The law of diminishing marginal productivity states. Law of Diminishing Marginal Productivity. An isoquant map is

In order to reflect the influence of a variable factor on production, the concepts of aggregate (total), average and marginal product are introduced. These are natural indicators that are measured in units such as: pieces, meters, kilograms, etc.

Total Product (TP) is the quantity of an economic good produced using a certain amount of a variable factor. Typically, in the short run, the variable factor is labor (L), i.e. the number of workers employed in the production process. Capital (K) is considered a constant (unchangeable) factor.

By dividing the total product by the amount of variable factor consumed, we can get average product(AR):

AP = TP/ L

Average product shows how much product (in pieces, kilograms, etc.) one worker produces on average.

Marginal product (marginal product) usually defined as the increase in total product resulting from infinitesimal increments in the amount of the variable factor used:

MP = DTP/DL

Marginal product shows how many additional units of output are produced by an additional worker.

The total product (TP) will increase with increasing use of the variable factor (L) in production, but this growth has certain limits within the framework of a given technology. Since the same amount of capital will account for more and more units of labor (number of workers), the return from each subsequent worker will sooner or later begin to decline, and accordingly The growth of the total product will also begin to decrease.

Law of Diminishing Marginal Productivity argues that with the increasing use of any production factor(assuming the rest remain unchanged), sooner or later a point is reached at which the additional use of a variable factor leads to a decrease in the relative and then absolute volumes of output. An increase in the use of one of the factors (while the others are fixed) leads to a consistent decrease in the return on its use.

Law of Diminishing Returns has never been proven strictly theoretically, it is derived experimentally (first in agriculture, and then in relation to other industries). It reflects the actually observed fact of certain proportions between various factors. Their violation, expressed in excessive growth in the use of one of the resources, can quite quickly exhaust the boundaries of the interchangeability of resources and ultimately lead to insufficiently efficient use of it (if other factors of production remain unchanged).

Law diminishing marginal productivity is not absolute, but relative.

Firstly, it is applicable only in the short term, when at least one of the factors of production remains unchanged.

Secondly, Technological progress is constantly pushing its boundaries.

21. THE CONCEPT OF PRODUCTION COSTS AND THEIR TYPES: CONSTANT, VARIABLE, TOTAL, AVERAGE, MARGINAL COSTS.

Production costs represent monetary expressions of the costs of production factors associated with the firm's production of products and services.

Fixed costs(fixed cost)– These are costs whose value in the short term does not change with an increase or decrease in production volume. They are designated FC.

Fixed costs include costs associated with the use of buildings and structures, machinery and production equipment, rent, major repairs, as well as administrative costs.

Variable costs(variable cost)- These are costs, the value of which varies depending on the increase or decrease in production volume.

Variable costs include the cost of raw materials, electricity, auxiliary materials, and labor. They are designated VC.

Unlike fixed costs, the value of which does not depend on changes in production, variable costs increase or decrease in proportion to output.

General costs (total cost)- a set of constants and variable costs firms in connection with the production of products in the short term. They are denoted by TC or C. Total costs are a function of output (Q): TC = f(Q).

The part of the costs that does not change with an increase or decrease in production is called fixed costs, the other part, depending on the size of production, is called variable. Total costs are the sum of:

where FC (Fixed Cost) - fixed costs;

VC (Variable Cost) - variable costs.

Since fixed costs do not change as production volume increases, then average fixed costs represent a smaller and smaller value per unit of product. Average fixed costs are designated AFC (Average Fixed Cost):

where Q is the volume of production.

Average variable costs AVC (Average Variable Cost) are determined by dividing variable costs by production volume Q:

They reach their minimum when the technologically optimal size of the enterprise is reached.

Average total costs can be obtained by dividing total costs by the number of products produced:

or by adding average fixed costs (AFC) and average variable costs (AVC):

ATC = AFC + AVC = (FC+VC) /Q.

Marginal cost(marginal cost)- it is the increment in total costs caused by an infinitesimal increase in production.

Marginal cost usually refers to the costs associated with production. last unit of production:

MC = dTC/dQ = dVC/dQ

Determining MC is very important for a company, since it allows you to determine those costs, the magnitude of which it can always control. Marginal costs show the amount of costs that a firm will incur if it increases production by the last unit of output, or what it will save if it reduces production by that unit.

22. NATIONAL ECONOMY:
MAIN OBJECTS, SUBJECTS AND GOALS

National economy- is an integral system of relationships between economic entities regarding the production, distribution and use of the national product. The national economy has complex with structure, which can be considered from the point of view of the criteria:

1. Reproductive structure. The criterion for its selection is the features of management and functions subjects macroeconomics: households, business and government. They are elements of the reproductive structure.

2. Social structure . Here the structural elements are combined according to the criteria various forms property, types of labor and income, groups of enterprises.

3. Industry structure. It is distinguished by the criterion of homogeneity of production functions performed, products produced, services and other results.

4. Territorial structure. It is distinguished by the criterion of the location of productive forces.

5. Infrastructure. It is distinguished according to the criterion of the service characteristics of a particular production.

6. Structure of foreign economic relations. It is distinguished by the criterion of interaction between subjects of one or several countries.

Objectives of macroeconomics:

1. The main and defining goal is the economic growth. The more goods and services produced in the economy, the higher the standard of living of the population.

2. Economic efficiency is the second goal of macroeconomics. Given that the resources of any national economy are limited, they must be used efficiently. Efficient production develops with minimal costs and losses.

3. O ensuring a high level of employment. If employment is maintained at its natural level, it means that there is full employment.

4. C stable price level, meaning the absence of sharp jumps in its dynamics.

5. Maintaining an equilibrium foreign trade balance(balance between exports and imports). This balance ensures a stable exchange rate of the national currency.

6. Economic freedom, which is determined by three main questions: what, how and for whom to produce. Economic freedom does not mean that it has no boundaries, although they are flexible.

7. Fair income distribution. The goal of equitable distribution of income is to ensure that no group of the population remains in extreme poverty. It is important to avoid both excessive differentiation in living standards and equalization.

8. The task is becoming more and more urgent maintaining a balance of interaction with environment . Production should be carried out on the basis of resource-saving, nature-protective, waste-free technological systems. This goal is important not only for national economies, but is a global problem.

9. Increased free time as the basis for the harmonious development of personality. Free time is one of the general indicators of a country’s standard of living and the volume of needs of the population, since the amount and structure of free time reflects all aspects related to the material well-being and cultural level of people.

To represent the law of diminishing marginal productivity, production with one variable factor must be considered. Let us take labor as a variable factor, and capital as a constant factor:

Q = f (L, K const)

There is a certain limit to the growth of production volumes when one factor increases while the others remain constant. This property production function called the law of diminishing returns or productivity.

To reflect the influence of the variable factor (L) on production and graphically illustrate this law, it is necessary to introduce the following concepts:

Total or total product (TP) is the amount of an economic good produced using a certain amount of a variable resource and increasing as one of the factors increases.

Average Product (AP)- this is the ratio of the total product to the amount of the variable factor used in production, or the amount of additional products obtained by using an additional unit of the variable product.

AR = TP/x, where x is a variable factor, in our case it is L.

Marginal product (MP) is the ratio of the change in the total product to the change in the variable factor or the amount of additional output obtained by using an additional unit of the variable resource.

MP = DTP/Dx

The total product (TP) will increase with the increase in the use of a variable factor in production, but this growth will have a certain size within the framework of a given technology.

Rice. 3.6. Dynamics of productivity by total product

With a constant state of technology at the first stage of production (from 0 to A), an increase in labor costs contributes to an increasingly complete use of capital, i.e. both marginal and total productivity increases and this is expressed in the growth of average and marginal product. At the same time, MP>AR. If at the first stage (from 0 to A) the total product increases more slowly than the use of the variable factor, then at the second stage (segment AB) the total product grows faster than the amount of the variable factor used.

Rice. 4.6. Dynamics of productivity by average and marginal product

At point A marginal product reaches its maximum. At the second stage - segment AB - the value of the marginal product decreases and at point B it becomes equal to the average product. Here the equality MR = AP is valid.

At the third stage (segment BC), the marginal product is less than the average product (MP<АР), в результате чего совокупный продукт растет медленнее, чем затраты переменного фактора и при наступлении четвертой стадии (после точки С) предельный продукт становится меньше нуля (МР<0).

As a result, an increase in a variable factor leads to a decrease in total output. However, for this law to operate, it is necessary that all units of the variable factor be qualitatively homogeneous and the addition of more and more new units does not lead to a qualitative change in technology.

Thus, the law of marginal productivity (return) states that with the increase in the use of any production factor (with the rest remaining unchanged), sooner or later a point is reached at which the additional use of a variable factor leads to a relative or even absolute decrease in the volume of output, those. an increase in one of the factors leads to a consistent decrease in the returns of its use.

Note that this law has never been proven theoretically, but was derived exclusively experimentally. Initially it was based on the agricultural industry, then it was applied to other industries. The law of marginal productivity is relative in nature, since it can only be applied in the short term, when at least one of the factors of production remains unchanged. Secondly, technical progress is constantly being improved, therefore expanding the boundaries of application of this law.

In the short-term time interval, when one factor of production remains unchanged. The effect of the law presupposes the unchanged state of technology and production technology. If in production process the latest inventions and other technical improvements will be applied, then an increase in output can be achieved using the same production factors, i.e. technical progress can change the boundaries of the law.

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

Marginal labor productivity (marginal product of labor - $MP_L$) is the increase in production volume from each subsequent unit of labor:

$MP_L=\frac (\triangle Q_L)(\triangle L)$,

those. the productivity gain to total product ($TP_L$) is equal to

$MP_L=\frac (\triangle TP_L)(\triangle L)$

The marginal product of capital $MP_K$ is determined similarly.

Based on the law of diminishing returns, let us analyze the relationship between total ($TP_L$), average ($AP_L$) and marginal products ($MP_L$), (Fig. 1).

The movement of the total product ($TP$) curve can be divided into three stages. At stage 1, it rises upward at an accelerating pace, since the marginality of the product ($MP$) increases (each new worker brings more product than the previous one) and reaches a maximum at point $A$, i.e. the rate of growth of the function is maximum. After point $A$ (stage 2), due to the law of diminishing returns, the $MP$ curve falls, i.e., each hired worker gives a smaller increase in the total product compared to the previous one, therefore the growth rate of $TP$ after $TC$ slows down . But as long as $MP$ is positive, $TP$ will still increase and reach a maximum at $MP=0$.

Figure 1. Dynamics and relationship of total, average and marginal products

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

The configuration of the average product curve $AP$ 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 total output ($TP$) than the third, $MP$ decreases, so the average output of the four workers also decreases.

Economies of scale

Manifests itself in changes in long-term average production costs ($LATC$).

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

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

Figure 2. The firm's long-run and average cost curve.

The reaction of $LATC$ to changes in the parameters (scale) of a firm can be different (Fig. 3).

Figure 3. Dynamics of long-term average costs

Figure 4.

Let's assume that $F_1$ is a variable factor while the other factors are constant:

Total product($Q$) is the quantity of an economic good produced using a certain amount of a variable factor. Dividing the total product by the amount of the variable factor expended gives the average product ($AP$).

Marginal product ($MP$) is defined as the increase in total product obtained as a result of infinitesimal increments in the amount of the variable factor used:

$MP=\frac (\triangle Q)(\triangle F_1)$

Factor substitution rule: the ratio of the increases in two factors is inversely related to the magnitude of their marginal products.

Law of Diminishing Marginal Productivity states that with the increase in the use of any production factor (with the rest remaining unchanged), sooner or later a point is reached at which the additional use of a variable factor leads to a decrease in the relative and then absolute volumes of output.

Note 1

The law of diminishing returns has never been proven strictly theoretically; it is derived experimentally.

Factors of production are used in production only when their productivity is positive. If we denote the marginal product in monetary terms by $MRP$, and marginal costs by $MRC$, then the rule for the use of resources can be expressed by equality.

Law of Diminishing Marginal Productivity

The essence of the law.

As the use of factors increases, total output increases. However, if a number of factors are fully involved and against their background only one variable factor increases, then sooner or later a moment comes when, despite the increase in the variable factor, the total volume of production not only does not grow, but even decreases.

The law states: An increase in a variable factor with fixed values of the rest and unchanged technology ultimately leads to a decrease in its productivity.

Operation of the law.

The law of diminishing marginal productivity, like other laws, operates as a general trend and manifests itself only when the technology used remains unchanged and in a short period of time.

To illustrate the operation of the law of diminishing marginal productivity, the following concepts should be introduced:

- total product - production of a product using a number of factors, one of which is variable and the rest are constant;
- average product - the result of dividing the total product by the value of the variable factor;
- marginal product - an increase in the total product due to an increase in a variable factor by one.

If the variable factor is incremented in continuously infinitesimal quantities, then its productivity will be expressed in the dynamics of the marginal product, and we will be able to track it on the graph (Fig. 15.1).

Let's build a graph where the main line OABCy - dynamics of the total product.

1. Divide the total product curve into several segments: About, VS, SO.
2. On the segment OB we arbitrarily take a point A, in which the dynamics of the overall product (OM) coincides with the variable factor (OR).
3. Connect points 0 and A - we get D OAR, the angle formed by the sides OA And OR, let's denote a. Attitude AR To OR - average product, also known as 1§ a.

Rice. 15.1.

4. Let's draw a tangent to the point A. It will intersect the axis of the variable factor at the point N. D will form APN Where AP/NP - marginal product, also known as tg ß.

On the entire segment Oß tg a< tg ß, т.е. средний продукт меньше предельного. Следовательно, имеется возрастающая отдача от переменного фактора и The law of diminishing marginal productivity does not apply.

On the segment Sun the growth of the marginal product decreases against the background of the continued growth of the average product. At point C, the marginal and average products are equal to each other and both are equal to tg u. Thus, it began to appear law of diminishing marginal productivity.

On the segment CD the average and marginal products are reduced, and the marginal product decreases faster than the average. The total product continues to grow. Here the effect of the law is fully manifested.

Beyond the point D, Despite the growth of the variable factor, an absolute reduction even in the total product begins. It is difficult to find an entrepreneur who would not feel the effect of the law beyond this point.

Isoquant and isocost. Producer equilibrium. Economies of scale

Product output isoquant.

The production function can be represented graphically in the form of special curves - isoquants.

Product isoquant - it is a curve showing all combinations of factors within the same output. For this reason it is often called line of equal output.

Isoquants in production perform the same function as indifference curves in consumption, so they are similar: they also have a negative slope on the graph, have a certain proportion of factor substitution, do not intersect with each other, and the further they are located from the origin, the greater the result of production they reflect ( Fig. 16.1).

Isoquants can take different forms:

A) linear - when it is assumed that one factor is completely replaceable by another;
b) in the shape of an angle - when strict complementarity of resources is assumed, without which production is impossible;
V) broken curve, expressing the limited possibility of substituting resources;
G) smooth curve - the most general case of interaction between production factors (Fig. 16.2).

The marginal rate of technical substitution of resources.

An isoquant shift is possible by increasing the growth of attracted resources of those

Rice. 16.1.

a, b, c, c1- various combinations; U* U g U g "U) ~ product isoquants

Rice. 16.2.

nic progress and is often accompanied by a change in its slope. This slope always determines the marginal rate of technical substitution of one factor by another (MRTS). The marginal rate of technical substitution of one factor by another represents the amount by which one factor can be reduced by using an additional unit of another factor, keeping output constant:

where L/LG5 is the maximum rate of technical substitution of one factor by another.

Producer equilibrium.

Isoquant - the result of the interaction of production factors. But in a market economy there are no free factors. Consequently, production possibilities are not least limited by the financial resources of the entrepreneur. The role of the budget line in this case is played by the isocost.

Isocosta - line that limits the combination of resources to the monetary costs of production, which is why it is often called line of equal costs. With its help, the budgetary capabilities of the manufacturer are determined.

The manufacturer's budget constraints can be calculated as follows:

Where WITH - manufacturer's budget constraint; r - price of capital services (hourly rent); A" - capital; and> - price of labor services (hourly wage); I - work.

Even if an entrepreneur uses his own funds rather than borrowed funds, these are still resource costs and should be considered. Factor price ratio g/t shows the slope of the isocost (Fig. 16.3).

Rice. 16.3.

TO- capital; I - work

An increase in the entrepreneur's budgetary capabilities shifts the isocost to the right, and a decrease - to the left. The same effect is achieved under conditions of constant costs when market prices for resources decrease or increase.

By combining isoquant and isocost graphs, you can determine producer balance, those. that optimal set of resources that, given the available financial costs, gives the best result (Fig. 16.4).

The value of factors used in production is scale of production. Returns to scale (i.e. the result of production activities) can be:

Rice. 16.4.

U g U2 Uy ~ isoquants; E- optimum point

A) constant, if the result of production increases in the same proportion as the resources;
b) decreasing, if the result of production increases in a smaller proportion;
V) increasing, if the result of production increases in a greater proportion (Fig. 16.5).

In the short-term time interval, when one factor of production remains unchanged. The effect of the law presupposes the unchanged state of technology and production technology. If the latest inventions and other technical improvements are applied to the production process, then an increase in output can be achieved using the same production factors, that is, technological progress can change the scope of the law.

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