2 theory of production costs, the law of diminishing returns. The Law of Diminishing Marginal Returns of Factors of Production

The law of diminishing returns interacts with another economic principle - increasing. It determines how the costs of production factors, resources and the output of goods and services will be correlated. First of all, it takes into account how the increase in costs will affect the amount of products that are manufactured. And this is assuming that other factors remain unchanged.

This is clearly seen in the following example. Four hundred units of some product are produced using several factors acting in combination. The number of employees was originally two hundred. One can trace what the gradual increase in this factor will lead to (without changing the others), by increasing the number of employees by twenty people each time. It will become clear that an increase in the resource does not contribute to the growth of output, and hence income, but, on the contrary, slows down its pace. Its productivity behaves exactly the same - it falls. This is how the law of diminishing returns works.

The reason for this effect is quite obvious. The ratio between production resources must always be maintained, since they “work” well only in combination. As a rule, initially all factors are coordinated with each other. Naturally, when one of them increases while the others remain fixed, there is a disproportion. And in such conditions, when other resources (for example, a sufficient amount of equipment, space, etc.) do not correspond to an increase in the labor force, there can be no question of full profit.

AT in general terms The law of diminishing returns has the following formulation: "The growth in the output of a certain type of product due to an increase in one factor with the rest fixed gradually falls."

There is one feature that was not previously emphasized. Growth in the output of a good does not fall immediately after one factor has been increased. At first, if the ratio of resources is not strongly disturbed, there may even be an increase in performance. But it doesn't last long. Starting from a certain volume of output of goods, the disproportions are violated, and the law of diminishing productivity comes into force. If you look big picture, then this process is as follows: the return of one always depends on its costs or quantity. And this is assuming that other factors remain unchanged.

There are indicators such as average and marginal returns. The latter shows how the increase in output and the increase in resource are related to each other. The average defines how the volume of goods that was produced correlates with the costs that caused this release.

And this means that the law of diminishing returns will come into force only when the costs reach such a value that will correspond to the most rational combination of factors. What happens if costs rise a little? In this case average return equals the limit and reaches its maximum.

Considering the law of diminishing ultimate return, it is impossible to avoid operating with such a concept as “marginal (marginal) values”. They are also called relative increments. The marginal value of an indicator in the economy is its increase due to a change in the factor affecting it by only one unit. That is, the marginal product is the growth of its production due to the fact that one more unit of the factor affecting the output is used. In our case - an additional resource.

So, the law of diminishing returns says that when increasing the use of one factor in order to increase the result, one must not forget that the effect also depends on the ratio of the resource that is involved in circulation with others, and not only on its size.

Law of diminishing returns

The operation of the law of diminishing returns was not taken into account in the pre-perestroika period of the functioning of the domestic economy. One of the main directions of increasing the efficiency of production was its concentration. The construction of the largest enterprises was a characteristic feature for all sectors of the economy.

The law of diminishing returns, or the law of diminishing marginal product, or the law of varying proportions, are all different names for the same law. Consider two definitions that explain the law of diminishing returns from different angles.

Marginal - close to the limit, located on the edge. In Russian, the most accurate meaning is expressed by the words "additional", "additional".

Law of diminishing returns reads: as the use of a factor of production increases (with other factors fixed), eventually a point is reached at which the additional use of that factor leads to a decrease in output.

Starting from a certain moment, the successive addition of units of a variable resource (for example, labor) to an unchanged, fixed resource (for example, capital or land) gives a decreasing additional, or marginal, product per each subsequent unit of the variable resource. In other words, if the number of employees serving this line of activity will increase, then the growth in production will occur after a certain point more and more slowly, as the number of workers in production increases.

In fact, if on your garden plot you, without cultivating the land, get a crop equal to 8 buckets (80 kg) per hundred square meters, then after one cultivation of the land (weeding, watering, hilling) the crop will be 94 kg, after two treatments - 102 kg, after three - 105 kg. It is clear that the return of each subsequent processing with equal total costs of living and materialized labor will decrease.

This law is valid not only for agricultural production, but also for other industries. What happens if the number of workers increases to, say, 20 people?

The additional, or marginal, product of additional workers will be reduced. At the same time, we assume that each additional worker is equivalent to the main worker both in terms of individual productivity and in terms of qualifications. The marginal product starts to decrease because more workers are employed with the same amount of capital funds.

Consider an example.

Table 1. Illustration of the law of diminishing returns: the change in output depending on the change in the value of variable resources

Table 1 provides a visual numerical illustration of the law of diminishing returns. Shows the total amount of products that can be obtained by combining one or another amount labor resources with constant resources (the value of the latter is assumed to be unchanged). The next column reflects marginal productivity - it shows the change in output associated with the investment of each additional unit of labor resource. Note that in the absence of labor costs, output zero(an enterprise without people cannot produce products). The arrival of the first three workers is accompanied by increasing returns, since their marginal products are 8, 12, and 16, respectively. However, in the future, starting from the fourth worker, the marginal product (increase in total production) consistently decreases, so that for the ninth worker it is reduced to zero, and for the tenth - twelfth worker it has a negative value. Average productivity (or output per worker, also called labor productivity) is shown in the right column.

For clarity, we present a graphical representation of the resulting dependence. In the second figure, three phases are clearly visible: 1) total output is increasing at an accelerating pace; 2) the rate of elevation slows down; 3) returns are decreasing.

Rice. 1. Law of diminishing returns.

Rice. 2. Marginal and average performance

(1 - average performance, 2 - marginal performance).

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 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 on 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 a production function is 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 the marginal product from the variable factor indicates the limited possibilities for increasing output, which reaches maximum values ​​when the marginal product becomes equal to zero for a certain amount of the 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). production function 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 FROM 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 FROM, 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;

Average product from 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 improve overall efficiency, the firm should increase the use of the variable resource, at least up to stage II. Although the effectiveness of the variable factor decreases in stage II, increasing 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 prevents it from reaching this stage, the firm must stimulate demand for its product or use excess capacity to produce 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 its decrease 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 the factor is redistributed between different production processes, which ensures the leveling of the level of marginal productivity of the variable factor, the total return on this factor increases, and the maximum efficiency of the use of 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 is that in a short period, when the value production capacity is fixed, the marginal productivity of a variable factor will decrease starting from a certain level of costs 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 vacant jobs 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 the problem of their surplus, that is, workers will underutilize their working 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 the negative marginal return of the labor resources used, that is, when 9 people work in this firm.
A graphic representation of the law of diminishing returns is shown in Figure 5.3.

As you join all 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 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 invariability 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. After all, 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.

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