Marginal productivity of a factor of production. Labor productivity. Indicators and measurement methods. Factors of labor productivity growth. Marginal productivity of labor Determination of average and marginal productivity of labor

The efficiency of using labor resources at an enterprise is expressed in changes labor productivity, the resulting indicator of the enterprise’s performance, which reflects how positive sides work, and all its shortcomings.

Labor productivity, which characterizes the efficiency of labor inputs in material production, is determined by the quantity of products produced per unit of working time, or labor inputs per unit of output. There is a distinction between the productivity of living labor and the productivity of aggregate, social labor.

The productivity of living labor is determined by the expenditure of working time in a given production, on this enterprise, and performance social labor- costs of living and social labor. With scientific and technological progress and production improvement, the share of social labor costs increases, as the worker’s equipment with ever new means of labor increases (from the simplest machines to electronic complexes). However, the main trend is that the absolute value of the costs of both human and social labor per unit of output is decreasing. This is precisely 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);

labor intensity of manufacturing products (reverse indicator).

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

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

where b is production output per unit of time; I -- labor intensity of production; V -- volume of products produced, rub.; T -- costs of living labor for production, rub.

Product output is the most common and universal indicator of labor productivity. Depending on the units in which the volume of production is measured, the definition of output in in physical terms, as well as indicators of normal working hours.

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

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

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

When using temporary working time standards, production is determined in standard hours, mainly at individual workplaces, in teams, in sections, as well as in workshops when producing heterogeneous and unfinished products that cannot be measured either in kind or in monetary terms .

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

The labor intensity of a product expresses the cost of working time to produce a unit of product. Determined per unit of production in physical terms across the entire range of products and services; at large assortment products at an enterprise are determined by typical products to which all others are reduced. In contrast to the output 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 through cooperation, organizational structure production, allows you to closely link the measurement of productivity with the identification of reserves for its growth, to compare labor costs for identical products in different workshops of the enterprise.

Depending on the composition of included labor costs, they are distinguished:

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

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

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

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

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

tfloor=ttech+tobs+tcontrol.

An important step analytical work the enterprise is to search for reserves of labor productivity, develop organizational and technical measures for the implementation of these reserves and the direct implementation of these measures. Reserves for growth of labor productivity are understood as not yet used opportunities for saving the costs of living and embodied labor. Intra-production reserves are due to improvement and the 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 personnel structure, 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 workers is determined by the following formula:

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

Percentage of reduction in the number of employees of the enterprise.

The increase in labor productivity of workers at the enterprise P (%) due to an increase in the share of cooperative supplies 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 increase in labor productivity due to better use of working time is calculated using the formula:

where is the effective annual working time of one worker, respectively, in the base 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.

An individual enterprise, deciding how many workers it should hire, must determine the price of demand for labor, i.e. the level wages. The price of demand 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.

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

Marginal productivity of labor is calculated based on the marginal product of labor, which is understood as the increase in output produced as a result of hiring one more additional unit of labor.

Consequently, the management of the enterprise, based on the need to optimize all attracted resources, will use or displace labor, reaching the level of maximum productivity. And no one will force him to act differently, since the interests of the enterprise’s survival in a competitive environment are at risk.

In such a situation, the problem of excess labor arises, i.e. unemployment, underemployment. The problem of rational use of labor becomes equally important both for enterprise managers, i.e. employers, and for government agencies departments that should resolve issues of social protection of people who are temporarily unemployed.

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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 embodied labor per unit of production 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 = V o / V b or I pt = T b / T o;

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

ΔPT = [(V 0 - V b)/V b ] × 100 or ΔPT = [(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 - labor productivity growth rate, %;

ΔPT - rate of increase in labor productivity, %.

Labor productivity planning for sections, workshops, and workplaces is carried out using the direct method using 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 headcount savings from the development and implementation of each measure to increase labor productivity (E i) are determined;

the total savings in numbers (E h) is calculated under the influence of all technical and economic factors and measures (E h = ∑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 measures (ΔPT) using the formula ΔPT = E h × 100 / (Ch r - E h), where Ch r is the number of industrial production personnel , necessary to fulfill the annual production volume while maintaining the output (productivity) of the base (past) period, people.

The level of labor productivity at an enterprise and the possibility of increasing it are determined by a number of factors and growth reserves. Labor productivity growth factors are understood as the reasons causing changes in its level. Reserves for increasing labor productivity at an enterprise mean unused real opportunities for saving labor resources. Factors of labor productivity growth depend on the industry of the enterprise and a number of other reasons, but it is generally accepted to distinguish the following groups of factors:

Promotion technical level production;

Improving the organization of production and labor;

Changes in production volume and structural changes in production;

Changes in external, natural conditions;

Other factors.

In market economic conditions, the concept of marginal labor productivity is becoming increasingly widespread, according to which an additional increase in the number of workers 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 output that an enterprise will receive by hiring one additional worker.

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

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

If the marginal product of labor is less than the marginal cost of labor, then profits begin to decrease with the last worker 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 latter accepted employee, is equal to the marginal cost of paying for his labor.

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

The standard number (N h) is the established number of workers of a certain professional and qualification composition necessary to carry out specific production, management functions or scope of work. Based on headcount standards, labor costs are determined by profession, specialty, group or type of work, individual functions, for the entire enterprise, workshop or its structural division.

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

The payroll number of employees of an enterprise is an indicator of the number of employees on the payroll as of a certain date or date, for example, 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 characterizes the number of payroll employees who report to work on a given day, including those on business trips. This is the required number of workers to complete the production shift task for production.

Average number of employees - the number of employees on average for a certain period (month, quarter, since 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 resulting amount by the number of calendar days of the month.

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

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

N h = T pl / (F n × K in),

where Tpl is the planned labor intensity of the production program, standard hours;

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

K vn - coefficient of fulfillment 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 production, multiplied by the planned output. The method of calculating the number of personnel based on the labor intensity of the production program is the most accurate and reliable, since it requires the application of labor standards. Determining the number of workers according to production standards is more simplified and less accurate due to pricing of products (works, services).

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

N h = OP pl / (N exp × K in),

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

N vyr is the planned production rate in the same units of measurement and for the same period of time.

Planning the number of main workers in hardware processes and auxiliary workers performing work for which there are service standards comes down to determining the total number of service objects, taking into account work shifts:

N h = K o / N o × C × K sp,

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

C - number of work shifts;

Ksp is the coefficient for converting the number of workers present to the payroll;

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

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

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

N h = M × C × K sp,

where M is the number of jobs.

The number of service personnel can also be determined by aggregated service standards, for example, the number of cleaners can be determined by the number of square meters of premises, wardrobe 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 controllability standards and a number of other factors.

In addition to the number of employees, a quantitative characteristic of the labor potential of the enterprise and/or its internal divisions 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 average number workers (H sp) for the average duration of the working period in days or hours (T rv):

F rt =H sp ×T rv.

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

T rv = (T k – T in – T prz – T o – T b – T u – T g – T pr)× P cm – (T km + T p + T s),

where Tk is the number of calendar days in a year;

T in - number of days off per year;

T prz - quantity holidays per year;

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

T b - absenteeism due to illness and childbirth;

T y - duration of study holidays, days;

T g - time to perform state and public duties, days;

T pr - other absences permitted by law, days;

P cm - duration of the work shift, h;

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

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

T s - loss of working time due to shortened working hours on holidays, h.

IN economic theory There are the concepts of “total”, “marginal” and “average product” of a variable factor of production.

Total factor product ( TR)- this is the total volume of product output obtained within a given production function and measured in physical units.

The concept of the total product of a factor allows us to identify the relationship between the volume of output and changes in the quantity of one resource while the quantity of others remains constant. For example, the production function Q =/(L) expresses the dependence of total production on the number of units of labor used L, provided that the quantity of other factors of production is constant.

Graphically, this production function is shown in Fig. 13.1.

Rice. 13.1.

Q- quantity of products, pcs.; L- quantity of variable factor (number of workers]

The concept of the total product of a factor makes it possible to understand what the marginal and average product of a factor is.

The marginal product of a factor of production (MP Z), calculated in physical units, shows the change in output caused by the use of an additional unit of a given factor (L) with the number of all others remaining constant. The marginal product of a factor is calculated as follows:

Where MP L- marginal product of the factor L A Q- change in the total volume of production; A L- change in the amount of factor L.

Average factor product ( AP L) is determined by dividing the volume of output by the amount of factor L used:

The average product of a factor (labor) shows how much output is produced per unit of labor. The average product of labor is often called an indicator of labor productivity.

The curves of the total, marginal and average product of the variable factor are shown in Fig. 13.2.

Rice. 13.2.

Point L on a segment OA represents the inflection point where the total product curve changes its convexity. This is because the growth of total product accelerates up to this point because the marginal product of the variable factor L on the segment O A growing quickly. This means that each additional unit of factor L increases total production by a greater amount compared to the previous one. Exactly the point A on the total product curve corresponds to the maximum value of the marginal product.

On the segment AC the growth of the total product slows down, since the marginal product of the factor L starts to decline. This means that each additional unit of factor L increases total production by a smaller amount compared to the previous one.

Dot IN on the curve ( TP L) shows the value of the total product at which the marginal and average products are equal.

At point C, the total product curve begins to decline as the marginal product takes on negative values. This means that a further increase in the amount of a variable factor will lead to a reduction in the value of the total product.

There is a certain relationship between the marginal and average products of a variable factor. The marginal product reaches its maximum value earlier than the average product. Marginal product curve ( MP L) intersects the average product curve (APj) at the maximum point of the latter. And indeed, when the value of the marginal product is higher than the value of the average product, then the curve AP l increases. And vice versa, when the value of the marginal product is less than the value of the average product, the curve AP L decreases.

The considered curves of total, average and marginal products reflect the trend known as the law of diminishing marginal productivity (return) of factors of production. This law states: as the quantity of a variable factor increases, with the quantity of all others remaining constant, a limit will be reached, after which the marginal product of the variable factor will begin to decrease.

The theory of marginal productivity of factors is important for determining the optimal combination production resources when releasing products.

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

By 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 and its price ( TR=Q*P).

The economic activities of a company can be divided into two types:

We can say that commercial activity is secondary to production, that is, there cannot be firms on the market that carry out only commercial activities, because someone 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 a firm can produce on the volume of resource inputs. The production function equation can be written as follows:

In the presented formula, the output volume (maximum at given costs) is indicated by the letter Q(quantity - from English quantity, volume), letters F(factor - factor, English) denotes 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) factors of production 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 a dependence of output ( Q), which is primarily determined by the volume of invested capital ( capital, K) and the amount of labor applied (labor, L). Then the production function equation will take the form:

Factors of production that we consider in the production function of a company can be either variable or constant. What does it mean?

Now let’s 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 central place in economic theory is occupied by the problem of distribution of the social product. 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; the number of units of output produced per unit of production 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 then is the marginal productivity?

Let a farmer own a plot of land of 1 hectare. Each additional quantity of potatoes grown on this plot requires additional labor. Then what will be the productivity of each subsequent 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 point the marginal productivity will begin to decrease (i.e. the eleventh person will increase the total amount of potatoes collected by 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) acted 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 start of 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 a certain point, the marginal productivity of each subsequent unit of the variable factor decreases.

Law of diminishing returns 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 on price. In the same way, the law of diminishing returns underlies the explanation of profit-maximizing behavior of the producer.

The manufacturer has certain production equipment located in a limited area occupied by the enterprise. It faces a key production question: how much output should it produce? What is this best edition (Q)? After all, you can increase or decrease output by hiring more or fewer workers, processing more or less raw materials, etc. How to react to a change (for example, an increase) in the price of a product - rush to increase the scale of production? This is where it is necessary to take into account the law of diminishing returns. Let's consider the stages of production and the influence of the law of diminishing returns using the example of a company.

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

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

Profit is the difference between revenue for a product and the cost of producing that product. What does profit consist of, how is it distributed, etc. - we will look at “Company Profit” in class.

There are:

The total product increases with increasing use of the variable factor, but the growth of the total product has limitations - technological. That is, the possibilities of production (achieving the best result) are limited by the technologies that it uses in production. In total, there are 4 stages of production (provided that the production function will have the form: Q = f (L, K)). First, let's look at how the total product schedule changes ( TR) depending on changes in the values ​​of average and marginal products:

Stage 1: labor costs increase, capital is used in greater volumes, marginal and average product increase, and:

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

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

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

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

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

Stage 4: marginal product becomes negative

An increase in a 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 at which the marginal product is zero, that is, after point 3, the marginal product will begin to take negative values. This means that it becomes unprofitable for the manufacturer, given the technologies and production volumes, 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 returns to agriculture, without extending it to other branches of production. The limited constant production factor of land, the relatively low rate of technical progress compared to other industries, the relatively stable range of crops grown - all these circumstances determined the visibility of the law in question in agricultural production. But already at the end of the 19th and beginning of the 20th centuries. scientists have come to understand the universality of this law. Indeed, in an industrial enterprise there are always constant factors of production. This includes both the available equipment 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 subsequent unit of the variable factor used will cause a smaller increase in output than the previous one. True, in the long run, when the manufacturer has the opportunity to change technology and production size, the total product curve shifts upward, which means that it becomes possible to use more of the variable factor with a positive result.

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