), the components of the PM - costs and outputs - cannot be swapped, because production is an irreversible process. The convexity of the P. m. Shows, in particular, the fact that the return on the processed resources decreases with an increase in the volume of processing.

Properties of production sets

Consider an economy with l goods. It is natural for a particular firm to regard some of these goods as factors of production and some as manufactured products. It should be noted that this division is rather arbitrary, since the company has sufficient freedom in choosing the range of products and cost structure. When describing the technology, we will distinguish between output and costs, presenting the latter as output with a minus sign. For the convenience of presenting the technology, products that are neither consumed nor produced by the firm will be referred to its output, and the volume of production of these products is considered equal to 0. In principle, a situation is not excluded in which the product produced by the firm is also consumed by it in the production process. In this case, we will consider only the net output of a given product, that is, its output minus costs.

Let the number of factors of production be equal to n, and the number of types of manufactured products equal to m, so that l = m + n. We denote the vector of costs (in absolute value) through r 2 Rn +, and the volume of outputs through y 2 Rm +

The vector (−r, yo) will be called the vector of net outputs. The set of all technologically admissible vectors of net outputs y = (−r, yo) constitutes the technological set Y. Thus, in the case under consideration, any technological set is a subset of Rn - × Rm +

This description of production is general in nature. At the same time, it is possible not to adhere to a rigid division of goods into products and factors of production: the same good can be spent with one technology, and with another, it can be produced.

Let us describe the properties of technological sets, in terms of which a description of specific classes of technologies is usually given.

1. Non-emptiness. Technological set Y is not empty. This property means the fundamental possibility of carrying out production activities.

2. Closure. Technological set Y is closed. This property is rather technical; it means that the technological set contains its own boundary, and the limit of any sequence of technologically admissible vectors of net output is also a technologically admissible vector of net outputs.

3. Freedom of spending. This property can be interpreted as the ability to produce the same amount of output, but at a greater cost, or less output at the same cost.

4. Absence of "cornucopia" ("no free lunch"). if y 2 Y and y> 0, then y = 0. This property means that the production of goods in a positive quantity requires costs in a non-zero volume.

< _ < 1, тогда y0 2 Y. Иногда это свойство называют (не совсем точно) убывающей отдачей от масштаба. В случае двух благ, когда одно затрачивается, а другое производится, убывающая отдача означает, что (максимально возможная) средняя производительность затрачиваемого фактора не возрастает. Если за час вы можете решить в лучшем случае 5 однотипных задач по микроэкономике, то за два часа в условиях убывающей отдачи вы не смогли бы решить более 10 таких задач.

fifty . Non-decreasing returns to scale: if y 2 Y and y0 = _y, where _> 1, then y0 2 Y.

In the case of two goods, where one is expended and the other is produced, increasing returns mean that the (maximum possible) average productivity of the input factor does not decrease.

500. Constant returns to scale - a situation when a technological set satisfies conditions 5 and 50 simultaneously, that is, if y 2 Y and y0 = _y0, then y0 2 Y 8_> 0.

Geometrically constant returns to scale means Y is a cone (possibly not containing 0). In the case of two goods, when one is expended and the other is produced, constant returns mean that the average productivity of the input factor does not change when the volume of production changes.

5. Nonincreasing returns to scale: if y 2 Y and y0 = _y, where 0< _ < 1, тогда y0 2 Y. Иногда это свойство называют (не совсем точно) убывающей отдачей от масштаба. В случае двух благ, когда одно затрачивается, а другое производится, убывающая отдача означает, что (максимально возможная) средняя производительность затрачиваемого фактора не возрастает. Если за час вы можете решить в лучшем случае 5 однотипных задач по микроэкономике, то за два часа в условиях убывающей отдачи вы не смогли бы решить более 10 таких задач.

fifty . Non-decreasing returns to scale: if y 2 Y and y0 = _y, where _> 1, then y0 2 Y. In the case of two goods, when one is expended and the other is produced, the increasing return means that the (maximum possible) average productivity of the input factor does not decrease.

500. Constant returns to scale - a situation when a technological set satisfies conditions 5 and 50 simultaneously, that is, if y 2 Y and y0 = _y0, then y0 2 Y 8_> 0.

Geometrically constant returns to scale means Y is a cone (possibly not containing 0).

In the case of two goods, when one is expended and the other is produced, constant returns mean that the average productivity of the input factor does not change when the volume of production changes.

6. Convexity: The convexity property means the ability to "mix" technologies in any proportion.

7. Irreversibility

Suppose that 5 bearings can be produced from a kilogram of steel. Irreversibility means that it is impossible to produce a kilogram of steel from 5 bearings.

8. Additivity. if y 2 Y and y0 2 Y, then y + y0 2 Y. The additivity property means the ability to combine technologies.

9. Permissibility of inaction:

Theorem 44:

1) From the nonincreasing returns to scale and additivity of the technological set, its convexity follows.

2) Non-increasing returns to scale follow from the convexity of the technological set and the permissibility of inaction. (The converse is not always true: with non-increasing recoil, the technology may not be convex)

3) A technological set has the properties of additivity and non-increasing returns to scale if and only if it is a convex cone.

Not all permissible technologies are equally important from an economic point of view.

Efficient technologies stand out among the admissible ones. An admissible technology y is usually called effective if there is no other (different from it) admissible technology y0 such that y0> y. Obviously, this definition of efficiency implicitly implies that all goods are desirable in some sense. Efficient technologies constitute the effective frontier of the technological set. Under certain conditions, it becomes possible to use the effective frontier in the analysis instead of the entire technological set. In this case, it is important that for any admissible technology y there is an effective technology y0 such that y0> y. In order for this condition to be fulfilled, it is required that the technological set be closed, and that within the technological set it would be impossible to increase the output of one good to infinity without reducing the output of other goods.

TECHNOLOGICAL METHOD- a general concept that combines the two: T. p. production (production method, technology) and T. p. consumption; a set of basic characteristics ( ingredients) of the production process (respectively - consumption) one or another product... IN economic and mathematical model T. s., Or technology (activity), is described by a system of inherent numbers ( vector): e.g. cost rates and release various resources per unit of time or per unit of production, etc., including coefficients material consumption, labor intensity, capital intensity, capital intensity.

For example, if x = (x 1 , ..., x m) is the vector of resource costs (listed under the numbers i = 1, 2, ..., m), but y = (y 1 , ..., y n) is the vector of production volumes of products j = 1, 2, ..., n, then technologies, technological processes, production methods can be called pairs of vectors ( x, y ). Technological acceptability means here the possibility of obtaining from the expended (used) ingredients of the vector x product vector y .

The totality of all possible acceptable technologies ( XY) forms technological or industrial set given economic system.

VECTOR- an ordered set of a certain number of real numbers (this is one of many definitions - the one that is accepted in economic and mathematical methods). For example, the daily shop plan can be written in a 4-dimensional vector (5, 3, -8, 4), where 5 means 5 thousand parts of one type, 3 - 3 thousand parts of the second type, (-8) - metal consumption in t, and the last component, for example, savings of 4 thousand kW. h of electricity. As you can see, the number of components ( coordinates) V. arbitrarily (in this case, the workshop plan may consist not of four, but of any other number of indicators); it is unacceptable to swap them; they can be either positive or negative.

Vectors can be multiplied by a real number (for example, if you increase the plan by 1.2 times in all indicators, you get a new V. with the same number of components). Vectors containing an equal number of additive components of the same name can be added and subtracted.

Letter designation V. is customary to be highlighted in bold (although this is not always observed).

The sum of vectors x = (x 1 ,..., x n) and y = (y 1 , ..., y n) is also V. ( x + y ) = (x 1 + y 1 , ..., x n + y n).

Dot product of vectors x and y is called a number equal to the sum of the products of the corresponding components of these V .:

Vectors x and y are called orthogonal if their dot product is zero.

Equality B. - component, that is, two V. are equal if their corresponding components are equal.

Vector 0 - (0, ..., 0) null;

n-dimensional V. - positive ( x > 0) if all of its components x i Above zero, non-negative (x ≥ 0) if all of its components x i greater than 0 or equal to zero, i.e. x i≤ 0; and semi-positive if, in this case, at least one component x i≥ 0 (notation x ≥ 0); if V. have an equal number of components, their ordering (complete or partial) is possible, i.e., introduction on the set of vectors binary relation “> ”: x > y , x ≥y , x ≥ y depending on whether the difference is positive, semi-positive or non-negative x - y.

The Law of Diminishing Returns- a statement that if the use of any one factor of production and at the same time the costs of all other factors are saved (they are called fixed), then the physical volume marginal product produced with the help of the specified factor will decrease (at least from a certain stage).

PRODUCTION BEAM- locus of points showing a proportional increase in the number resources when using a certain technological method with increasing intensity.

For example, if a combination of 3 units. capital (funds) and 2 units. labor (i.e., a combination of 3 K + 2L) gives 10 pts. some product, then combinations of 6 K + 4L, 9K + 6L, giving respectively 20 and 30 units. etc., will lie on the graph on a straight line called P. l. or technological beam. At a different combination of factors P. l. will have a different slope. Due to the indivisibility of many factors of production the number of technological methods and, accordingly, P. l. is accepted as final.

For example, if a brigade of three miners is working in a coal face and one more is added to them, the output will increase by a quarter, and if you add the fifth, sixth, seventh, the increase in output will decrease, and then it will stop altogether: the miners in cramped conditions will simply interfere each other.

The key concept here is marginal labor productivity (more broadly - marginal productivity of a factor of production δ Y/δ x). For example, if two factors are considered, then with an increase in the costs of one of them (the first or the second), its marginal productivity falls.

The law is applicable in the short term and for this technology (its revision changes the situation).

Let the number of factors of production be equal to n, and the number of types of products produced is equal to m, so that l = m + n. We denote the vector of costs (in absolute value) by r Rn +, and the volume of outputs by y Rm +. The vector (−r, yo) will be called vector net issues... The set of all technologically admissible vectors of net outputs y = (−r, yo) is technological multitude Y. Thus, in the case under consideration, any technological set is a subset of Rn - × Rm +.

Let us describe the properties of technological sets, in terms of which a description of specific classes of technologies is usually given.

1. Non-emptiness

Technological set Y is not empty.

This property means the fundamental possibility of carrying out production activities.

2. Closure

Technological set Y is closed.

This property is rather technical; it means that the technological set contains its own boundary, and the limit of any sequence of technologically admissible vectors of net output is also a technologically admissible vector of net outputs.

3. Freedom of spending:

if y Y and y0 6 y, then y0 Y.

This property can be interpreted as the ability to produce the same amount of output, but at a greater cost, or less output at the same cost.

4. Absence of a "cornucopia" ("no free lunch")

if y Y and y> 0, then y = 0.

This property means that for the production of goods in a positive quantity, costs in a non-zero volume are required.

Rice. 4.1. Technological multitude with increasing returns to scale.

5. Nonincreasing returns to scale:

if y Y and y0 = λy, where 0< λ < 1, тогда y0 Y.

This property is sometimes called (not quite accurately) diminishing returns to scale. In the case of two goods, when one is spent and the other is produced, diminishing returns mean that the (maximum possible) average productivity of the expended factor does not increase. If in an hour you can solve, at best, 5 problems of the same type in microeconomics, then in two hours in conditions of diminishing returns you could not solve more than 10 such problems.

fifty . Non-decreasing returns to scale:

if y Y and y0 = λy, where λ> 1, then y0 Y.

In the case of two goods, where one is expended and the other is produced, increasing returns mean that the (maximum possible) average productivity of the input factor does not decrease.

500. Constant returns to scale - a situation where a technological set satisfies conditions 5 and 50 at the same time, i.e.

if y Y and y0 = λy0, then y0 Y λ> 0.

Geometrically constant returns to scale means Y is a cone (possibly not containing 0).

Rice. 4.2. Convex technology set with diminishing returns to scale

The convexity property means the ability to "mix" technologies in any proportion.

7. Irreversibility

if y Y and y 6 = 0, then (−y) / Y.

Suppose that 5 bearings can be produced from a kilogram of steel. Irreversibility means that it is impossible to produce a kilogram of steel from 5 bearings.

8. Additivity.

if y Y and y0 Y, then y + y0 Y.

The additivity property means the ability to combine technologies.

9. Permissibility of inaction:

Theorem 44:

1) The nonincreasing returns to scale and additivity of the technological set lead to its convexity.

2) Nonincreasing returns to scale follow from the convexity of the technological set and the permissibility of inaction. (The converse is not always true: with non-increasing returns, the technology may not be convex, see Fig. 4.3 .)

3) The technological set has the properties of additivity and non-increasing

returns to scale if and only if it is a convex cone.

Rice. 4.3. Nonconvex technology set with nonincreasing returns to scale.

Not all permissible technologies are equally important from an economic point of view. Among the permissible ones stand out efficient technologies... An admissible technology y is usually called effective if there is no other (different from it) admissible technology y0 such that y0> y. Obviously, this definition of efficiency implicitly implies that all goods are desirable in some sense. Effective technologies make up effective frontier technological set. Under certain conditions, it becomes possible to use the effective frontier in the analysis instead of the entire technological set. In this case, it is important that for any admissible technology y there is an effective technology y0 such that y0> y. In order for this condition to be fulfilled, it is required that the technological set be closed, and that within the technological set it would be impossible to increase infinitely the output of one good without decreasing the output of other goods. It can be shown that if the technological

Rice. 4.4. The effective frontier of the technological set

Since the set has the property of freedom of spending, the effective boundary uniquely specifies the corresponding technological set.

Initial courses and courses of intermediate complexity, when describing the behavior of a manufacturer, rely on the representation of his production set by means of a production function. The pertinent question is under what conditions on a production set such a representation is possible. Although it is possible to give a broader definition of the production function, here and below we will only talk about “one-product” technologies, that is, m = 1.

Let R be the projection of the technological set Y onto the space of cost vectors, i.e.

R = (r Rn | yo R: (−r, yo) Y).

Definition 37:

The function f (): R 7 → R is called production function representing technology Y, if for each r R the value f (r) is the value of the following problem:

yo → max

(−r, yo) Y.

Note that any point of the effective boundary of the technological set has the form (−r, f (r)). The converse is true if f (r) is an increasing function. In this case, yo = f (r) is the effective frontier equation.

The following theorem gives the conditions under which a technological set can be represented by ??? production function.

Theorem 45:

Let, for a technological set Y R × (−R), for any r R, the set

F (r) = (yo | (−r, yo) Y)

closed and bounded from above. Then Y can be represented by a production function.

Note: The fulfillment of the conditions of this statement can be guaranteed, for example, if the set Y is closed and has the properties of non-increasing returns to scale and absence of cornucopia.

Theorem 46:

Let the set Y be closed and have the properties of nonincreasing returns to scale and the absence of a cornucopia. Then for any r R the set

F (r) = (yo | (−r, yo) Y)

closed and bounded from above.

Proof: The closedness of the sets F (r) follows directly from the closedness of Y. Let us show that F (r) are bounded from above. Suppose this is not the case and for some r R there is

there is an unboundedly increasing sequence (yn) such that yn F (r). Then, due to the nonincreasing return to scale (−r / yn , 1) Y. Therefore (due to closedness), (0, 1) Y, which contradicts the absence of a cornucopia.

Note also that if the technological set Y satisfies the hypothesis of free spending, and there is a production function f () representing it, then the set Y is described by the following relation:

Y = ((−r, yo) | yo 6 f (r), r R).

Let us now establish some relationships between the properties of the technological set and the production function that represents it.

Theorem 47:

Let the technological set Y be such that the production function f (·) is defined for all r R. Then the following is true.

1) If the set Y is convex, then the function f (·) is concave.

2) If the set Y satisfies the free spending hypothesis, then the converse is also true, i.e., if the function f (·) is concave, then the set Y is convex.

3) If Y is convex, then f () is continuous on the interior of R.

4) If the set Y possesses the property of freedom of spending, then the function f (·) does not decrease.

5) If Y has the property of not having a cornucopia, then f (0) 6 0.

6) If the set Y possesses the property of admissibility of inaction, then f (0)> 0.

Proof: (1) Let r0, r00 R. Then (−r0, f (r0)) Y and (−r00, f (r00)) Y, and

(−αr0 - (1 - α) r00, αf (r0) + (1 - α) f (r00)) Y α,

since the set Y is convex. Then, by the definition of the production function

αf (r0) + (1 - α) f (r00) 6 f (αr0 + (1 - α) r00),

which means the concavity of f (·).

(2) Since the set Y has the property of free spending, the set Y (up to the sign of the cost vector) coincides with its subgraph. And the subgraph of a concave function is a convex set.

(3) The fact to be proved follows from the fact that the concave function is continuous in the interior

its scope of definition.

(4) Let r 00> r0 (r0, r00 R). Since (−r0, f (r0)) Y, then by the property of freedom of spending (−r00, f (r0)) Y. Hence, by the definition of the production function, f (r00)> f (r0), that is, f (·) does not decrease.

(5) The inequality f (0)> 0 contradicts the assumption that there is no cornucopia. Hence, f (0) 6 0.

(6) Under the assumption of admissibility of inactivity (0, 0) Y. Hence, by definition

Assuming the existence of a production function, the properties of technology can be described directly in terms of this function. Let us show this with the example of the so-called elasticity of scale.

Let the production function be differentiable. At the point r, where f (r)> 0, we define

local elasticity of scale e (r) as:

If at some point e (r) is equal to 1, then it is assumed that at this point constant returns to scale, if more than 1 - then increasing returns, less - diminishing returns to scale... The above definition can be rewritten as follows:

P ∂f (r) e (r) = i ∂r i r i.

Theorem 48:

Let the technological set Y be described by the production function f () and

in at the point r, e (r)> 0. Then the following is true:

1) If the technological set Y has the property of decreasing returns to scale, then e (r) 6 1.

2) If the technological set Y has the property of increasing returns to scale, then e (r)> 1.

3) If Y has the property of constant returns to scale, then e (r) = 1.

Proof: (1) Consider the sequence (λn) (0< λn < 1), такую что λn → 1. Тогда (−λn r, λn f(r)) Y , откуда следует, что f(λn r) >λn f (r). We rewrite this inequality as:

	f (λn r) - f (r)
Passing to the limit, we have		λn - 1
Passing to the limit, we have
			∂ri	ri 6 f (r).



Thus, e (r) 6 1.
Properties (2) and (3) are proved similarly.

Technological sets Y can be specified in the form implicit production functions g (). By definition, a function g () is called an implicit production function if the technology y belongs to the technological set Y if and only if g (y)>

Note that such a function can always be found. For example, a function is suitable such that g (y) = 1 for y Y and g (y) = −1 for y / Y. Note, however, that this function is not differentiable. Generally speaking, not every technological set can be described by one differentiable implicit production function, and such technological sets are not something exceptional. In particular, the technological sets considered in the initial courses of microeconomics are often such that two (or more) inequalities with differentiable functions are needed to describe them, since additional constraints on the nonnegativity of production factors must be taken into account. To take into account such constraints, vector implicit

Concept 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 labor, by comparing the number and number 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 together with the loss of interest in the concept they understood the meaning of the subject-technological set only in connection with the individual.

Therefore, it is still a discovery that PTM associated with, which only sometimes can coincide with the economy of the state. The phenomenon of subject-technological set turned out to be not as simple as economists thought. 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 yardstick for comparing the development of countries.

subject-technological set

The people themselves are a product of a fairly high standard of living, which the steppe hominids achieved thanks to the appearance of some stable ones in their flocks. If for primates - gathering as a way of obtaining resources from the territory of a natural complex did not require the joining of efforts of several individuals, then hunting for large ungulates, which became the main way of ensuring 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 lying around and it is difficult to find a sharpened stick, so the hominids had to carry hunting tools with them. Together with clothes that appeared along with upright posture, the consequence of which was the deprivation of hair, and simply because of the cool climate of the steppes, STAI-PLEMENA acquire a certain set, in other words - many- items, the presence of which provides members with a hungry level of existence.

People appear together with luxury, that is, objects for which the hominids did not have time before - neither simply to appropriate objects from Nature that interested them, nor to make them by labor, since there was neither the need nor the opportunity to constantly carry them with them. Luxury items include all advanced tools., after all, for people, as one of the species of mammals, a set of vital benefits is enough for life, the production of which fully provided the subject set that was in flocks of hominids. As a biological being, a person millions of years ago could and lived above the level of the hominids with the same set of objects, but in humans it is so strong that people did not stop at the level of hominids, as it should have been for a species of animals that reached the level of prosperity. People did not have the opportunity to improve living conditions in the natural environment, so they begin to create their own artificial environment from objects of labor.

In the tribes of people he continued to act, inherited from the hominids, in the flocks of which only the leader could be the first consumer of any luxury (beautiful feathers as an example of "charm"). When the leader had a lot of feathers, he presented them to his entourage - members of high status. Such bestowing practice among other members of the tribe, it gave rise to the belief that the possession of a thing from the daily life of the leader increases the status of the owner in the hierarchy. Consumption according to status forced members of society with high rank 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 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 appeared in the everyday life of hierarchs, in copies, became the subject of consumption of high-status members, and lust 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 prestigious things has continued for thousands of years, multiplying the multitude of objects, so now we live surrounded by millions of objects that make people's lives MUCH MUCH COMFORTABLE than the ancestor's hominid lifestyle.

But biologically, a person is still the same hominid with a hierarchical instinct, which he implements in a field called -. Subject-technological set is another difference between humans and animals - this is a new artificial habitat that humans create thanks to scientific and technological progress, which is the driving force of which. As you can see, there is nothing sacred in ECONOMIC DEVELOPMENT, only satisfaction is one of the instincts.

We can say that every person is familiar, since he is born and lives surrounded by many objects, but the idea of an object-technological set appeared when they decided compare wealth of different states. And here subject-technological set turned out to be a good indicator of wealth or the degree of development. In one case, comparison by assortment is possible - 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). In another case, we can say that one society is richer than another, but then to the parameter of the assortment it is necessary to add a characteristic of the quality and technological perfection of the compared items (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 perfect and fundamentally new products and - new technologies is quite obvious, therefore, which a certain society has, presupposes not just a list of objects, but also set of technologies, allowing 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 a given state to produce all these items. And the connection with technology is supposed to be mechanical - literally, if the state has technology, then nothing prevents the production of the corresponding product.

However, with the advent of the world 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, maybe even not produced on the territory of this state and, conversely, only parts are produced, not finished products.

Here I must say that inconsistency 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 inconsistency I didn’t notice, even more - in the understanding of the previous theories - the economies of all states were equal (the difference was accepted only in size - one could be more or less than the other) and as soon as the technology was given, the OPPORTUNITY to produce anything appeared immediately.
The fact that practice refuted these theoretical assumptions did not prevent the old economic science from giving recipes for developing countries to build production of any technological complexity. A very common example is Romania, which, according to economists, has no obstacles to reaching the level of the United States of America, at least in the sphere of production, although it is clear that in order for the subject and technological set of Romania to become as large as in USA, it is necessary to have at least no less people in production. However, if the assortment of the subject-technological set of the United States exceeds the number of residents of Romania, then it is not clear who in Romania will be able to produce so many items.
There are objective limitations for development - and they are rather reduced not only to the size of the system of division of labor that can be created in the country (for example, India, where the population theoretically makes it possible to create the largest in the world, but from the theoretical possibility - India did not become richer) , and in. For example, Finland for a short time managed to take the place of the most advanced country in the production of mobile phones. But after all, the manufactured Nokia phones did not all remain within the subject-technological set of Finland, they replenished the subject set of many countries. Therefore, we must conclude - power of the 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 massive solvent DEMAND for a product.

As you can see now - 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 object set that was the first). This system can be inside or external supersystem in relation to the population. Secondly, 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 that has PMT, the system of division of labor, then it is necessary to talk about its CLOSEness, since objects from a set - as produced, so in this system and consumed.

Its scientific value subject and technological set receives with opening new object in the economy which is named which is closed, in which the items that are produced are also consumed in it. An example of a reproductive complex can be in, but the following - such as, and especially - could have a combination of several.

The term subject-technological set used it already in the first works on, when he was interested in the interaction of developed and developing countries. It was then that I began to use term subject-technological set, as a kind of characteristic of the systems of division of labor that have developed in different countries. Then it was not very clear with which entity it was connected PMT, so term subject-technological set used to characterize states when comparing them. Here he 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 concepts of PMT 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 scientific and technological 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 everyday 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 together with oblivion of all technological achievements, if the replacing system of division of labor is not able to ensure reproduction PTM in its entirety.

At the beginning of our era, a demographic crisis begins in Europe, so that the tribes cannot bud, and the desire to withdraw the surplus 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 the natural state of the period of the formation of states, which in Europe, due to the initial small size of the population that was developing it, 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 old everyday products of the Romans. The collapse of the subject set was so great that many Roman technologists were completely forgotten and 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, the water supply system in the upper floors of multi-storey buildings.

I have outlined the basic nuances of the concept subject-technological set but must lead definition of the subject-technological set from the official Glossary of Neo-Economics:

THE CONCEPT OF THE SUBJECT-TECHNOLOGICAL SET (Ptm)

This is 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 of producing 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 each period of time we have subject-technological set(PTM) different in power. As the division of labor deepens PTM expanding.

The importance of this concept is determined by the fact that it is PTM determines the possibility of scientific and technological progress. With the poor PTM new inventions, even if they manage to be implemented in the form of prototypes, as a rule, do not have a chance to go into series if they require certain products or technologies that are absent in PTM... They just turn out to be too expensive.

Related materials

Before you only excerpt from Chapter 8 of The Age of Growth in which gives description of the subject-technological set:

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 made up of technologies, that is, methods of producing goods sold on the market from and with the help of the items included in this set. I.e knowledge of the correct sequences of actions with 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 it is suddenly necessary, the restoration of the elements PTM can 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 spend enormous efforts in order to make it somehow work. But in the 18th century, hundreds of these machines worked quite successfully.

But, in general, PTM while it is expanding rather. 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 met, but let's assume that this may be so.

The second extreme case is when new elements of a set are formed as combinations of already existing elements. PTM... Such cases are just not uncommon. Already Schumpeter saw innovation as new combinations of what already exists. Let's take the same personal computers. In a sense, they cannot be said to have been "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 consists in the fact that the initial hypothesis: "this thing will be bought" - has completely come true. Although, if you think about it, then it was not at all obvious, and the greatness of the discovery lies precisely in this.

As we understand it, most of the new elements PTM represent a mixed case: closer to the first or the second. So, the historical tendency, it seems to me, is that the share of inventions close to the first type is decreasing, and the share of the second is increasing.

In general, in the light of my story about the series devices BUT and device B it is clear why this is happening. More details - in Chapter 8 of the book by clicking on the button:

Description of technology: production function, many factors of production used, isoquant map.

Production function - the technological dependence between the cost of resources and the output of products.

Formally, the production function looks like this:

Let us assume that the production function describes the output depending on the cost of labor and capital, that is, consider a two-factor model. The same amount of production can be obtained with different combinations of the costs of these resources. You can use a small number of machines (that is, get along with a small investment of capital), but you will have to spend a lot of labor; it is possible, on the contrary, to mechanize certain operations, to increase the number of machines and thereby reduce labor costs. If, for all such combinations, the largest possible volume of output remains constant, then these combinations are depicted by dots lying on the same isoquant... That is, an isoquant is a line of equal output or quantity. In the graph, x1 and x2 are the resources used.

Fixing a different amount of production, we get a different one from a quantum, that is, the same production function has isoquant map.

Isoquant properties:

isoquants have a negative slope... There is an inverse relationship between resources, that is, by reducing the amount of labor, it is necessary to increase the amount of capital in order to stay at the same level of production
isoquants are convex with respect to the origin... As already mentioned, while decreasing the use of one resource, it is necessary to increase the use of another resource. The bulge of the indifference curve with respect to the origin is a consequence of the fall in the marginal rate of technological substitution (MRTS). The third ticket tells about MRTS in detail. The gentle downward descent of the isoquant indicates a decrease in the rate of substitution of one resource for another as the share of this good in production decreases.
the absolute value of the slope of the isoquant is equal to the limiting rate of technological substitution. The angle of inclination of the isoquant at a given point shows the rate according to which one resource can be replaced by another without gaining or losing the amount of the good produced.
isoquants do not intersect... The same release level cannot be characterized by several isoquants, which contradicts their definition.

For any release level, it is possible to construct an isoquant

Mathematical justification and economic meaning of the decrease in the marginal rate of technological substitution.

Consider (substitution of labor for capital). That is, how much capital the producer is willing to give up in order to get 1 unit of labor. It is necessary to prove that this indicator is decreasing.
)

But since Q = const, therefore, dQ = 0

As you know, the marginal product of labor decreases (since a rational producer works in the second stage of production), therefore, with an increase in labor, MPL will decrease, and MPK will increase, since the amount of capital decreases, therefore, it will decrease.

The economic reason for the decrease in MRTS is that in most industries the factors of production are not completely interchangeable: they complement each other in the production process. Each factor can do what another factor of production cannot do or can make worse.

Elasticity of substitution of factors of production (conventional and logarithmic representation). Isoquant curvature and technology flexibility

The elasticity of substitution of factors of production is an indicator used in economic theory that shows how many percent it is necessary to change the ratio of factors of production when their marginal rate of substitution changes by 1% so that the volume of output remains unchanged.

Let us determine the marginal rate of replacement of capital by labor with technology

Then from the previous ticket it follows:

When plotting MRTS corresponds to the tangent of the slope of the tangent to the isoquant at the point indicating the required volumes of labor and capital to produce a given volume of output.

With a given technology, each value of the capital-labor ratio (point on the isoquant) corresponds to its own ratio between the marginal productivity of the factors of production. In other words, one of the specific characteristics of technology is how much the ratio of the marginal productivity of capital and labor changes with a small change in the capital-labor ratio, that is, the amount of capital used. This is graphically displayed by the degree of curvature of the isoquant. The quantitative measure of this property of technology is the elasticity of substitution of production factors, which shows how many percent should change the capital-labor ratio so that when the ratio of factor productivity changes by 1%, output remains unchanged. We denote; then the elasticity of substitution of factors of production

atQ= const

This is the logarithmic representation. Pzdc)

Let us denote - the marginal rate of substitution of the th factor by the th factor, and - the ratio of the number of these factors used in production. Then the elasticity of substitution will be equal to:

Moreover, it can be shown that

The only thing that I could not find was the conclusion of this "...".

The curvature of the isoquant illustrates the elasticity of substitution of factors when a given volume of product is released and reflects how easily one factor can be replaced by another. In the case when the isoquant is similar to a right angle, the probability of replacing one factor with another is extremely small. If the isoquant has the form of a straight line with a downward slope, then the probability of replacing one factor with another is significant. (for more details see about different types of functions in the fifth ticket)

Moreover, when the isoquanta is continuous, it characterizes the flexibility of the technology. That is, the company has a huge number of production options.

For an excellent understanding of this shit, check out the 5th, everything is spelled out there.

Special types of production functions (linear, Leontief, Cobb-Douglas, CES): analytical, graphical and economic presentation; the economic meaning of the coefficients; returns to scale; elasticity of output by factors of production; elasticity of substitution of factors of production.

Perfect resource interchangeability or linear production function

If the resources used in the production process are absolutely replaceable, then they are constant at all points of the isoquant, and the map of isoquants looks like in Figure 14.2. (An example of such production is a production that allows both full automation and manual production of a product).

Q = a * K + b * L, where K: L = b / a is the proportion of substitution of one resource for another (b-point of intersection of Q1 axis OK, a- axis OL)

Constant returns to scale, elasticity of substitution of resources is infinite, MRTSlk = -b / a, elasticity of output with respect to labor - c, and capital - a.

Fixed structure of resource use, also known as Leonov's function

If the technological process excludes the substitution of one factor for another and requires the use of both resources in strictly fixed proportions, the production function has the form of a Latin letter, as in Figure 14.3.

An example of this kind is the work of a digger (one shovel and one person). An increase in one of the factors without a corresponding change in the amount of another factor is irrational, therefore, only angular combinations of resources will be technically effective (the corner point is the point where the corresponding horizontal and vertical lines intersect).

Q = min (aK; bL); Constant returns to scale, K: L = b: a proportion of addition, MRTSlk = 0, elasticity of substitution 0, elasticity of output 0.

Cobb-Douglas function

A-characterizes the technology.

The elasticity of substitution of factors can be any, returns to scale (1-constant, less than one - decreasing, more than one increasing), elasticity of output with respect to factors of production for capital - alpha, for labor - beta, elasticity of substitution of factors

FunctionCES

The CES function (CES - English Constant Elastisity of Substitution) is a function used in economic theory that has the property of constant elasticity of substitution. It is sometimes also used to model a utility function. This function is primarily used to simulate a production function. Some other popular production functions are special or limiting cases of this function.

Return to scale depends on: greater than 1, increasing returns to scale, less than 1 - diminishing returns to scale, equal to 1 - constant returns to scale.

FOR THIS TICKET I COULD NOT FIND THE ELASTICITY OF THE ISSUE ANYWHERE NORMAL

The concept of economic costs. Isocosts, their economic meaning.

Economic costs- the value of other benefits that could be obtained with the most profitable use of the same resources. In this case, one speaks of "opportunity costs".

Opportunity costs arise in a world of limited resources, and therefore all human desires cannot be satisfied. If the resources were unlimited, then no one action would be carried out at the expense of another, that is, the opportunity cost of any action would be equal to zero. Obviously, in the real world of limited resources, the opportunity cost is positive.

Based on the concept of opportunity costs, we can say that economic costs- these are the payments that the firm is obliged to make, or the income that the firm is obliged to provide to the supplier of resources in order to divert these resources from use in alternative industries.

These payments can be either external or internal.
External costs are payments for resources (raw materials, fuel, transportation services - everything that the firm does not produce itself to create a product) to suppliers who do not belong to the owners of the given firm.

In addition, the firm can use certain resources that belong to itself. Own and self-used resource costs are unpaid, or internal, costs. From the firm's point of view, these internal costs are equal to the cash payments that could be received for a self-used resource if it were best used in the best possible way. normal profit as the minimum remuneration of an entrepreneur, necessary for him to continue his business and not switch to another. Thus, the economic costs look like this:

Economic costs = External costs + Internal costs (including normal profit)

Isocosta- a straight line showing all combinations of factors of production at a fixed volume of total costs.

The set of isoquants of an individual firm (map of isoquants) show the technically possible combinations of resources that provide the firm with the appropriate output volumes.

When choosing the optimal combination of resources, the manufacturer must take into account not only the technology available to him, but also their financial resources, as well as prices of relevant factors of production.

The combination of these two factors determines the area of economic resources available to the producer (his budget constraint).

B the manufacturer's budget constraint can be written as an inequality:

P K * K + P L * L TC, where

P K, P L - the price of capital, the price of labor;

TC - the total costs of the firm for the acquisition of resources.

If the manufacturer (firm) fully spends its funds on the acquisition of these resources, we get the following equality:

P K * K + P L * L = TC

On the graph, the isocost is determined in the L, K axes, therefore, for construction, it is convenient to bring the equality into the following form:

Is the isocosta equation.

The slope of the isocosta line is determined by the ratio of market prices for labor and capital: (- P L / P K)

K

L

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Production set and its functions. Technological sets

subject-technological set

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