Answer

Entrepreneurs acquire factors of production in the markets, organize production and produce products. production function - this is a technological relationship between the number of factors of production used and the maximum possible output produced during a certain period of time. Such a technological connection exists for each specific level of technological development. The production function expresses the maximum output for each combination of factors of production. The function can be represented as a table, a graph, or analytically as an equation.

If the entire set of resources necessary for production is represented as the costs of labor, capital and materials, then the production function will take the following form:

Q \u003d F (T, K, M),

where Q is the maximum volume of products produced with this technology in a given ratio: labor - T, capital - K, materials - M.

The production function shows the relationship between factors and makes it possible to determine the share of each in the creation of goods and services.

Graphically, the relationship between factors of production can be depicted as an isoquant. An isoquant is a curve that reflects various options combinations of resources that can be used to produce a certain amount of output. The set of isoquants forms an isoquant map that shows alternatives to the production function. Isoquants have the following properties:

Isoquants cannot intersect, because are the locus of equal outputs;

Isoquants are strictly convex to the origin and have a negative slope;

The higher and to the right of the isoquant, the greater the volume of output it characterizes.

The production function can only be determined empirically (experimentally), i.e. through measurements based on actual performance.

Question 7. Production possibilities of the economy

Answer

common property economic resources is their limited number, so the economy is constantly faced with the question of an alternative choice: an increase in the production of one product (commodity bundle) means the rejection of the production of a part of another. The society seeks to ensure full employment and full production in order to satisfy its needs as much as possible. concept full time characterizes the economically expedient use of all resources. Under in full production implies an efficient allocation of resources, providing the greatest output.

Alternative Choice in economics can be characterized by production possibility curve, each point of which reflects the maximum possible output of two products with given resources. Society determines which combination of these products it chooses. The functioning of the economy on the frontier of production possibilities testifies to its efficiency and the correctness of the choice of the method of production of goods. Points outside the production possibilities curve contradict the accepted condition.

The number of other products that must be sacrificed in order to get any amount of this product is called alternative ( imputed) production costs this product. It is necessary to distinguish between the opportunity costs of an additional unit of goods and the total (or total) opportunity costs. The lack of perfect elasticity or fungibility of resources has been established. It follows from this that when switching resources from the production of one product to another, each additional unit of product will require the attraction of an increasing number of additional products. This phenomenon has been named the law of increasing opportunity costs. In this way, opportunity cost law reflects the process of constant increase in opportunity costs.

The theory of opportunity costs and the production possibilities curve are used in the justification of investment programs and projects, as well as in the formation of the optimal product structure, the study of consumer behavior and in solving other issues that require the redistribution of resources.

Question 8

Answer

Factors of production (funds or capital) go through three stages: the purchase of factors of production; the process of production, where the combination of means of production and labor power takes place; sale of goods and profit.

The continuously repeating production process is called reproduction. Distinguish simple (decreasing) and extended reproduction. Simple reproduction provides a recreation of the previously achieved state of the economy - this is production on an unchanged scale. Decreasing production is typical for the crisis conditions of the economy. Under it, the scale of production is reduced. Expanded production is characterized by a constant increase in the scale of production. Allocate intensive and extensive types of expanded reproduction. At intensive type of expansion of the scale of production is achieved through qualitative improvement and best use factors of production, the use of more efficient technologies, the growth of labor productivity. Extensive type is characterized by a quantitative increase in factors of production.

The successive passage of production assets (capital) through three stages forms circulation of productive assets. The circulation of production assets, considered as a continuously repeating process, is called turnover of funds (capital). The turnover time of funds consists of production time and circulation time. The turnover of funds (capital) ends when, in the process of selling goods, the owner of the funds fully reimburses the capital advanced into the factors of production.

Depending on the specifics of turnover, production assets are divided into basic, employees long time, and negotiable, that are consumed during one production cycle.

Distinguish physical and obsolescence fixed production assets. The process of compensating for the depreciation of fixed production assets by gradually including their value in the costs of producing the goods created is called depreciation. The ratio of the amount of annually transferred depreciation deductions to the cost of labor instruments as a percentage is called depreciation rate.

circulation funds enterprises include finished products and cash enterprises. Together with revolving production assets they form working capital enterprises. turnover working capital is an important indicator of the effectiveness of their use.

Production efficiency in as a whole is determined by the ratio of the effect (result) and the cause that causes it. The most important indicators of production efficiency are: labor productivity, labor intensity, capital-labor ratio, capital productivity, capital intensity, material intensity.

Question 9. Product as a result of production

Answer

Product is the result of the expedient activity of people - labor (a thing or service) and at the same time acts as a condition for the flow of the labor process. The product ensures the reproduction of personal and material factors of production.

Distinguish between the material and social aspects of the product. Naturally real the side of a product is the combination of its properties (mechanical, chemical, physical, etc.) that make this product a useful thing that can satisfy a human need. This property of the product is called consumer value. public side product lies in the fact that each product, being the result of human labor, accumulates a certain amount of this labor.

A product made by an individual manufacturer acts as single or individual product. The result of all social production is public a product that represents the entire mass of use values ​​created in society and serves as the basis of its material and spiritual life.

According to its natural-material form, the social product is divided into means of production and personal consumption items. Means of production returned during production. They serve to replace worn-out production assets and to increase (expand) them. Items for personal consumption finally leave the sphere of production and enter the sphere of consumption. The division of the social product into means of production and articles of personal consumption makes it possible to divide all material production into two major subdivisions: production of means of production(1 division) and production of consumer goods(2 division).

In the conditions of a commodity economy, the social product has a value, the external manifestation of which is price. The cost of a product is determined by the total (cumulative) costs of its production, i.e., the costs of past (reified) labor and the costs of living labor. In Western literature, the term "good" is often used instead of the term "product".

I. ECONOMIC THEORY

10. Production function. Law of diminishing returns. scale effect

production function is the relationship between a set of factors of production and the maximum possible volume of product produced using this set of factors.

The production function is always concrete, i.e. intended for this technology. New technology is a new productivity feature.

The production function determines the minimum amount of input needed to produce a given amount of product.

Production functions, no matter what kind of production they express, have the following general properties:

1) An increase in production due to an increase in costs for only one resource has a limit (you cannot hire many workers in one room - not everyone will have places).

2) Factors of production can be complementary (workers and tools) and interchangeable (production automation).

In its most general form, the production function looks like this:

where is the volume of output;
K- capital (equipment);
M - raw materials, materials;
T - technology;
N - entrepreneurial abilities.

The simplest is the two-factor model of the Cobb-Douglas production function, which reveals the relationship between labor (L) and capital (K). These factors are interchangeable and complementary.

,

where A is a production coefficient showing the proportionality of all functions and changes when the basic technology changes (in 30-40 years);

K, L- capital and labor;

Elasticity coefficients of output for capital and labor inputs.

If = 0.25, then a 1% increase in capital costs increases output by 0.25%.

Based on the analysis of the coefficients of elasticity in the Cobb-Douglas production function, we can distinguish:
1) a proportionally increasing production function, when ( ).
2) disproportionately - increasing);
3) decreasing.

Let us consider a short period of a firm's activity, in which labor is the variable of two factors. In such a situation, the firm can increase production by using more labor resources. The graph of the Cobb-Douglas production function with one variable is shown in Fig. 10.1 (curve TP n).

In the short run, the law of diminishing marginal productivity applies.

The law of diminishing marginal productivity operates in the short run when one factor of production remains unchanged. The operation of the law presupposes an unchanged state of technology and production technology, if in manufacturing process the latest inventions and other technical improvements are applied, an increase in output can be achieved using the same production factors. That is, technological progress can change the boundaries of the law.

If capital is a fixed factor and labor is a variable factor, then the firm can increase production by employing more labor. But on the law of diminishing marginal productivity, a consistent increase in a variable resource, while the others remain unchanged, leads to diminishing returns of this factor, that is, to a decrease in the marginal product or marginal productivity of labor. If the hiring of workers continues, then in the end, they will interfere with each other (marginal productivity will become negative) and output will decrease.

The marginal productivity of labor (marginal product of labor - MP L) is the increase in output from each subsequent unit of labor

those. productivity gain to total product (TP L)

The marginal capital product MP K is defined similarly.

Based on the law of diminishing productivity, let's analyze the relationship between total (TP L), average (AP L) and marginal products (MP L) (Fig. 10.1).

There are three stages in the movement of the total product (TP) curve. At stage 1, it rises at an accelerating pace, since the marginal product (MP) increases (each new worker brings more production than the previous one) and reaches a maximum at point A, that is, the growth rate of the function is maximum. After point A (stage 2), due to the law of diminishing returns, the MP curve falls, that is, each hired worker gives a smaller increment in the total product compared to the previous one, so the growth rate of TP after TS slows down. But as long as MP is positive, TP will still increase and peak at MP=0.

Rice. 10.1. Dynamics and relationship of the total average and marginal products

At stage 3, when the number of workers becomes redundant in relation to fixed capital (machines), MR becomes negative, so TP begins to decline.

The configuration of the average product curve AR is also determined by the dynamics of the MP curve. At stage 1, both curves grow until the increment in output from newly hired workers is greater than the average productivity (AP L) of previously hired workers. But after point A (max MP), when the fourth worker adds less to the total product (TP) than the third, MP decreases, so the average output of four workers also decreases.

scale effect

1. Manifested in a change in long-term average production costs (LATC).

2. The LATC curve is the envelope of the firm's minimum short-term average cost per unit of output (Figure 10.2).

3. The long-term period in the company's activity is characterized by a change in the number of all production factors used.

Rice. 10.2. Curve of long-run and average costs of the firm

The reaction of LATC to a change in the parameters (scale) of a firm can be different (Fig. 10.3).

Rice. 10.3. Dynamics of long-term average costs

Stage I: positive effect of scale	An increase in output is accompanied by a decrease in LATC, which is explained by the effect of savings (for example, due to the deepening of the specialization of labor, the use of new technologies, the efficient use of waste).
Stage II: constant returns to scale	When the volume changes, the costs remain unchanged, that is, an increase in the amount of resources used by 10% caused an increase in production volumes also by 10%.
Stage III: negative scale effect	An increase in production (for example, by 7%) causes an increase in LATC (by 10%). The reason for the damage from the scale can be technical factors (unjustified gigantic size of the enterprise), organizational reasons (growth and inflexibility of the administrative and management apparatus).

production function

Parameter name	Meaning
Article subject:	production function
Rubric (thematic category)	Economy

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production functions are called economic-mathematical models that link variable costs with output values. The concepts of "costs" and "output" are related, as a rule, to the production process; this explains the origin of the name of this type of models. If the economy of a region or a country as a whole is considered, then aggregated production functions are developed, in which the output is an indicator of the total social product. Particular cases of production functions are release features (dependence of production volume on the availability or consumption of resources), cost functions (the relationship between the volume of production and production costs), capital cost functions (dependence of capital investments on the production capacity of the enterprises being created), etc.

Multiplicative forms of representation of production functions are widely used. In its most general form, the multiplicative production function is written as follows:

Here the coefficient A determines the dimension of quantities and depends on the chosen units of measurement of costs and output. Factors X i represent influencing factors and may have different economic content depending on what factors affect the output R. The power parameters α, β, ..., γ show the share in the growth of the final product that each of the factors contributes; they're called coefficients of elasticity of production with respect to costs of the corresponding resource and show by what percentage the output increases with an increase in the cost of this resource by one percent.

The sum of elasticity coefficients has importance to characterize the properties of the production function. Suppose that the costs of all types of resources increase in k once. Then the value of output in accordance with (7.16) will be

Therefore, if , then with an increase in costs in To times the output also increases in k once; the production function in this case is linearly homogeneous. At E > 1 the same increase in costs will lead to an increase in output by more than To times, and at E < 1 – менее чем в To times (the so-called scale effect).

An example of multiplicative production functions is the well-known Cobb-Douglas production function:

N - national income;

A – coefficient of dimension;

L, K - the volume of applied labor and fixed capital, respectively;

α and β are coefficients of elasticity of national income to labor L and capital TO.

This function was used by American researchers in the analysis of the development of the US economy in the 30s of the last century.

The efficiency of resource use is characterized by two main indicators: average (absolute ) efficiency resource

and marginal efficiency resource

The economic meaning of μi is obvious; depending on the type of resource, it characterizes such indicators as labor productivity, capital productivity, etc. The value v i shows the marginal increase in product output with an increase in the cost of the i-th resource by a "small unit" (by 1 ruble, by 1 standard hour, etc.).

Many points n -dimensional space of production factors (resources) that satisfy the condition of output constancy R (X ) = C, called isoquant. The most important properties isoquants are as follows: isoquants do not intersect each other; larger the release corresponds to the isoquant that is more distant from the origin; if all resources are absolutely necessary for production, then isoquants have no common points with coordinate hyperplanes and coordinate axes.

In material production, the concept of interchangeability of resources. In the theory of production functions, the possibilities of substitution of resources characterize the production function in terms of various combinations of inputs of resources that lead to the same level of output. Let's explain this in conditional example. Let the production of a certain amount of agricultural products require 10 workers and 2 tons of fertilizer, and if only 1 ton of fertilizer is applied to the soil, 12 workers will be required to obtain the same crop. Here, 1 ton of fertilizer (the first resource) is replaced by the labor of two workers (the second resource).

The conditions for equivalent interchangeability of resources at some point follow from the equality dP = 0:

From here marginal rate of substitution (equivalent substitutability) of any two resources k and l given by the formula

(7.20)

The marginal rate of substitution as an indicator of the production function characterizes the relative efficiency of interchangeable factors of production when moving along the isoquant. For example, for the Cobb-Douglas function, the marginal rate of replacement of labor costs by capital costs, i.e. production assets has the form

(7.21)

The minus sign on the right-hand side of formulas (7.20) and (7.21) means that with a fixed volume of production, an increase in one of the interchangeable resources corresponds to a decrease in the other.

Example 7.1. Consider an example of the Cobb-Douglas production function, for which the coefficients of output elasticity for labor and capital are known: α = 0.3; β = 0.7, as well as labor and capital costs: L = 30 thousand people; TO = 490 million rubles. Under these conditions, the marginal rate of replacement of production assets by labor costs is equal to

Thus, in this conditional example, at those points of the two-dimensional space ( L, K ), where labor and capital resources are interchangeable, a decrease in production assets by 7 thousand rubles. can be offset by an increase in labor costs per person, and vice versa.

Related to the concept of the marginal rate of substitution is the concept elasticity of resource substitution. The coefficient of elasticity of substitution characterizes the ratio of the relative change in the ratio of resource costs k and l to a relative change in the marginal rate of substitution of these resources:

This coefficient shows by what percentage the ratio between fungible resources must change in order for the marginal rate of replacement of these resources to change by 1%. The higher the elasticity of resource substitution, the more widely they can replace each other. With infinite elasticity () there are no boundaries for the interchangeability of resources. With zero elasticity of substitution () there is no possibility of replacement; in this case, the resources complement each other and must be used in a certain ratio.

Consider, in addition to the Cobb-Douglas function, some other production functions widely used as econometric models. Linear production function has the form

are the estimated parameters of the model;

, - factors of production, mutually substitutable in any proportions (elasticity of substitution ).

The isoquants of this production function form a family of parallel hyperplanes in a non-negative orthant n -dimensional space of factors.

Many studies use production functions with constant elasticity of substitution.

(7.23)

The production function (7.23) is a homogeneous function of the degree P. All elasticities of substitution of resources are equal to each other:

Therefore, this function is called function with constant elasticity of substitution (CES function ). If , the elasticity of substitution is less than one; if , the value is greater than one; when , the CES function is transformed into a multiplicative power production function (7.16).

Two factor function CES has the form

At n = 1 and p = 0, this function is transformed into a function of the type of the Cobb-Douglas function (7.17).

In addition to production functions with constant coefficients of elasticity of output from resources and constant elasticity of resource substitution, in economic analysis and forecasting, functions of more general view. An example is the function

This function differs from the Cobb-Douglas function by the factor , where z = K/L- capital-labor ratio (capital-labor ratio) of labor, and in it the elasticity of substitution takes various meanings depending on the level of capital-labor ratio. In this regard, this function belongs to the type production functions with variable elasticity of substitution (VES functions ).

Let us turn to the consideration of a number of issues of the practical use of production functions in the economy.

chemical analysis. Macroeconomic production functions are used as a tool for forecasting the volume of gross output, final product and national income, to analyze the comparative efficiency of production factors. Thus, an important condition for the growth of production and labor productivity is an increase in the capital-labor ratio of labor. If for the Cobb-Douglas function

set the condition of linear homogeneity , then from the ratio between labor productivity ( P/L ) and capital-labor ratio ( K/L )

(7.24)

it follows that labor productivity grows more slowly than the capital-labor ratio, since . This conclusion, like many other results of production function analysis, is always valid for static production functions that do not take into account improvements. technical means labor and qualitative characteristics of the resources used, i.e. regardless of technological progress. To estimate the parameters of the model (7.24), it is linearized by taking a logarithm:

Along with a quantitative increase in the amount of resources used (labor resources, production assets, etc.) the most important factor production growth is served by scientific and technological progress, which consists in improving technical means and technology, improving the skills of workers, and improving the organization of production management. Static econometric models, including static production functions, do not take into account the factor of technical progress; therefore, dynamic macroeconomic production functions are used, the parameters of which are determined by processing time series. Technological progress is usually reflected in production functions in the form of a time-dependent trend in the development of production.

For example, the Cobb-Douglas function, taking into account the technological progress factor, takes the following form:

In model (7.25), the factor reflects the trend in the development of production associated with scientific and technological progress. In this multiplier t - time, and λ - the rate of growth of output due to technical progress. In the practical use of model (7.25), to estimate its parameters, linearization is carried out by taking logarithms, similarly to model (7.24):

It should be especially noted that when constructing production functions, as for all multifactorial econometric models, it is very important point is the correct selection of influencing factors. In particular, it is necessary to get rid of the phenomena of multicollinearity of factors and the phenomena of autocorrelation within each of them. This issue is described in detail in paragraph 7.1 of this chapter. When estimating the parameters of production functions based on statistical observations, including time series, the main method is the method of least squares.

Consider the application of production functions for economic analysis and forecasting on a conditional example from the field of labor economics.

Example 7.2. Let the output of the industry be characterized by a production function of the Cobb-Douglas type:

R - the volume of output (million rubles);

T - the number of industry employees (thousand people);

F - the average annual cost of fixed production assets (million rubles).

Suppose the parameters of this production function are known and equal: a = 0.3; β = 0.7; dimension factor A = = 0.6 (thousand rubles/person) 0.3. The value of the average annual cost of fixed production assets is also known F = 900 million rubles. These conditions require:

• 1) determine the number of industry employees required to produce products in the amount of 300 million rubles;
• 2) find out how output will change with an increase in the number of employees by 1% and the same volumes of production assets;
• 3) evaluate the interchangeability of material and labor resources.

To answer the question of the first task, we linearize this production function by taking the logarithm in natural base;

whence it follows that

Substituting the initial data, we get

Hence (thousand people).

Let's consider the second task. Since , this production function is linearly homogeneous; in accordance with this, the AIR coefficients are the coefficients of output elasticity for labor and funds, respectively. Consequently, an increase in the number of employees in the industry by 1% with a constant volume of production assets will lead to an increase in output by 0.3%, i.e. the issue will amount to 300.9 million rubles.

Turning to the third task, we calculate the marginal rate of replacement of production assets with labor resources. According to formula (7.21)

Thus, subject to the interchangeability of resources to ensure the constancy of output (i.e., when moving along the isoquant), a decrease in the production assets of the industry by 3.08 thousand rubles. can be compensated by an increase in labor resources by 1 person, and vice versa.