The manufacturing process is seen as the transformation of resources into products. The content of the production process lies in the fact that in the production process there is a process of transforming resources into economic goods for production and consumer purposes. Technology reflects the form of a stable interconnection of production factors. For a manufacturer, not only technology is important, but also a combination of production factors. Technological dependence between the structure of inputs (production factors) and the maximum possible output is expressed using production function.

Production function - the relationship between the input combination of factors of production (labor L, capital K) and the volume of production (Q):

Q = f (K, L).

The two-factor production function can be represented graphically (Figure 12):

ΔK

ΔLL Fig 5.1.1 Map of isoquants

Ql; Q2; Q3 - isoquant map .

Isoquanta(equal product curve) shows the different cost combinations that produce the same output. The negative slope of the isoquant measures marginal rate of technological replacement of resources(MRTS LK): MRTS LK = -ΔK / ΔL, which shows how much K should be abandoned in order to increase the number of workers L.

Production function properties:

♦ An increase in the cost of one of the resources while the cost of another resource remains unchanged, allows you to increase the output Q of the product, that is, the function increases from any of its arguments.

♦ An isoquant can be drawn through any point of the plane.

♦ All isoquants have a negative slope.

♦ The isoquant, showing the larger output Q of the product, is located to the right and above.

♦ If one of the factors = 0, then the output Q of the good = 0.

So, the isoquants are concave to the origin (at each point of the isoquant, the factor has a different performance), show only the effective area of ​​use of production factors, reflect the possibility of substitution.

Compare isoquant map and indifference curve map: General indicators:

♦ Negative tilt angle.

♦ Do not overlap with each other.

♦ The consumer and the firm behave like buyers (ie, as consuming economic agents).

Differences:

♦ Isoquanta shows a certain number of units of a product Q, and indifference curves do not have a quantitative, but only an ordinal assessment.

♦ A firm, when acquiring resources K and L, is not guaranteed to receive the maximum profit when producing Q goods, and in the indifference curves for the consumer when consuming a set of goods on the farthest indifference curve, maximization of utility is guaranteed.

Short term- the period during which at least one factor of production remains unchanged. The task of microeconomic analysis of production in the short term is to determine the change in the quantity of a variable factor of production per volume of output, i.e. identify the conditions for the effectiveness of the variable factor of production.

So in short term(SR) at least one of the factors of production is fixed. Suppose that capital (K) is a constant factor, and labor (L) is a variable factor.

In conditions when one resource is variable, the following concepts are used:

♦ total product of labor (TP L);

♦ average product of labor (AP L): AP L = TP L / L;

♦ marginal product of labor (MP L): MP L = Δ TP / ΔL.

The relationship between TP L, AP L and MP L is shown in Fig. 13.

♦ If MP L> AP L, then AP L is increasing;

♦ If MP L< АР L , то AP L убывает;

♦ If MP L = AP L, then AP L max.

Rice. 13. The relationship of the general, average and marginal product of labor

Production in the short term can be divided into 3 stages:

stage 1 - from 0 to L 2, where AP L = max;

stage 2 - from L 2 to L 3, where the value of MP L - 0;

1 and 3 stages are not desirable for the company, because at the 1st stage - an excess of capital relative to labor, and at the 3rd stage - an excess of labor relative to capital.

The law of diminishing marginal productivity shows that, starting from a certain moment, an increase in the volume of use of one resource with a constant volume of another leads to a decrease in the marginal product of the variable factor (MP L).

The law of diminishing marginal productivity reflects the following:

♦ the inevitability of a decrease in the return on the variable factor;

♦ opportunities to increase production in the short term are limited;

♦ the nature of the operation of the law is determined by the peculiarities of the technology of production of goods;

♦ Applicable only to short-term conditions.

Long term in the activities of the firm is sufficient to change all the resources involved. Therefore, in long term all factors of production are variables.

The long-term strategy of a firm can be viewed in two aspects:

1. K and L change simultaneously, but in different directions, which is expressed through an isoquant. MRTS LK determines the amount of capital that can be replaced by each unit of labor at Q - const.

MRTS LK depends on the marginal products of the factors of production (K and L). The larger the marginal product of labor, the less it is needed to replace capital, i.e. there is an inverse relationship between the MRTS and the marginal products of the factors of production.

2. K and L change simultaneously and in the same direction. The relationship between the increase in factors of production and the volume of output is characterized by economies of scale.

Positive economies of scale- when the volume of output increases to a greater extent than the cost of resources.

Constant economies of scale- when the volume of output increases in the same proportion as the cost of resources.

Negative economies of scale - when the volume of output increases to a lesser extent than the cost of resources. Let us show the effect of scale graphically (Fig. 14).

The closer the isoquants are to each other, the more the positive economies of scale are manifested. Stable spacing between curves characterizes constant economies of scale. The greater the distance between isoquants, the greater the negative economies of scale. So, if in the short term it is important for the firm to find the optimal ratio of production factors (K, L), then in the long term the problem of choosing the required scale of the firm's activities is solved.

The nature of economies of scale:

♦ Due to the peculiarities of the technology.

♦ Determined empirically.

♦ Determines the optimal production size.

The law reflects the influence of the costs of a variable factor of production on the change in the volume of production with the constancy of all other factors.

The essence of the law is that if we successively attach units of a variable resource ( labor force) to a constant factor (equipment), then from a certain moment the marginal product for each subsequent unit of production will not increase, as in the beginning, but decrease.

The law states: an increase in the variable factor with fixed values ​​of the rest and the invariability of the technology ultimately leads to a decrease in its performance.

Let's consider in more detail the operation of the law using an example.

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

In order to illustrate the operation of the law of diminishing marginal productivity, the following concepts should be introduced:

General 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 division total product by the value of the variable factor;

Limit product- the increment of the total product due to the increment of the variable factor.

If the variable factor is incremented continuously by infinitely small values, then its performance will be expressed in the dynamics of the marginal product, and we will be able to track it on the graph (Figure 6).

Figure 6 - Action of the law of diminishing marginal productivity

Let's build a graph where the main line OABSV is the dynamics of the total product:

Let's divide the curve of the total product into several segments: ОВ, ВС, СD.

On the segment OB, we arbitrarily take a point A, at which the total product (OM) is equal to the variable factor (OP).

Let's connect the points O and A - we get the OAP, the angle of which from the point of the coordinates of the graph will be denoted by α. The ratio of AP to OR is the average product, it is also tg α.

Draw a tangent line to point A. It will cross the axis of the variable factor at point N. An APN will be formed, where NP is the marginal product, aka tg β.

On the entire segment OB tg α< tg β, т. е. средний продукт растет медленнее предельного. Следовательно, имеется возрастающая отдача от переменного фактора и закон убывающей предельной производительности своего действия не проявляет.

In the BC segment, the growth of the marginal product decreases against the background of the continuing growth of the average product. At point C, the marginal and average products are equal to each other and both are equal to γ. Thus, the law of diminishing marginal productivity began to emerge.

On the CD segment, the average and marginal products are reduced, and the marginal one is faster than the average. At the same time, the overall product continues to grow. Here the operation of the law is fully manifested.

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

Similar information:

1. A) Establishing the compliance of this specific act with the signs of a particular corpus delicti provided for by the criminal law.

The law of diminishing marginal productivity

The essence of the law.

With an increase in the use of factors, the total volume of production 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 an increase in the variable factor, the total volume of production not only does not grow, but even decreases.

The law states: an increase in the variable factor with fixed values ​​of the rest and the invariability of the technology ultimately leads to a decrease in its performance.

Operation of the law.

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

In order to illustrate the operation of the law of diminishing marginal productivity, the following concepts should be introduced:

• - common 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 - the increment of the total product due to the increment of the variable factor by one.

If the variable factor is incremented continuously by infinitely small values, then its performance will be expressed in the dynamics of the marginal product, and we can track it on the graph (Fig. 15.1).

Let's build a graph where the main line is OABS - the dynamics of the overall product.

• 1. Let's divide the curve of the total product into several segments: About, Sun, CO.
• 2. On the segment ОВ, we arbitrarily take the point A, in which the dynamics of the overall product (OM) coincides with the variable factor (OP).
• 3. Connect the points 0 and A - we get D OAR, the angle formed by the sides OA and OP, denote by a. Attitude AR To OR - average product, aka 1§ a.

Rice. 15.1.

4. Draw a tangent to the point A. It will cross the axis of the variable factor at the point N. D will be formed 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 manifest itself.

On the segment Sun the growth of the marginal product is contracting against the background of the continuing growth of the average product. At point C, the limiting and average products are equal to each other and both are equal to tg at. So it began to show the law of diminishing marginal productivity.

On the segment CD the average and marginal products are reduced, and the marginal one is faster than the average. At the same time, the overall product continues to grow. Here the operation of the law is fully manifested.

Behind the point D, despite the growth of the variable factor, an absolute reduction in even the total product begins. It is difficult to find an entrepreneur who does not feel the operation of the law beyond this point.

Isoquant and isocost. Manufacturer's balance. Economies of scale

Isoquant of production output.

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

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

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

Isoquants can have different forms:

• a) linear - when it is assumed that one factor is completely replaceable by another;
• b) in the shape of an angle - when a rigid complementarity of resources is assumed, outside of which production is impossible;
• v) broken curve, expressing the limited ability to substitute resources;
• G) smooth curve - the most common case of interaction of factors of production (Fig. 16.2).

The marginal rate of technical substitution of resources.

The shift of the isoquant is possible by raising the growth of the attracted resources of those

Rice. 16.1.

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

Rice. 16.2.

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

where L / LH5 is the marginal rate of technical substitution of one factor for another.

Manufacturer's balance.

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

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

A manufacturer's budget constraint can be calculated as follows:

where WITH - manufacturer's budget constraint; d - the price of capital services (hourly rent); A "- capital; and> - price of labor services (hourly wages); I - work.

Even if the entrepreneur uses not borrowed money, but own funds- this is still a cost of resources, and they should be considered. Factor price ratio g / t shows the slope of the isocost (Fig. 16.3).

Rice. 16.3.

TO- capital; I - work

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

By combining the graphs of the isoquant and isocost, it is possible to determine producer equilibrium, those. the optimal set of resources that, given the available financial costs gives the best result (fig. 16.4).

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

Rice. 16.4.

Y y y2 yy ~ 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 greater proportion (fig. 16.5).

The law of diminishing marginal productivity is one of the generally accepted economic statements, according to which the use of one new production factor over time leads to a decrease in the volume of output. Most often, this factor is additional, that is, it is not at all obligatory in a particular industry. It can be applied deliberately, directly in order to reduce the number of manufactured goods, or due to the coincidence of some circumstances.

What is the theory of decreasing productivity based on?

As a rule, the law of diminishing marginal productivity plays a key role in the theoretical part of production. It is often compared to the diminishing clause in consumer theory. The comparison is that the supply mentioned above tells us how much each individual buyer, and the consumer market, in principle, maximizes the product produced, and also determines by this the nature of the demand for pricing policy... The law of diminishing marginal productivity affects precisely the steps that the manufacturer takes, to maximize profits and the dependence of the set price on demand on his part. And in order for all these complicated economic aspects and the questions have become clearer and more transparent for you, we will consider them in more detail and with specific examples.

Pitfalls in the economy

To begin with, let's define the very meaning of the wording of this statement. The law of diminishing marginal productivity is by no means a decrease in the quantity of goods produced in one way or another for all centuries, as it appears on the pages of history textbooks. Its essence lies in the fact that it works only if it is unchanged if something is deliberately "inscribed" into the activity that slows down everyone and everything. Of course, this law does not apply in any way when it comes to changing performance features, introducing new technologies, etc., and so on. In this case, you say, it turns out that there is more in a small enterprise than in its larger counterpart, and this is the essence of the whole question?

Carefully reading the words ...

In this case, we are talking about the fact that productivity is reduced due to variable costs (material or labor), which, accordingly, are larger in a large enterprise. The law of diminishing marginal productivity is triggered when this marginal productivity of the variable factor reaches its maximum in terms of costs. That is why this wording has nothing to do with increasing the production base in any industry, no matter what it is characterized by. In this matter, we only note that an increase in the volume of manufactured commodity units does not always lead to an improvement in the state of the enterprise and the whole business as a whole. It all depends on the type of activity, because each a separate kind there is an optimal limit for the growth of production. And if this borderline is exceeded, the efficiency of the enterprise, accordingly, will begin to decline.

An example of how this difficult theory works

So, in order to understand how exactly the law of diminishing marginal productivity works, let us consider it with an illustrative example. Suppose you are the manager of a certain enterprise. There is a production base in a specially designated area, where all the equipment necessary for the normal functioning of your company is located. And now everything depends on you: to produce more or less goods. To do this, you need to hire a certain number of workers, draw up an appropriate daily routine, and purchase the required amount of raw materials. The more employees you have, the tighter you schedule, the more basics will be required for your product. Accordingly, production volumes will increase. It is on this that the law of diminishing marginal productivity of factors that affect the quantity and quality of work is based.

How does this affect the sales price of a product

We go further, and we take into consideration the question of Of course, the owner is a master, and he himself has the right to set the desired payment for his goods. However, it is still worth focusing on market indicators that have long been established by your competitors and predecessors in this area of ​​activity. The latter, in turn, has a tendency to constantly change, and sometimes the temptation to sell a certain consignment of goods, even if "not released", becomes great when the price reaches its maximum on all exchanges. In such cases, in order to sell as many commodity units as possible, one of two options is chosen: increasing the production base, that is, the raw materials and the area on which your equipment is located, or hiring more employees, working in several shifts, and so on. Further. It is here that the law of diminishing marginal productivity comes into force, according to which each subsequent unit of the variable factor brings a smaller increment general production than each previous one.

Features of the formula for decreasing productivity

Many, having read all this, will think that this theory is nothing more than a paradox. In fact, it occupies one of the fundamental positions in economics, and it is based not at all on theoretical calculations, but on empirical ones. The law of diminishing labor productivity is a relative formula derived from many years of observation and analysis of activities in various spheres of production. Going deeper into the history of this term, we note that for the first time it was voiced by a French financial expert named Turgot, who, as a practice of his activities, considered the features of work Agriculture... So, for the first time "the law of diminishing soil fertility" was derived in the 17th century. He said that the constant increase in labor applied to a certain piece of land leads to a decrease in the fertility of this plot.

A bit of economic theory by Turgot

Based on the materials that Turgot presented in his observations, the law of diminishing labor productivity can be formulated as follows: "The assumption that increased costs will lead to an increased volume of product in the future is always false." Initially, this theory had a purely agricultural background. Economists and analysts argued that it was impossible to grow more and more crops to feed many people on a plot of land that does not exceed 1 hectare. Even now, in many textbooks, in order to explain to students the law of diminishing marginal productivity of resources, it is the agricultural industry that is used as a clear and most understandable example.

How it works in agriculture

Let's now try to understand the depth of this question, which is based on a seemingly so banal example. We take a certain piece of land on which every year we can grow more and more quintals of wheat. Until a certain point, each addition of additional seeds will bring an increase in production. But a turning point comes when the law of diminishing productivity of a variable factor comes into force, implying that the additional costs of labor, fertilizers and other parts required in production begin to exceed the previous level of income. If you continue to increase the volume of production on the same plot of land, then the decline in the former profit will gradually turn into a loss.

But what about the competitive factor?

Assuming that this economic theory has no right to exist in principle, we get the following paradox. Suppose growing more and more spikelets of wheat on one piece of land will not be so expensive for the producer. He will spend on each new unit of his products in the same way as on the previous one, while constantly only increasing the volume of his goods. Consequently, he will be able to perform such actions endlessly, while the quality of his products will remain the same high, and the owner will not have to purchase new territories for further development... Based on this, we find that the entire amount of wheat produced can be concentrated on a tiny patch of soil. In this case, such an aspect of the economy as competition, simply excludes itself.

We form a logical chain

Agree that this theory has no logical background, since everyone has known since time immemorial that every wheat on the market differs in price depending on the fertility of the soil on which it was grown. And now we come to the main thing - it is the law of diminishing returns to productivity that explains the fact that someone cultivates and uses more fertile soil in agriculture, while others are content with less quality and suitable soils for such activities. Indeed, otherwise, if every additional centner, kilogram or even gram could be grown on the same fertile plot of land, then no one would have thought of cultivating lands less suitable for agricultural industry.

Features of past economic doctrines

It is important to know that in the 19th century, economists still wrote the mentioned theory exclusively in the field of agriculture, and did not even try to take it outside this framework. All this was explained by the fact that it was in this industry that such a law had the largest amount of obvious evidence. Among these, one can name a limited production area (this is a land plot), a fairly low rate of all types of work (processing was carried out manually, wheat also grew naturally), in addition, the range of crops that can be grown was quite stable. But given the fact that scientific and technological progress has gradually covered all areas of our life, this theory quickly spread to all other areas of production.

Towards modern economic dogma

In the 20th century, the law of diminishing productivity has finally and irrevocably become universal and applicable to all types of activity. The costs that were used to increase the resource base could become more, however, without territorial increase, further development simply could not be. The only thing that manufacturers could do without expanding their own boundaries of activity was to purchase more efficient equipment. Everything else - an increase in the number of employees, work shifts, etc. - inevitably led to an increase in production costs, and incomes grew at a much lower percentage, in relation to the previous indicator.

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

If capital is a 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 a diminishing return of this factor, that is, to a decrease in the marginal product or marginal productivity of labor. If the hiring of workers continues, then in the end they will interfere with each other (marginal productivity will become negative), and the volume of output will decrease.

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

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

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

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

The marginal product of capital $ MP_K $ is determined in a similar way.

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

There are three stages in the movement of the total product ($ TP $) curve. At stage 1, it rises upward at an accelerating rate, since the limit of the product ($ MP $) increases (each new worker brings more output than the previous one) and reaches a maximum at the point $ A $, that is, the growth rate of the function is maximum. After the point $ A $ (stage 2), due to the law of diminishing returns, the curve $ MP $ falls, that is, each hired worker gives a smaller increment in the total product compared to the previous one, so the growth rate of $ TP $ after $ TC $ slows down ... But as long as $ MP $ is positive, $ TP $ will still increase and reach its 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 curve of the average product $ AP $ is also determined by the dynamics of the $ MP $ curve. At stage 1, both curves grow until the increment in the volume of output from newly hired workers is greater than average productivity($ AP_L $) previously hired workers. But after the point $ A $ ($ max MP $), when the fourth worker adds less than the third to the total product ($ TP $), $ MP $ decreases, so the average output of the four workers also decreases.

Economies of scale

It manifests itself in the change 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 the activity of the company is characterized by a change in the number of all used production factors.

Figure 2. Curve of long-run and average costs of the firm

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

Figure 3. Dynamics of long-term average costs

Figure 4.

Suppose $ F_1 $ is a variable factor, while the other factors are constant:

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

The marginal product ($ MP $) is defined as the increase in the total product obtained as a result of infinitely small increments in the amount of the variable factor used:

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

Factor substitution rule: the ratio of the gains of the two factors is inversely related to the value of their marginal products.

The law of diminishing marginal productivity argues that with an increase in the use of a production factor (with the rest unchanged), sooner or later a point is reached at which additional use of a variable factor leads to a decrease in the relative and further absolute volumes of output.

Remark 1

The law of diminishing productivity has never been proven strictly theoretically, it was derived experimentally.

Factors of production are used in production only when their productivity is positive. If we denote the marginal product in monetary terms through $ MRP $, and marginal cost- through $ MRC $, then the resource usage rule can be expressed by equality.