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Producer behavior. Technology as a constraint

Features of inflationary processes in modern Russia.

1. The concept of production and PF. Production set.

2. Profit maximization problem

3. Manufacturer's equilibrium. Technical progress

4. The problem of cost minimization.

5. Aggregation in the theory of production. The equilibrium of the firm and the industry in the d / av period

(self) offer competitive firms having alternative goals

Production- activity aimed at the production of the maximum amount of material goods, depends on the number of factors of production used, given by the technological aspect of production.

Any technological process can be represented using the vector of net outputs, which will be denoted by y. If, according to this technology, the firm produces the i-th product, then the i-th coordinate of the vector y will be positive. If, on the contrary, the i-th product is spent, then this coordinate will be negative. If a certain product is not consumed and is not produced according to this technology, then the corresponding coordinate will be equal to 0.

The set of all technologically available net output vectors for a given firm will be called the production set of the firm and denoted by Y.

Production set properties:

1. The production set is not empty, i.e. The firm has access to at least one technological process.

2. The production set is closed.

3. Absence of a "cornucopia": if y 0 and y ∊Y, then y=0. You can't produce something without spending anything (no y<0, т.е. ресурсов).

4. Possibility of inactivity (liquidation): 0∊Y. in reality, sunk costs may exist.

5. Freedom of spending: y∊Y and y` y, then y`∊Y. The production set includes not only optimal, but also technologies with lower outputs/resource costs.

6. irreversibility. If y∊Y and y 0, then –y Y. If 1 of the second good can be produced from 2 units of the first good, then the reverse process is not possible.

7. Convexity: if y`∊Y, then αy + (1-α)y` ∊ Y for all α∊. Strict convexity: for all α∊(0,1). Property 7 allows combining technologies to obtain other available technologies.

8. Returns to scale:

If, in percentage terms, the volume of factors used has changed by ∆N, and the corresponding change in output was ∆Q, then the following situations take place:

- ∆N = ∆Q there is a proportional return (an increase in the number of factors led to a corresponding increase in output)

- ∆N< ∆Q there is increasing returns (positive economies of scale) – i.e. output increased in a greater proportion than the number of inputs increased

- ∆N > ∆Q there is diminishing returns (negative economies of scale) – i.e. an increase in costs leads to a smaller percentage increase in output

Scale effect is relevant in long term. If the increase in the scale of production does not lead to a change in labor productivity, we are dealing with unchanged returns to scale. Decreasing returns to scale are accompanied by a decrease in labor productivity, while increasing returns to scale are accompanied by its increase.

If the set of goods that are produced is different from the set of resources that are used, and only one good is produced, then the production set can be described using a production function.

production function(PF) - reflects the relationship between the maximum output and a certain combination of factors (labor and capital) and at a given level of technological development of society.

Q=f(f1,f2,f3,…fn)

where Q is the output of the firm for a certain period of time;

fi - the amount of the i-th resource used in the production of products;

Generally, there are three factors of production: labor, capital and materials. We restrict ourselves to the analysis of two factors: labor (L) and capital (K), then the production function takes the form: Q = f (K, L).

Types of PF may vary depending on the nature of the technology, and can be represented in three forms:

The linear PF of the form y = ax1 + bx2 is characterized by constant returns to scale.

Leontief PF - in which resources complement each other, their combination is determined by technology and production factors are not interchangeable.

PF Cobb-Douglas- a function in which the factors of production used have the property of interchangeability. General form features:

Where A is the technological coefficient, α is the labor elasticity coefficient, and β is the capital elasticity coefficient.

If the sum of the exponents (α + β) is equal to one, then the Cobb-Douglas function is linearly homogeneous, that is, it shows constant returns when the scale of production changes.

For the first time, the production function was calculated in the 1920s for the US manufacturing industry, in the form of equality

For the Cobb-Douglas PF, it is true:

1. Since a< 1 и b < 1, предельный продукт каждого фактора меньше среднего продукта (МРК < АРК и MPL < APL).

2. Since the second derivatives of the production function with respect to labor and capital are negative, it can be argued that this function is characterized by a diminishing marginal product of both labor and capital.

3. With decreasing MRTSL value, K gradually decreases. This means that the isoquants of the production function have a standard form: they are smooth isoquants with a negative slope, convex to the origin.

4. This function is characterized by a constant (equal to 1) elasticity of substitution.

5. The Cobb-Douglas function can characterize any type of returns to scale, depending on the values of the parameters a and b

6. The function under consideration can serve to describe various types technical progress.

7 The power parameters of the function are the output elasticity coefficients for capital (a) and for labor (b), so that the equation for the output growth rate (8.20) for the Cobb-Douglas function becomes GQ = Gz + aGK + bGL. Parameter a, thus, characterizes, as it were, the "contribution" of capital to the increase in output, and parameter b characterizes the "contribution" of labor.

The PF is based on a number of "production features". They deal with the output effect in three cases: (1) a proportional increase in all costs, (2) a change in the cost structure with constant output, (3) an increase in one factor of production with the rest unchanged. case (3) refers to the short-term period.

The production function with one variable factor is:

We see that the most effective change in the variable factor X is observed in the segment from point A to point B. Here, the marginal product (MP), having reached its maximum value, begins to decrease, the average product (AP) still increases, common product(TR) receives the largest gain.

Law of diminishing returns(the law of diminishing marginal product) - defines a situation in which the achievement of certain volumes of production leads to a decrease in the output of finished products per additional unit of resource introduced.

As a rule, this volume can be produced by various ways production. This is because the factors of production are interchangeable to a certain extent. It is possible to draw isoquants corresponding to all the production methods necessary for the output in a given volume. As a result, we get an isoquant map that characterizes the relationship between all possible combinations of inputs and output sizes and, therefore, is a graphical illustration of the production function.

Isoquant ( line of equal output - isoquant) - a curve that reflects all combinations of factors of production that provide the same output.

The set of isoquants, each of which shows the maximum output achieved by using certain combinations of resources, is called the isoquant map. The farther the isoquant is located from the origin, the more resources are involved in the production methods located on it and the larger the output sizes that are characterized by this isoquant (Q3> Q2> Q1).

The isoquant and its shape reflect the dependence given by the PF. In the long run, there is a certain complementarity (completeness) of factors of production, however, without a decrease in output, a certain interchangeability of these factors of production is also likely. Thus, various combinations of resources can be used to produce a good; it is possible to produce this good by using less capital and more labor, and vice versa. In the first case, production is considered technically efficient in comparison with the second case. However, there is a limit to how much labor can be replaced by more capital without reducing production. On the other hand, there is a limit manual labor without the use of machines. We will consider the isoquant in the technical substitution zone.

The level of interchangeability of factors reflects the indicator marginal rate of technical substitution. - the proportion in which one factor can be replaced by another while maintaining the same output; reflects the slope of the isoquant.

MRTS = - ∆K / ∆L = MP L / MP K

In order for output to remain unchanged when the number of factors of production used changes, the quantities of labor and capital must change in different directions. If the amount of capital is reduced (AK< 0), то количество труда должно увеличиваться (AL >0). Meanwhile, the marginal rate of technical substitution is simply the proportion in which one factor of production can be replaced by another, and as such is always positive.

Isoquants and isoclines of the PF

If we turn again to the analogy method, then, as in the case of the consumer behavior model, in modeling theory production processes we can distinguish the concept of the indifference curve of the manufacturer. This concept can correspond to many sets of production factors, which correspond to the same amount of product produced, that is:

The set of points satisfying equality (4.1) is called isoquant PF ( iso- constant, quantity- amount). Each isoquant corresponds to a different level of product production ( y ), and isoquants that are more distant from the zero point (point of inactivity) correspond to higher values y . Isoquants also have the same properties as indifference curves (they are parallel to each other, do not intersect with the abscissa and ordinate axes, etc.) For a two-factor PF, the isoquant will essentially express the functional dependence of capital costs on labor costs at a given level of output:

The manufacturer, by varying technologies, can choose different combinations of factors of production and at the same time maintain a constant level of production. According to the isoquant, an increase in one factor will lead to a decrease in the other. Therefore, there must be a characteristic that allows one to evaluate the compensation of one factor by another. Such a characteristic is marginal rate of substitution(similar to the same characteristic in consumer utility theory):

, (4.2)

which shows what increase in the factor j compensate for the decrease in the factor i per unit so that the level of production of the product remains the same (factor substitution i factor j ).

Accordingly, the reverse substitution (of factor j by factor i) will be characterized by reciprocal: .

According to the relationship between the elasticity coefficient and the marginal product (4.1), the marginal rate of substitution can be expressed as:

(4.3)

According to (4.1), for the two-factor PF we have:

- the marginal rate of substitution of capital by labor;

is the marginal rate of substitution of labor by capital.

According to (4.3), for a two-factor model, the marginal rate of substitution can also be expressed in terms of elasticity coefficients:

, where to - capital-labor ratio.

Along with isoquants, an important role in the PF is played by isoclines are the sets of points in the economic area for which the marginal rate of substitution i -th factor j -m is constant:

Using the concept of an isocline (isocline), one can transform an arbitrary set of factors (L,K) to the set (Y,MRS) , that is, by solving the system of equations:

will be:

Homogeneous PF with a constant marginal rate of substitution of labor by capital and degree of homogeneity δ=1 belongs to the class of linear functions, that is .

Thus, for a two-factor PF, each point of the isoquant is characterized by the costs of capital and labor or the marginal rate of substitution of labor by capital MRS LK and capital-labor ratio k . If we turn to the geometric representation, then MRS LK is equal to the slope of the tangent to the given point of the isoquant, and the value of k is equal to the slope of the ray emerging from the origin and passing through the given point of the isoquant (see Fig. Rice. 4.2).

Figure 4.2

For example, at the point AT the value of labor costs is greater than at the point BUT , hence the value MRS LK at the point AT less than point BUT . Accordingly, the point AT will correspond to a lower value of capital-labor ratio than at the point BUT .

Thus, the relationship between the change in capital-labor ratio and the marginal rate of labor substitution of capital becomes obvious, that is, we again come to the concept of elasticity, namely the elasticity of the substitution of labor by capital, which shows how much the capital-labor ratio will change when the marginal rate of substitution of labor by capital changes by one percent. :

(4.4)

It can also be shown graphically that, as the curvature of the isoquant increases, the elasticity Eσ decreases (see Rice. 4.3).

Figure 4.3

Note that in both cases at the points BUT and AT values MRS LK remain the same, and the value of capital-labor ratio at the point BUT higher than point AT . Another important property follows from this: for a homogeneous PF, the elasticity of the substitution of labor by capital depends only on the capital-labor ratio and remains constant along the rays starting from the zero point.

Let's express the connection between MRS LK and k with constant elasticity Eσ . According to (4.4) we have:

(4.5)

Assuming addiction MRS LK(k) , we can write (4.5) as an ordinary differential equation:

(4.6)

Integration (4.6) gives:

or after conversion:

, where

Consequently, the condition for the elasticity of the replacement of labor by capital to be constant gives a power-law relationship between the quantities MRS LK and k . Accordingly, the case of unit elasticity will correspond to a linear relationship between the indicated quantities:

The introduction of the concept of constant elasticity of substitution led to the general form of a homogeneous PF, for which the elasticity of factor substitution is constant. Such PFs are called PFs. CES class (Constant Elasticity of Substitution). The functions of this class were first proposed Arrow by Kenneth and Solow Robert in 1961. The functions of this class assume that the substitution of labor by capital is possible only within certain limits and there are no technologies that would allow producing a given amount of a product at the cost of production factors below certain critical values. (Geometrically, this means that it is possible to construct asymptotes to the isoquant, and they will correspond to the minimum possible values of labor and capital. It is possible to derive mathematical relations of the asymptotes, in this presentation we will not present this material.)

Many PFs are, in fact, special or limiting cases of CES functions, the main characteristics of which are given in Table 4.1.

Table 4.1

The concept of the production system and the production process. Technological process and technological set

The main task of any production process is the creation of added value and a new economic product, which then participates in subsequent processes of exchange and consumption. It is known that the production process is a condition for the emergence of consumption processes, on the one hand, and on the other hand, the cessation of consumption leads to the cessation of the production process. Consequently, the development of production processes is determined by the economic behavior of the consumer. This relationship can be represented as the following conceptual model for the functioning of an economic entity:

The central link is the production process model, which links the input variables of the production system with the output; the model of the resource market is a necessary condition for the functioning of the production process; product market model necessary condition the existence and resumption of the production process; decision-making model - the choice of the best decision in a certain sense of the commodity producer on output volumes based on information about market conditions and production capabilities.

Modern ideas in the field of modeling production processes are based on theories economists -neoclassical , who proposed a model of an "economic" person, whose economic behavior is determined by the utility function.

Thus, manufacturing process is the process of creating added value by purposefully transforming one set of goods into another. economic system, in which the production process is organized and takes place, is called production system or production. The goal of any production system is a desired specific final future state or outcome. economic activity. From a neoclassical point of view economic theory the producer's objectives are to maximize revenue or profit, or to minimize costs. Consumed goods in the production process are called production factors goods received as a result of the production process - production products.

From this point of view, any production system with a complex internal structure is a "black box", while the information about production factors(input information) and the product of production (result), and the unknown internal structure is described using some production function. At the same time, it must be remembered that the “black box” model is useful for an economist, but useless for a manager reforming organizational structure and processes within the system.

In addition to the concept of production functions, for modeling production processes, such concepts as the concept of elasticity of production factors, the marginal rate of substitution of production factors are important, since resources in the production system can act as substitute goods. In addition, in a real production process it is impossible to produce a product in the complete absence of any production factor, that is, we can talk about the complementarity of production factors, that is, about their complementarity.

Technology is a technical way of converting factors of production into products. There is a huge number of available technologies, from which manufacturers choose the most effective. Technology defines the relationship between an element u from among the factors of production and an element v from the product area. Technological process is a set of relationships between elements u i and vj (), so it is the simplest model production process. In turn, the set of technological processes forms technological set . Technological sets have the following properties:

1. the impossibility of the existence of a "horn of plenty", that is, a zero technological process (without the cost of production factors) belongs to the technological set and means inaction;

2. the technological set is convex, i.e. technological processes can be combined (some technological process may be a convex combination of others);

3. the technological set is limited from above, which is associated with the limited (exhaustible) resources (factors of production);

4. the technological set is closed, that is, it has boundaries.

Effective technological processes are described by points lying on the effective boundary of a convex technological set.

The method of technological sets makes it possible to describe multi-product production, since a strict transition from technological sets to production functions is possible by aggregating production factors and products.

In conclusion, we note that there are two alternative approaches to solving the problem of optimal control of production processes. The first approach considers the problem of maximizing the production of a product under fixed budget constraints. The solution to this problem is based on the analysis of the production function of the production system, taking into account the market value of labor and capital and the size of the production budget. The second approach solves the minimization problem production costs at a given level of production. This problem is solved using the cost function, which can be calculated from the available production function. These two approaches lead to the same result when solving optimization problems. ( Remember duality!).

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 that are not 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 participation (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 process is a set of processes that result in all necessary changes in the object of labor, i.e., it turns into finished products.
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. In continuous processes, there are 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 of the material flow, which can be sequential, 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.

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Producer behavior. Technology as a constraint

History of the search for solution methods

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