The law of diminishing returns in simple terms. Opportunity cost and the law of diminishing returns

A change in the volume and costs of production by a firm depends on the possibilities of changing the quantity and structure of economic resources used to manufacture products, which are largely determined by the type of market period.

First of all, let us consider the patterns of change in volume and various kinds production costs in short term period.

The change in the volume of production and costs in the short run is associated with the operation of the law of diminishing returns. It operates only in the short run, when homogeneous units of a certain variable resource are added to a fixed resource. Law of diminishing returns means that, starting from a certain moment, the successive addition of identical units of some variable resource (for example, labor) to a constant one (for example, capital or land) gives a decreasing marginal product per each additional unit of the variable resource, i.e. its marginal productivity decreases. Marginal product and marginal productivity are denoted and defined in the same way. marginal product(MP - marginal product) is the additional product produced by each additional unit of a variable resource. Respectively, ultimate performance(MP stands for marginal productivity) is the incremental productivity of each additional unit of a variable resource. Marginal product (marginal productivity) is defined as the change in gross product in physical terms (total output) associated with the attraction of an additional unit of a variable resource.

If labor is the variable resource, then MP can be defined as follows:

where MP is the marginal product (marginal productivity);

ΔTR (ΔQ) - change in the gross product in physical terms (change in the total volume of production);

ΔL is the change in the variable labor resource.

At ΔL = 1, the formula takes the following form: MP = ΔTP = ΔQ.

It is necessary to explain the reasons for the law of diminishing returns in the short run. Imagine the law of diminishing returns based on the data presented in Table. When compiling the table, it was assumed that real capital, i.e., equipment, is a constant resource for a given firm, and living labor is a variable resource.

Law of diminishing returns

The third column shows the change in marginal product (marginal productivity) in the process of using additional units of labor with a constant amount of capital in the short run. When the first three workers are involved, the marginal product increases from 15 to 20 units. Starting with the fourth unit of labor, the law of diminishing returns applies: marginal product decreases. At the same time, for the ninth worker, it is equal to zero. The marginal product of the tenth worker is negative.

The data in the fourth column shows the change in the average product (average productivity). Average product(AP - average product) - this is the volume of production per unit of variable resource on average. Average performance(AP - average productivity) is the average productivity of a unit of a variable resource: AP = Q / L. The average product also increases with the first four workers, and then, starting with the fifth unit of labor, decreases.

Let's graphically represent the relationship between marginal, average and gross product.

The graphs show that gross product (total output) increases as long as marginal product is positive. At a marginal product equal to 0, it is the maximum value. When the marginal product becomes negative, the firm's gross product begins to decrease.

There is also a certain mathematical relationship between marginal and average product (marginal and average productivity), which is shown in Fig. As long as the marginal product of each additional worker exceeds the average product produced before he was hired, the average product increases. As soon as the marginal product of an additional worker falls below the average before he was hired, the average product begins to decrease. This relationship should be illustrated using Table. and fig. The equality of the marginal and average product (marginal and average productivity) also follows from the established dependence: MP = AP at the maximum value of the average product (average productivity). On fig. this is shown by the intersection point of the MP and AP graphs, corresponding to the maximum value of the AP.

Having considered the operation of the law of diminishing returns and the change in the volume of output in the short run, we proceed to the analysis of production costs.

The factors of production must be used by the firm with a certain proportionality between fixed and variable factors. It is impossible to arbitrarily increase the number of variable factors per unit of a constant factor, since in this case law of diminishing returns(see 2.3).

In accordance with this law, a continuous increase in the use of one variable resource, combined with an unchanged amount of other resources, at a certain stage will lead to the cessation of the growth of returns, and then to its decrease. Often the operation of the law assumes the invariance of the technological level of production, and therefore the transition to a more advanced technology can increase returns regardless of the ratio of constant and variable factors.

Let us consider in more detail how the return on a variable factor (resource) changes in a short-term time interval, when part of the resources or factors of production remains constant. Indeed, for a short period, as already noted, the company cannot change the scale of production, build new workshops, purchase new equipment, etc.

Assume that the company in its activities uses only one variable resource - labor, the return of which is productivity. How will the costs of the firm change with a gradual increase in the number of hired workers? First, consider how output will change with an increase in the number of workers. As the equipment is loaded, production increases rapidly, then the increase gradually slows down until there are enough workers to fully load the equipment. If you continue to hire workers, they will not be able to add anything to the volume of output. In the end, there will be so many workers that they will interfere with each other, and output will decrease.

See also:

Any production process has the characteristic feature that, with a constant amount of a constant factor, an increase in the use of a variable factor will inevitably lead to a decrease in its productivity. This is due to changes in returns from the variable factor. First initial stage, when

1 Since we are talking about single changes in the factor, the change in the total product should also be measured in physical units, i.e. MP L "f(K, L + 1) -f(K, L).

an insignificant amount of a variable factor is involved in production, each additional unit of the latter turns into an increase in the marginal product from this factor. However, as the use of a variable factor increases, the growth of its marginal product stops and then begins to decline. This dependence is called the "law of diminishing returns" or "the law of diminishing marginal productivity of a variable factor."

As the use of the variable factor increases, while other factors remain unchanged, a point is always reached at which the use of an additional amount of the variable factor leads to a constantly decreasing increase in the product, and then to its absolute reduction.

The reason for the law of diminishing returns lies in the violation of the balance in production between constant and variable factors. Low efficiency at low equipment load can be increased by introducing an additional amount of a variable factor into production, which will lead to an increase in output to an increasing extent. On the contrary, excessive loading of equipment will result in a drop in efficiency and a decrease in output.

The operation of the law of diminishing returns leads to four important conclusions:

1) there is always a cost area when their increase is not
leads to a decrease in the total product (all the first private products
water are positive). This area of ​​costs is called "economic
what area";

2) in a short-term period, when at least one of the fact
production tori remains unchanged, the volume is always reached
application of a variable factor from which the increase in the last
leads to a decrease in its marginal product;

3) there is scope for change within the economic domain
factor from which a further increase in its use is
it is treated by a decrease in the volume of output;

4) the possibility of increasing output in the short term,
those. by increasing the application of the variable factor are limited.

Indicators of return on a variable factor are the marginal and average products, which characterize the level of marginal and average productivity of the factor of production. In view of the fact that the law of diminishing returns reflects changes in increments of the total product, the very operation of the law manifests itself in changes in the marginal product from a variable factor. It is the slowdown in growth, and then the decrease in marginal product, that causes the decrease in

the appearance of the average product, and at a certain moment - and the reduction of the total product (Table 4.1).

Table 4.1 Production results with one variable

At the same time, it should be taken into account that, firstly, the law of diminishing returns is applicable only to the conditions of the short-term period; secondly, the intensity of the action of the "law" is due to the peculiarities of the technology and manifests itself in different production processes in different ways.

Product curves from a variable factor

Since the product is a function of a variable factor, it is possible to give a graphical representation of the change in the values ​​of the product depending on the change in the values ​​of the variable factor. On the horizontal axis we plot the values ​​of the variable factor, and on the vertical axis - the values ​​of the product. Connecting the obtained points, we get product curves from variable factor: the curve of the total product, the curve of the average product and the curve of the marginal product of the variable factor.

Given the operation of the law of diminishing returns, the production process can be represented as three constituent parts, each of which is characterized by a special type of return on the variable factor - growing, constant and decreasing productivity of the variable factor.

In the case of increasing returns to a variable factor, the nature of the production process is such that each additional unit of the variable factor yields a greater increase in total output than the previous unit of the factor. Such production function expressed by the equation

where a and b- some constant coefficients;

X- the amount of variable factor applied.

Production will be characterized by an increase in the average (AR X= Q: X \u003d (aX + bX 2): X \u003d a + bX) and marginal (MP X \u003d dQ: dX \u003d a + 2bX) products (Fig. 4.1).

The part of the production process characterized by a constant return on the variable factor reflects a linear relationship between the amount of the input variable factor and the total product and is expressed by the function Q= Oh. Since the return on each subsequent unit of the variable factor remains unchanged, the marginal product is equal to the average product, and their values ​​are constant: AR X= Q:X = aX:X= a and MP X \u003d dQ: dX \u003d a(Fig. 4.2).

type function Q \u003d bX - cX 2 will reflect the dependence of that part of the production process, which is characterized by diminishing returns on the variable factor. Since in this case the involvement in the production of each additional unit of the variable factor leads to a decrease in the marginal product MP X = dQ: dX= = b- 2cX, then this causes a fall in the growth of the total product, and, consequently, the average product AR X \u003d Q: X \u003d (bX- cX 2): X \u003d b - cX(Fig. 4.3). The fall in marginal product from a variable factor indicates the limited possibilities for increasing output, which reaches maximum values ​​when marginal product becomes zero with some amount of variable factor Xn. Since the use of it is beyond the magnitude X n will lead to a decrease in the total product, this indicates the limited use of the variable factor itself, since beyond such a boundary, production becomes technologically inefficient: with a large cost of the factor, we get a smaller result.

Each of the considered functions reflects only separate stages of the production process. Combined together, they give an idea of ​​the patterns of change in the product from a variable factor in the short term (Fig. 4.4). The production function of such production is described by an equation of the type Q = aX + + bX 2 - cX 3. For a given function, each point on the total product curve shows the maximum output for each individual value of the variable factor.

Average and marginal product curves can be constructed using the total product curve. Since the slope of the beam passing through the origin and a point on the curve (angle α),

shows the average values ​​of the function, and the slope of the tangent at any point of the curve (angle β) - the values ​​of the increments of the function for unit changes in the variable, then the average product (AR X) in any point on the total product curve is equal to the slope of the beam passing through given point(the tangent of the angle α), and the marginal product (MR X)- the slope of the tangent to this point (the tangent of the angle β).

Comparing the angles, it is easy to see that as the variable factor increases, the values ​​of the average and marginal products will change. At the initial stage (tga.< tgβ) the growth of the total product is accompanied by an outpacing, in relation to the average, growth of the marginal product, which reaches a maximum at the point BUT. Then 82

marginal product begins to decline, while the average product continues to rise, reaching a maximum at the point AT, where it is equal to the marginal product. Thus, stage I is characterized by an increase in the return on the variable factor. At stage II, after the point AT, despite the decline in both the marginal and average products, the total product continues to grow, reaching a maximum at the point With at zero marginal product, i.e. at the point where the first derivative of the function is

zero, i.e. at (TP X) \u003d MP X \u003d 0=> (TPx)=max. Because on this

stage, output increases in proportion less than the increase in the variable factor, then it is appropriate to speak of diminishing returns from the variable factor. At stage III, after the point WITH, marginal product becomes negative and there is a decrease not only in the average, but also in the total product. Since the production function does not allow inefficient use of factors, this stage is outside the scope of the economic domain and is not part of the production function.

The relationship between aggregate, average and marginal products is expressed in several ways:

With an increase in the variable factor, the total product
where increases if marginal product values ​​are positive, and decreases
shrinks when marginal product values ​​are negative;

With the growth of the total product, the values ​​of the marginal product
it is always positive, and when it decreases, it is negative;

The total product reaches its maximum when the marginal
the product is zero;

The average product of the variable factor increases until
its values ​​are below the values ​​of marginal product, and decreases if
they are above the values ​​of marginal product;

In the case of equality of the values ​​of the average and marginal product
tov average - reaches its maximum.

The nature of the changes in the values ​​of the product with an increase in the amount of a variable factor is the result of the interaction of all factors of production. Stage I is inefficient due to the imbalance between the fixed and variable resource while underutilizing the former. In order to increase overall efficiency, the firm should increase the use of the variable resource, at least up to stage II. Although the efficiency of the variable factor decreases in stage II, an increase in its use increases the return on the constant factor and leads to an increase in overall efficiency. Stage III characterizes the exhaustion of the effectiveness of constant

resource and the overall efficiency begins to decline, which means the absolute irrationality of the implementation of production with so many variable factors. Optimal in terms of overall production efficiency is stage II. Therefore, the firm must use the amount of variable resources that ensures it stays within this stage. If the demand for the firm's product does not allow it to reach this stage, the firm must stimulate demand for its product or use excess production capacity for the production of other products.

Optimal the use of such an amount of a variable factor is considered at which the maximum output is achieved.

Since within the framework separate production production resource can be used in different production processes and for production various benefits, then the solution to the problem of its effective use is associated with ensuring such a distribution of the resource between various production processes, in which its marginal productivity will be the same in all processes where it is used (Fig. 4.5). Suppose some factor of production X applied to processes A and B at the same time. In process A, it is used in quantity X 1 and its ultimate performance

(MP A X) is equal to X 1N. In process B, the same factor is applied in quantity ^ and its marginal productivity (MR B X) is equal to X 4 T. Pre-

the unit productivity of a factor in process A is higher than its marginal productivity in process B, since X t N> X 4 T. Moving a certain amount of a factor from process B to process A would mean an increase in the return on the factor in process B and a decrease in its return in process A. But the total productivity of the factor would increase and output would increase. It is obvious that the increment in the volume of output will be achieved until the marginal productivity of the factor in both processes is equalized: X 2 N 1 = X 3 T 1. So as X 1 NN 1 X 2 > > X 4 TT 1 X 3, then KMNX 1 + OPTX 4< KLN t X 2 + OST t X 3 . This suggests that when a factor is redistributed between different production processes, which ensures the leveling of the level of marginal productivity of a variable factor, the total return on this factor increases, and the maximum efficiency of using the factor is achieved with such a distribution that ensures the same level of marginal productivity of the factor in all processes where it is applied.

4.3. PRODUCTION IN THE LONG TERM. SUBSTITUTION OF FACTORS OF PRODUCTION. TYPES OF PRODUCTION FUNCTIONS

Within a short period of time, the firm can combine fixed capacities with varying amounts of other inputs. In what way does the volume of production change in this case with the use of different amounts of resources? To this question in general view The answer is the law of diminishing returns.

The law of diminishing returns states that in the short run, when the amount of production capacity is fixed, the marginal productivity of a variable factor will decrease starting from a certain level of input of this variable factor.

The marginal product (productivity) of a variable factor of production, such as labor, is the increase in output resulting from the use of an additional unit of this factor.

The law of diminishing returns can be represented by the example of a small carpentry workshop for the manufacture of furniture. The workshop has a certain amount of equipment - turning and planing machines, saws, etc. If this firm were limited to just one or two workers, then the total output and labor productivity per worker would be very low. These workers would have to perform several labor tasks, and the advantages of specialization and division of labor could not be realized. In addition, a significant part of the working time would be wasted when the worker moves from one operation to another, preparing the workplace, etc., and the machines would simply be idle most of the time.
The workshop would be understaffed, machines would be underutilized, and production would be inefficient due to an excess of capital relative to the amount of labor. These difficulties would disappear as the number of workers increased. As a result of such changes, time losses during the transition from one operation to another would be eliminated. Thus, as the number of workers able to fill vacancies increases, the additional or marginal product produced by each successive worker will tend to increase due to the increase in production efficiency. However, such a process cannot be endless. A further increase in the number of workers creates a problem of their surplus, that is, workers will underutilize their work time. Under these conditions, there will be more labor in the workplace in proportion to the unchanged value of capital funds, i.e. machines, machine tools, etc. The total volume of production will begin to grow at a slower pace. This is the main content of the law of diminishing returns of the means of production (see Table 5.2).

The table shows how, with a change in the number of workers from 1 person to 9, the average labor productivity per 1 worker changes from 10 units to 6.8 units of production with a change in the total volume of production from 10 to 63. With a decrease in the volume of production to 62 units, there is negative marginal return of used labor resources, that is, when 9 people work at this company.
A graphic representation of the law of diminishing returns is shown in Figure 5.3.

As you join more variable resources (labor) to a constant amount of constant resources (in this case we are talking about machine tools, machines, etc.), the volume of production received from the activities of workers will first increase at a decreasing rate (15, 12, 10, etc. units according to Table 5.2.), then it will reach its maximum (63 units of the total volume), after which it will begin to decrease, dropping to 62 units.

The costs incurred by the enterprise in the production of a given volume of output depend on the possibility of changing the amount of all resources employed. The quantities of many resources used - living labor (i.e. human labor), raw materials, fuel, energy - can be changed fairly quickly. Other resources require more time to develop - for example, the capacity of an enterprise, that is, the area of ​​​​its production facilities and the number of machines and equipment in it, can only be changed over a long period of time. In some heavy industries, changing production capacity can take several years.

Since the change in the amount of resources used in the production process is spent different time, it is necessary to distinguish between short-term and long-term periods. short term- during which the enterprise cannot change its production capacities, but at the same time sufficient to change the degree of intensity of use of these fixed capacities.

The production capacity of the enterprise remains unchanged within the short run, but the volume of production can be changed by using more or less living labor, raw materials and other resources. Existing production capacities can be used more or less intensively within the short term.

long term is a period of time long enough to change the quantities all employed resources, including production facilities. From an industry perspective, the long run also includes enough time for existing companies to break up and leave the industry, and for new businesses to emerge and enter the industry. If a short term represents a period of fixed powers, then the long-term period is a period of varying powers.

When analyzing production costs, it is important to take into account the effect law of diminishing returns which says that, starting from a certain moment, the successive addition of units of a variable resource (for example, labor) to an unchanged fixed resource (for example, land) gives a decreasing additional, or marginal, product per each subsequent unit of a variable resource.

Let's illustrate the operation of the law graphically (see Fig. 1).

For example, in the production room there is equipment - turning, milling and other machines. If the company hired one or two workers, the total output would be low, since the workers would have to perform many operations, moving from machine to machine. In this case, time would be lost (used irrationally), and the equipment would be idle. Production would be inefficient due to the excess of capital over labor.

These difficulties would disappear as the number of workers increased. In this case, the equipment would be used more fully, and the workers would specialize in individual operations. However, a further increase in the number of workers gives rise to the problem of their surplus. Now the workers have to stand in line to use the machine, there are workers to be underutilized. Ultimately, the continued increase in the number of workers in the enterprise would lead to the filling of all free space and stop the production process.

Therefore, on the graph in Fig. 1, we observe that the total volume of production first grows, reaching the point Nopt, and then begins to decline, despite the increase in the amount of labor, that is, workers in the shop.