The concept of marginal labor productivity. Marginal Productivity Marginal Productivity Function

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

Under revenue, we will further understand 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=Q*P).

The economic activity of the company can be divided into two types:

We can say that commercial activity is secondary in relation to production, that is, there cannot be firms on the market that carry out only commercial activity, because someone else must also produce it.

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

production function- shows I the dependence of the amount of product that the company can produce on the volume of resource costs. The equation production function can be written as follows:

In the presented formula, the volume of output (maximum at a given cost) is denoted by the letter Q(quantity - from the English quantity, volume), in letters F(factor - factor, English) denotes the various factors of production that the 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 preparing a mathematical application to his fundamental work “Principles of Economics which is based on the concept of utility) and the theory of production (the main concept is productivity ).

In a simplified form, the production function can be represented as an output dependence ( 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?

FACTORS OF PRODUCTION
variables	permanent
Their costs depend on the size product release. That is, if the firm wants to increase output, then it should increase the amount of the variable factor.	Their costs do not depend on output size (up to a certain point)
You can change their size in the short term (number of employees - labor, raw materials, etc.)	It is impossible to change their value in the short term (the size of a plot of land, the size of a plant, technologies, etc.)

Now we will depict the main functions of the company in 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 the marginal productivity of labor and capital. Clark believed that the problem of the distribution of the social product occupies a central place in 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. The income of entrepreneurs and employees, according to Clark's theory, should correspond to the real contribution of capital and labor to the final product of production (output).

Performance(or total productivity) of each of the factors of production is determined; how many units of output are produced per unit of factor used.

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 ratio, the higher labor productivity.

What about the marginal productivity in this case?

Let the farmer own a plot of land of 1 hectare. Each additional amount of potatoes grown in this area 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 not twice as many potatoes 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 number of potatoes harvested less than than the tenth, etc.).

What is the reason for this situation? In our example, one of the factors of production (land) acted as a constant, and the other (labor) - as a 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 start of the work of the eleventh worker) begins to decrease. This is the meaning of the law of marginal productivity:

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

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 makes it possible to explain the behavior of a consumer who maximizes total utility, and thereby determine the nature of the demand function of price. In the same way, the law of diminishing productivity underlies the explanation of the profit-maximizing behavior of the producer.

The manufacturer has certain production equipment located in a limited area occupied by the enterprise. He faces the key question of production: how much should be produced? What is this best release (Q)? After all, output can be increased or decreased by hiring more or fewer workers, processing more or less raw materials, and so on. And how to respond to a change (for example, an increase) in the price of a commodity - to rush to increase the scale of production? This is where the law of diminishing productivity comes into play. Consider the stages of production and the impact of the law of diminishing productivity on the example of a firm.

Suppose there is a firm that uses one variable factor of production (eg labor). All other factors of production of this firm are constant, that is, one factor of production, for example, F1 varies depending on the size of the output, and all other factors (F2, F3...Fn) remain unchanged (const).

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

Profit is the difference between the revenue from a product and the cost of producing that product. What makes up the profit, how it is distributed, etc. - we will consider in the lesson "Profit of the company."

Distinguish:

total 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):
marginal 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 total product increases with the growth of the use of the variable factor, but the growth of the total product has technological limitations. That is, the possibilities of production (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 = f (L, K)). Let us first consider how the total product graph changes ( TR) depending on changes in the values ​​of the average and marginal products:

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

Total product (TP) grows more slowly than the amount of variable factor used.

2 stage: marginal product decreases and MP = AP

The total product (TR) is growing faster than the amount of the variable factor.

3 stage: marginal product continues to fall

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

4 stage: marginal product is negative

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

Based on the above 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 where marginal product is equal to zero, that is, after point 3, the marginal product will begin to take negative values. And this means that it becomes unprofitable for the manufacturer with these technologies and the size of production to continue to increase the variable factor.

The law of marginal productivity was derived not theoretically, but experimentally. 19th century economists limited the scope of the law of diminishing productivity to agriculture, not extending it to other branches of production. The limited nature of the permanent factor of land production, the relatively low rates of technical progress compared to other industries, the relatively stable range of crops grown - all these circumstances led to the visibility of the effect of the law in question in agricultural production. But already at the end of the 19th - beginning of the 20th 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 equipment available and the occupied territory. In a short period, when the technological process remains unchanged, and the quantity of at least one factor of production is fixed, a moment inevitably comes when each next unit of the variable factor used will cause a smaller increase in output than the previous one. True, in the long run, when the producer has the opportunity to change technologies and the size of production, the total product curve shifts upwards, which means that it becomes possible to use more of the 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, and the share of past labor increases, while the absolute value of the costs of living and materialized labor per unit of output is reduced. The change in labor productivity (IPT index) for a certain period in terms of output (B) or labor intensity (T) can be determined using the following formulas:

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

PT \u003d In 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 B 0 and B b - production output, respectively, in the reporting and base periods in the corresponding units of measurement;

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

PT - growth rate of labor productivity, %;

ΔPT is the growth rate of labor productivity, %.

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

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

the total population savings (Eh) are calculated under the influence of all technical and economic factors and measures (Eh = ∑E i);

the increase in labor productivity at the enterprise (in the workshop, on the site) is calculated, achieved under the influence of all factors and activities (ΔPT) according to the formula , necessary to fulfill the annual volume of production while maintaining the output (productivity) of the base (previous) 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. Under the factors of growth of labor productivity are understood the reasons for changes in its level. Under the reserves of labor productivity growth at the enterprise are meant unused real opportunities for savings. labor resources. Labor productivity growth factors depend on the sectoral affiliation of the enterprise and a number of other reasons, however, it is generally accepted to single out the following groups of factors:

Raising the technical level of production;

Improving the organization of production and labor;

Change in the volume of production and structural changes in production;

Changes in external, natural conditions;

Other factors.

In market conditions of management, the concept of marginal labor productivity is becoming more and more widespread, according to which an additional increase in the number of workers leads to an ever smaller increase in marginal product. At the same time, the marginal product of labor is understood as the amount of additional production that the enterprise will receive by hiring one additional worker.

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

When the marginal product of labor is greater than the marginal cost of labor, the number of people employed must be increased. total profit enterprises with an increase in the number of employees should increase.

If the marginal product of labor is less than the marginal cost of labor, then profits begin 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 worker is equal to the marginal cost of paying for his labor.

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

The headcount rate (N h) is the established number of employees of a certain professional and qualification composition, necessary to perform specific production, management functions or scope 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 the enterprise. It is measured by such indicators as payroll, attendance and average payroll number of employees.

The list number of employees of the enterprise is an indicator of the number of employees payroll on a specific date or date, such as 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 employment contracts(contracts).

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

The average number of employees is 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 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 calendar days month.

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

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

N h \u003d T pl / (F n × K vn),

where T PL is the planned labor intensity of the production program, normo-h;

F n - the normative balance of working time of one worker per year, h;

To vn - the coefficient of performance of time standards 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 of calculating the number of personnel by the labor intensity of the production program is the most accurate and reliable, as it requires the application of labor standards. Determining the number of workers according to production standards is more simplified and less accurate due to the pricing of products (works, services).

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

N h \u003d OP pl / (N vyr × K ext),

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

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

Planning the number of main workers in instrumental 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 work:

H h \u003d K o / N o × C × K sp,

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

C - the number of work shifts;

K cn - conversion factor attendance workers on the payroll;

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

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

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

H h \u003d M × C × K sp,

where M is the number of jobs.

The number of attendants can also be determined by the aggregated service standards, for example, the number of cleaners can be determined by the number of square meters of premises, the 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, quantitative characteristics labor potential enterprise and/or internal divisions can be represented as a fund of labor resources in man-days or man-hours. Such a fund (Frt) can be determined by multiplying average headcount workers (H cn) for the average duration of the working period in days or hours (T rv):

F rt \u003d H cn × T r.

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

T rv \u003d (T to - T in - T prz - T o - 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 in a year;

T prz - quantity public holidays per year;

T about - the duration of the next and additional holidays, days;

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

T y - duration study holidays, days;

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

T pr - other absences 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 the reduction in the length of the working day for adolescents, h;

T s - loss of working time due to a shortened 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, which reflects both the positive aspects of the work and all its shortcomings.

Labor productivity characterizes the efficiency of labor costs in material production, is determined by the quantity of products produced per unit of working time, or labor costs per unit of output. A distinction is made between the productivity of living labor and the productivity of total, social, labor.

The productivity of living labor is determined by the expenditure of working time in a given production, for this enterprise, and the productivity of social labor - the costs of living and social labor. As scientific and technological progress progresses, the improvement of production, the share of social labor costs increases, as the worker is equipped with more and more new means of labor (from the simplest machines to electronic complexes). However, the main trend is that the absolute value of the cost of both living and social labor per unit of output is declining. 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);

the complexity of manufacturing products (inverse indicator).

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

b \u003d W / T; t= T/V,

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

Product development is the most common and universal indicator of labor productivity. Depending on the units in which the volume of production is measured, a distinction is made between the definition of output in natural terms, as well as in terms of normalized working hours.

The productivity of labor is most clearly characterized by the indicator of output in physical terms. These are such units of measurement as tons, meters, pieces, etc., as a rule, typical for enterprises producing homogeneous products.

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

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

When using the norms of temporary working hours, output is determined in standard hours, mainly at individual workplaces, in teams, at sites, as well as in workshops when producing heterogeneous and unfinished products 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).

The labor intensity of production expresses the cost of working time for the production of a unit of output. Determined per unit of production in physical terms for 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 the rest are given. Unlike the output indicator, this indicator has a number of advantages: it establishes a direct relationship between the volume of production and labor costs, excludes the impact on the indicator of labor productivity of changes in the volume of supplies through cooperation, organizational structure production, allows you to closely link the measurement of productivity with the identification of reserves for its growth, compare labor costs for the same products in different workshops of the enterprise.

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

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

the labor intensity of production maintenance, including the labor costs of auxiliary workers, (tobs);

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

the complexity of production management, including the labor costs of engineers, employees, maintenance personnel and security (tupr),

total labor intensity, which is the labor costs of all categories of industrial and production personnel:

tpol=ttech+tobs+tcontrol.

An important milestone 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 to be the opportunities that have not yet been used to save the costs of living and materialized labor. Intra-production reserves are due to the improvement and most effective use technology and work force, reducing working time, saving 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 labor resources.

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

where - the percentage of growth 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 employees at the enterprise P (%) due to an increase in the share of cooperative deliveries of products is determined by the following formula:

where -- specific gravity cooperative supplies in the gross output of the enterprise, respectively, in the base and planned periods, %.

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

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

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

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

The marginal productivity of labor 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 output produced as a result of hiring another additional unit of labor.

Consequently, the management of the enterprise, based on the need to optimize all attracted resources, 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 under threat.

In such a situation, the problem of surplus labor force arises, that is, unemployment, underemployment. The problem of rational use of labor force is becoming equally important for both enterprise managers, i.e. employers, and for government agencies management, which should address the issues of social protection of people temporarily unemployed.

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