The concept of marginal productivity. Marginal productivity Marginal productivity function

Economic activity of the company - those actions that it carries out in order to receive revenue.

In what follows, we will understand revenue as the total income of the company after the sale of products - that is, the product of the quantity of products sold by its price ( TR \u003d Q * P).

The economic activity of a firm can be divided into two types:

We can say that commercial activity is secondary in relation to production, that is, there can be no firms on the market that carry out only commercial activities, because someone must also produce them.

So, both commercial and production activities are components of the economic activity of the firm, the economic activity of the firm can be described by the production function:

Production function - shows I the dependence of the amount of product that a firm can produce on the volume of resources. The production function equation can be written as follows:

In the formula presented, the volume of output (maximum at these costs) is indicated by the letter Q (quantity - from the English quantity, volume), in letters F (factor) refers to the various factors of production that a firm uses to maximize output. Letter f(function) shows that the maximum output ( Q) depends on the set (n) of production factors F.

The production function was proposed in 1890 by the English mathematician A. Berry, who helped A. Marshall (English neoclassicist, 1842-1924) in the preparation of a mathematical application to his fundamental work "The principles of economic which lies in the concept of utility) and production theory (the main concept is productivity ).

In a simplified form, the production function can be represented as a release dependency ( Q), which is primarily determined by the amount of invested capital ( capital, K) and the size of the applied labor (labor, L). Then the equation of the production function will take the form:

The factors of production that we consider in the production function of the firm can be both variable and constant. What does it mean?

PRODUCTION FACTORS
variables	permanent
Their costs depend on the size release of products. I.e, if the firm wants to increase volume of output, then it should increase the amount of the variable factor.	Their costs do not depend on production output (up to a certain point)
You can change their value in the short term (number of employees - labor, raw materials, etc.)	You cannot change their value in the short term (size of a plot of land, size of a plant, technology, etc.)

Now we will depict the main functions of the company on the diagram:

If the Austrian neoclassicists developed the theory of marginal utility, then the American neoclassicist John Bates Clark (1847-1938) proposed the theory of marginal productivity of labor and capital. Clarke believed that the problem of the distribution of the social product is central to economic theory. This distribution is made in accordance with the share of participation of each of the main factors of production (labor, capital and land) in the creation of the product. Incomes of entrepreneurs and employees, according to Clarke's theory, should correspond to the real contribution of capital and labor to the final product of production (output).

Performance (or overall productivity) of each of the factors of production is determined; by how many units of the produced output fall on the unit of the used factor of production.

For example, labor productivity is calculated as follows: the number of products produced is divided by the number of workers whose labor was involved in the production of these products. The greater the result of this relationship, the higher labor productivity.

What, then, is the marginal performance?

Let the farmer own a piece of land of 1 hectare. Each additional amount of potatoes grown on this site requires additional labor costs. Then what will be the productivity of each next unit of labor applied to the land?

Ultimate performance (MRP) of a factor of production is the increase in output that is caused by the use of an additional unit of this factor.

It can be assumed that at first the marginal productivity of labor will increase (two people will be able to produce potatoes not twice as much as one, but even more), at a certain moment the marginal productivity will begin to decrease (i.e. the eleventh person will increase the total amount of harvested potatoes less than the tenth, etc.).

What is the reason for this situation? In our example, one of the factors of production (land) acted as constant, and the other (labor) as variable. Accordingly, if the value of the variable factor increases (one person, two people, three, ten, eleven), and the size of the land plot does not change, then the marginal productivity from a certain moment (for example, from the beginning of the work of the eleventh employee) begins to decrease. This is the meaning of the law of marginal productivity:

If one of the factors of production is variable, and the others are constant, then, starting from some moment, the marginal productivity of each subsequent unit of the variable factor decreases.

The law of diminishing productivity plays the same role in the theory of the firm as the assumption of diminishing marginal utility in the theory of consumption. The assumption of diminishing marginal utility allows one to explain the behavior of the consumer who maximizes the total utility, and thereby determines the nature of the demand function on price. In the same way, the law of diminishing productivity underlies the explanation of profit-maximizing producer behavior.

The manufacturer has certain production equipment located in a limited area occupied by the enterprise. He is faced with a key manufacturing question: how much should be produced? What's this best release (Q)? After all, you can increase or decrease output by hiring more or fewer workers, processing more or less raw materials, etc. And how to respond to a change (for example, an increase) in the price of a product - to hasten to increase the scale of production? This is where it is necessary to take into account the action of the law of diminishing productivity. Consider the stages of production and the impact of the law of diminishing productivity on the example of a firm.

Let's say you have a firm that uses one variable factor of production (for example, labor). All other factors of production of this firm are constant, that is, one factor of production, for example, F1 changes depending on the size of the volume of output, and all the remaining factors (F2, F3 ... Fn) remain unchanged (const).

How is the influence of a variable factor of production reflected on production and output? Let us consider this influence taking into account the following classification of products, that is, products from the point of view of the manufacturer (firm).

Profit - this is the difference between revenue for products and the cost of manufacturing these products. What makes up the profit, how is it distributed, etc. - we will consider in the lesson "Profit of the company".

Distinguish:

Aggregate product

(total product, TR)

The total amount of an economic good that is produced using a variable factor of production

Average product

(average product, AR)

The value that can be obtained by dividing the total product by the amount of the variable factor (AR):

Limit product

(marginal product, MP)

An increase (increase) in the total product caused by an increase (increase) in the use of a variable factor of production by

unit (MP):

The aggregate product increases with the growth in the use of the variable factor, but the growth of the aggregate product has technological limitations. That is, the production capabilities (achieving the best result) are limited by the technologies that it uses in production. In total, 4 stages of production are distinguished (provided that the production function will look like: Q \u003d f (L, K))... First, consider how the graph of the total product changes ( TR) depending on changes in the values \u200b\u200bof the average and marginal products:

Stage 1: labor costs increase, capital is used in a larger volume, the marginal and average product increase, and:

The total product (TP) grows more slowly than the amount of variable used.

Stage 2: the value of the marginal product decreases and MP \u003d AP

The total product (TP) grows faster than the variable factor.

Stage 3:the value of the marginal product continues to decline and

The total product (TP) grows more slowly than the amount of the variable.

Stage 4:marginal product takes a negative value

An increase in the variable factor leads to a decrease in the output of the aggregate product.

Based on these graphs, you can evaluate and understand when it is necessary to stop increasing the variable factor in production. The total product reaches its maximum at the point at which the marginal product is zero, that is, after point 3, the marginal product begins to take negative values. This means that it becomes unprofitable for the manufacturer to continue to increase the variable factor with these technologies and production volumes.

The law of marginal productivity was derived not theoretically, but experimentally. Economists of the 19th century limited the scope of the law of diminishing productivity to agriculture, without extending it to other sectors of production. The limitedness of a constant factor of land production, a relatively low rate of technological progress compared to other industries, a relatively stable range of crops grown - all these circumstances have determined the visibility of the law in question in agricultural production. But already at the end of the Х1Х-beginning of the XX century. scientists have come to understand the universality of this law. Indeed, after all, in an industrial enterprise there are always constant factors of production. This is both the available equipment and the occupied territory. In a short period, when the technological process remains unchanged, and the amount of at least one factor of production is fixed, there will inevitably come a moment when each next used unit of a variable factor will cause a smaller increase in output than the previous one. True, in the long run, when the manufacturer has the opportunity to change technologies and the size of production, the curve of the total product shifts upward, which means that it becomes possible to use a larger amount of variable factor with a positive result.

An increase in labor productivity is manifested in the fact that the share of living labor in manufactured products decreases, while the share of past labor increases, while the absolute value of the costs of living and materialized labor per unit of output decreases. The change in labor productivity (IPT index) for a certain period in terms of production (B) or labor intensity (T) can be determined using the following formulas:

I pt \u003d V o / V b or I pt \u003d T b / T about;

PT \u003d V o / V b × 100 or PT \u003d (T b / T o) × 100;

ΔPT \u003d [(V 0 - V b) / V b] × 100 or ΔPT \u003d [(T b - T 0) / T 0] × 100,

where В 0 and В б - production output, respectively, in the reporting and base periods in the corresponding units of measurement;

T 0 and T b - the labor intensity of products in the reporting and base periods, standard-h or man-h;

PT is the growth rate of labor productivity,%;

ΔПТ - labor productivity growth rate,%.

Labor productivity planning for sections, workshops, workplaces is carried out by a direct method according to the formulas listed above. In general, for the enterprise (firm), labor productivity planning is carried out according to the main technical and economic factors in the following order:

the economy of the number from the development and implementation of each measure to increase labor productivity is determined (E i);

the total economy of the number (E h) is calculated under the influence of all technical and economic factors and measures (E H \u003d ∑E i);

the increase in labor productivity at the enterprise (in the shop, on the site) is calculated, achieved under the influence of all factors and measures (ΔPT) according to the formula ΔPT \u003d E h × 100 / (Ch p - E h), where Ch p is the number of industrial and production personnel required to fulfill the annual production volume while maintaining the output (productivity) of the base (past) period, people.

The level of labor productivity at the enterprise and the possibility of its increase are determined by a number of factors and growth reserves. The factors of growth in labor productivity are understood as the reasons for changes in its level. The reserves for the growth of labor productivity at the enterprise are understood to be the still unused real possibilities of saving labor resources. Factors in the growth of labor productivity depend on the industry sector of the enterprise and a number of other reasons, but it is generally accepted to distinguish the following groups of factors:

Raising the technical level of production;

Improving the organization of production and labor;

Change in production volume and structural changes in production;

Changes in external, natural conditions;

Other factors.

In the market economy, the concept of marginal labor productivity is becoming more widespread, according to which an additional increase in the number of employees leads to an ever-smaller increase in the marginal product. In this case, the marginal product of labor is understood as the amount of additional production that the company will receive by hiring one additional employee.

Multiplying the marginal product by its price, we get the monetary expression of the marginal product, or the marginal (or additional) income from the hiring of the last employee.

In the case when the marginal product of labor is greater than the marginal cost of wages, it is necessary to increase the number of employees, while the total profit of the enterprise with an increase in the number of employees should increase.

If the marginal product of labor is less than the marginal cost of wages, then profit begins to decrease with the last employee hired. Therefore, it is possible to increase profits only by reducing the number of employees.

Thus, profit maximization is possible only at such a level of employment in the enterprise, when the marginal income received as a result of the work of the last hired employee is equal to the marginal cost of remuneration of his labor.

PLANNING THE NUMBER OF EMPLOYEES OF THE ENTERPRISE (FIRM). CALCULATION OF THE BUDGET OF THE WORKING TIME

The headcount rate (N h) is the established number of employees of a certain professional and qualification composition, necessary to perform specific production, managerial functions or volumes of work. According to the norms of the number, labor costs are determined by professions, specialties, groups or types of work, individual functions, as a whole for the enterprise, workshop or its structural unit.

The number of employees is the most important quantitative indicator characterizing the labor resources of an enterprise. It is measured by such indicators as payroll, attendance and average number of employees.

The payroll number of employees of an enterprise is an indicator of the number of employees on the payroll for a certain number or date, for example, on May 20. It takes into account the number of all employees of the enterprise hired for permanent, seasonal and temporary work in accordance with the concluded labor agreements (contracts).

The turnout characterizes the number of employees on the payroll who came to work on a given day, including those on business trips. This is the number of workers required to complete a production shift assignment for production.

Average headcount - the average number of employees for a certain period (month, quarter, from the beginning of the year, for the year).

The average number of employees per month is determined by summing up the number of employees on the payroll for each calendar day of the month, including holidays and weekends, and dividing the amount received by the number of calendar days of the month.

Determination of the need for personnel at the enterprise (firm) is carried out separately for groups of industrial and production and non-industrial personnel. The initial data for determining the number of employees are: production program; time, production and service rates; nominal (real) budget of working time for the year; measures to reduce labor costs, etc. The main methods for calculating the quantitative need for personnel are calculations of the labor intensity of the production program; production rates; service standards; workplaces.

The standard for the number of workers (main workers-pieceworkers) (N h) according to the labor intensity of the production program is determined by the formula

H h \u003d T pl / (F n × K ext),

where T pl is the planned labor intensity of the production program, standard-h;

Ф n - standard balance of working time of one worker per year, h;

K vn - coefficient of fulfillment of time norms by workers.

The planned labor intensity of the production program is determined by the planned standard of labor costs per unit of output, multiplied by the planned output. The method for calculating the number of personnel according to the labor intensity of the production program is the most accurate and reliable, since it requires the application of labor standards. Determination of the number of workers according to production rates is more simplified and less precise in connection with the pricing of products (works, services).

When determining the number of workers according to production rates, the formula can be used:

H h \u003d OP pl / (H vyr × K ext),

where OP PL is the planned volume of production (work performed) in the established units of measurement for a certain period of time;

H vyr - planned production rate in the same units of measurement and for the same period of time.

Planning the number of main workers in the apparatus processes and auxiliary workers performing work for which there are service standards is reduced to determining the total number of service objects, taking into account the shift of work:

H h \u003d K o / N o × C × K cn,

where K about - the number of units of installed equipment;

С is the number of work shifts;

K cn - coefficient of conversion of the number of workers on the list;

N o - service rate (number of pieces of equipment serviced by one worker).

In discontinuous production K cn is defined as the ratio of the nominal fund of time to the useful (effective), and in continuous - as the ratio of the calendar fund of time to the useful (effective).

By jobs, the number of auxiliary workers is usually determined, for whom neither the amount of work nor the norms of service can be established (for example, crane operators, slingers, etc.):

H h \u003d M × C × K cn,

where M is the number of jobs.

The number of service personnel can also be determined by generalized service standards, for example, the number of cleaners can be determined by the number of square meters of floor space, cloakroom attendants - by the number of people served, etc.

The number of employees can be determined based on the analysis of industry average data, and in their absence - according to the standards developed by the enterprise. The number of managers can be determined taking into account the norms of manageability and a number of other factors.

In addition to the number of employees, a quantitative characteristic of the labor potential of an enterprise and / or its internal subdivisions can be presented as a fund of labor resources in man-days or man-hours. Such a fund (F rt) can be determined by multiplying the average number of employees (H sp) by the average duration of the working period in days or hours (T rw):

F rt \u003d H cn × T rv.

The duration of working time (T pw) in the planning period can be determined based on the working time budget using the following formula:

T pw \u003d (T k - T in - T prz - T about - T b - T y - T g - T pr) × P cm - (T km + T p + T s),

where T to - the number of calendar days in a year;

T in - the number of days off per year;

T prz - the number of holidays in a year;

T about - duration of regular and additional vacations, days;

T b - absence from work due to illness and childbirth;

T y - the duration of study leave, days;

T g - the time for the performance of state and public duties, days;

T pr - other absenteeism permitted by law, days;

P cm - the duration of the work shift, h;

T km - loss of working time due to a reduction in the length of the working day for nursing mothers, h;

T p - loss of working time due to a reduction in the length of the working day for adolescents, h;

T s - loss of working time due to a shorter working day on pre-holiday days, h.

The efficiency of the use of labor resources at the enterprise is expressed in the change in labor productivity, the resulting indicator of the enterprise's work, which reflects both the positive aspects of the work and all its disadvantages.

Labor productivity, characterizes the efficiency of labor costs in material production, is determined by the amount of products produced per unit of working time, or labor costs per unit of output. Distinguish between the productivity of living labor and the productivity of aggregate, social, labor.

The productivity of living labor is determined by the expenditure of labor time in a given production, in a given enterprise, and the productivity of social labor is determined by the expenditures of living and social labor. As scientific and technological progress, the improvement of production, the share of social labor costs increases, since the worker is equipped with more and more new means of labor (from simple machines to electronic complexes). However, the main tendency is that the absolute value of the costs of both living and social labor per unit of production is decreasing. This is the essence of increasing the productivity of social labor.

* The level of labor productivity is characterized by two indicators:

production output per unit of time (direct indicator);

laboriousness of production (reverse indicator).

These indicators of production and labor intensity can be represented by the following formulas:

B \u003d B / T; t \u003d T / B,

where L - production output per unit of time; I - the complexity of manufacturing products; B is the volume of products manufactured, rubles; T is the cost of living labor for the production of products, rubles.

Output is the most common and universal measure of labor productivity. Depending on the units in which the volume of production is measured, the definition of production in physical terms, as well as in terms of normalized working hours, is distinguished.

Labor productivity is most clearly characterized by the rate of production in kind. These are units of measurement such as tons, meters, pieces, etc., as a rule, typical for enterprises producing homogeneous products.

If an enterprise or a workshop produces several types or brands of similar products, then the output is determined in conventional units. For example, in blast-furnace shops, when determining the output, various types of smelted pig iron are reduced to limiting pig iron, in open-hearth shops various types of smelted steel are reduced to simple carbon steel, cement is to conditional Portland cement, etc.

The indicator of output in monetary terms is used to determine labor productivity at enterprises producing heterogeneous products.

When using the norms of temporary working time, output is determined in standard hours, mainly at individual workplaces, in teams, at sites, as well as in workshops when producing heterogeneous and incomplete production that cannot be measured either in kind or in monetary terms ...

Performance indicators also differ depending on the unit of measurement of working time. The output can be defined for one man-hour worked (hourly output), one man-day worked (daily output), for one average worker per year, quarter or month (annual, quarterly or monthly output).

Labor intensity of production expresses the cost of working time for the production of a unit of production. Determined per unit of production in kind across the entire range of products and services; with a large assortment of products at the enterprise, it is determined by typical products, to which all others are reduced. In contrast to the production indicator, this indicator has a number of advantages: it establishes a direct relationship between the volume of production and labor costs, eliminates the impact on the labor productivity indicator of changes in the volume of supplies for cooperation, the organizational structure of production, makes it possible to closely link the measurement of productivity with the identification of reserves for its growth, to compare labor costs for identical products in different departments of the enterprise.

Depending on the composition of included labor costs, there are:

technological labor intensity, including all the costs of basic workers, pieceworkers and time workers (ttech),

labor intensity of production services, including the labor costs of auxiliary workers, (tos);

production labor intensity - labor costs of all workers, both main and auxiliary:

labor intensity of production management, including labor costs of engineering and technical personnel, employees, service personnel and security (tpr),

full labor intensity, representing the labor costs of all categories of industrial and production personnel:

tpol \u003d ttech + tobs + ttr.

An important stage of analytical work at the enterprise is the search for reserves of labor productivity, the development of organizational and technical measures for the implementation of these reserves and the direct implementation of these measures. The reserves for the growth of labor productivity are understood as the still unused possibilities of saving the costs of living and materialized labor. Intra-production reserves are due to the improvement and the most efficient use of technology and labor, reduction of working time, economy of raw materials and materials, rational use of equipment. Intra-production reserves include reserves for reducing labor intensity, reserves for improving and using working time, reserves for improving the structure of personnel, reserves for saving objects of labor and reserves for saving means of labor.

* The increase in labor productivity due to an increase in production volumes and changes in the number of employees is determined by the following formula:

where is the percentage of increase in output at the enterprise in a given period;

The percentage of the decrease in the number of employees of the enterprise.

The growth of labor productivity of workers at the enterprise P (%) due to an increase in the share of cooperative deliveries of products is determined by the following formula:

where is the share of cooperative supplies in the gross output of the enterprise, respectively, in the base and planned periods,%.

The growth of labor productivity due to better use of the working time fund is calculated by the formula:

where is the effective annual fund of working time of one worker, respectively, in the baseline and planned periods, man-hour.

* It should be noted that the indicator of marginal labor productivity refers to a market economy, where labor is one of the factors of production and there is a labor market.

A separate enterprise, deciding how many workers it should hire, must determine the price of demand for labor, that is, the level of wages. The price of demand for any factor of production and labor is no exception here and depends on its marginal productivity, that is, on the marginal productivity of labor.

Marginal labor productivity is the increase in the volume of output caused by the use of an additional unit of labor under fixed other conditions.

The marginal productivity of labor is calculated on the basis of the marginal product of labor, which is understood as the increase in production produced as a result of hiring another additional unit of labor.

Consequently, the management of the enterprise, based on the need to optimize all the resources involved, will apply or displace labor, reaching the level of marginal productivity. And no one will force him to do otherwise, since the interests of the enterprise's survival in a competitive environment are threatened.

In such a situation, the problem of surplus labor force arises, i.e. unemployment, underemployment. The problem of rational use of the labor force is becoming equally important both for the managers of the enterprise, i.e., employers, and for the state administration bodies, which must solve the issues of social protection of people who are temporarily unemployed.

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