production called any human activity to transform limited resources - material, labor, natural - into finished products. The production function characterizes the relationship between the amount of resources used (factors of production) and the maximum possible output that can be achieved, provided that all available resources are used in the most rational way.
The production function has the following properties:
1 There is a limit to the increase in production that can be reached by increasing one resource and keeping other resources constant. If, for example, in agriculture increase the amount of labor with constant amounts of capital and land, then sooner or later there comes a point when output stops growing.
2 Resources complement each other, but within certain limits, their interchangeability without reducing output is also possible. Manual labor, for example, may be replaced by the use of more machines, and vice versa.
Manufacturing cannot create products out of nothing. The production process is associated with the consumption of various resources. The number of resources includes everything that is necessary for production activities - raw materials, energy, labor, equipment, and space.
In order to describe the behavior of a firm, it is necessary to know how much of a product it can produce using resources in various volumes. We will proceed from the assumption that the company produces a homogeneous product, the amount of which is measured in natural units - tons, pieces, meters, etc. The dependence of the amount of product that a company can produce on the volume of resource costs is called production function.
But an enterprise can carry out the production process in different ways, using different technological methods, different variants organization of production, so that the amount of product obtained with the same input of resources may be different. Firm managers should reject production options that give a lower output of the product if, for the same input of each type of resource, a higher output can be obtained. Similarly, they should reject options that require more input of at least one resource without increasing the yield of the product and reducing the cost of other resources. Options rejected for these reasons are called technically inefficient.
Let's say your company manufactures refrigerators. For the manufacture of the case, you need to cut sheet metal. Depending on how the standard sheet of iron is marked and cut, more or less parts can be cut out of it; accordingly, for the manufacture of a certain number of refrigerators, less or more standard iron sheets will be required. At the same time, the consumption of all other materials, labor, equipment, electricity will remain unchanged. Such a production option, which can be improved by more rational cutting of iron, should be recognized as technically inefficient and rejected.
technically efficient are called production options that cannot be improved either by increasing the production of a product without increasing the consumption of resources, or by reducing the costs of a resource without reducing output and without increasing the costs of other resources. The production function takes into account only technically efficient options. Its meaning is greatest the quantity of a product that an enterprise can produce given the volume of resource consumption.
Consider first the simplest case: an enterprise produces a single type of product and consumes a single type of resource. An example of such production is quite difficult to find in reality. Even if we consider an enterprise providing services at customers' homes without the use of any equipment and materials (massage, tutoring) and spending only the labor of workers, we would have to assume that workers go around customers on foot (without using transport services) and negotiate with customers without the help of mail and telephone.
production function- shows the dependence of the amount of product that a firm can produce on the amount of costs of the factors used
Q= f(x1, x2…xn)
Q= f(K, L),
where Q- output volume
x1, x2…xn– volumes of applied factors
K- volume of the capital factor
L- volume of labor factor
So, the enterprise, spending a resource in the amount X, can produce a product in quantity q. production function
The production function characterizes the maximum possible amount of production that can be obtained using a given combination of resources.
In the theory of production, a two-factor production function of the form Q = f(L, K) is traditionally used, characterizing the relationship between the volume of output (Q) and the amounts of labor resources (L) and capital (K) used. This is explained not only by the convenience of graphical display, but also by the fact that the specific consumption of materials in many cases depends little on the volume of output, and such a factor as production area is usually considered together with capital.
The production function is built for this technology. An improvement in technology that increases the maximum achievable output under any combination of factors is reflected by a new production function.
Although the production functions are different for different types production, however, have common properties.
There is a limit to the increase in output that can be achieved by increasing the cost of one resource, other things being equal.
This implies, for example, that in an enterprise with a given number of machines and production facilities, there is a limit to increasing production by attracting more workers.
The increase in production that can be achieved by increasing the number of workers employed in it will obviously approach zero. Indeed, it is possible to reach a point where each new worker in the enterprise will contribute to a reduction rather than an increase in output. This can happen if the worker is not provided with equipment for work and his presence interferes with the work of other workers and reduces their efficiency.
There is a certain complementarity of factors of production, in addition, without a reduction in the volume of production, a certain interchangeability of these factors is also possible.
Workers perform their jobs more efficiently if they are equipped with all necessary tools. Similarly, tools can be useless if workers are not skilled enough to use them.
4.1.1. ISOQUANT
Isoquant (line of equal output) - a curve representing an infinite number of combinations of factors of production (resources) that provide the same output.
Isoquants for the production process mean the same as indifference curves for the consumption process and have similar properties: they have a negative slope, are convex relative to the origin, and do not intersect with each other. The further the isoquant is from the origin, the greater the output it represents. At the same time, unlike indifference curves, where the total satisfaction of the consumer cannot be accurately measured, isoquants show real levels of production: 100 units, 300 thousand units. etc.
Isoquants (as well as indifference curves) can have different configurations (Fig. 4.1).
Rice. 4.1. Possible isoquant configurations
The linear isoquant (Fig. 4.1, a) assumes perfect substitution of production resources, so that a given output can be obtained using either labor, or only capital, or using infinitely possible combinations of both resources. The isoquant presented in fig. 4.1, b, is typical for the case of rigid resource complementarity: only one method of producing a given product is known, labor and capital are combined in the only possible ratio.
On fig. Figure 4.1c shows a broken isoquant, assuming limited substitution of resources (only at breakpoints) and few production methods. Finally, in fig. 4.1, d presents an isoquant, suggesting the possibility of continuous substitution of resources within certain limits, beyond which the replacement of one factor by another is technically impossible.
Many engineers, entrepreneurs, and manufacturing workers consider the broken isoquant to be the most realistic representation of the production capabilities of most modern industries. However, traditional economic theory usually operates with smooth isoquants, like the one shown in Fig. 4.1, d, since their analysis does not require the use of complex mathematical methods. In addition, isoquants of this type can be considered as some kind of approximate approximation of a broken isoquant. By increasing the number of production methods, and thus increasing the number of breakpoints, we can (in the limit) represent the broken isoquant as a smooth curve.
4.1.2. INTERCHANGEABILITY OF FACTORS OF PRODUCTION
The slope of the isoquant characterizes the marginal rate of technical substitution of one factor for another:
. (4.1)
The marginal rate of technical substitution of labor for capital is the amount by which capital can be reduced through the use of one additional unit labor at a fixed volume of output (Q = const).
Question 11. In the short run, a competitive profit maximizing or loss minimizing firm will not continue production if:
a) the price of the product is below the minimum average cost;
b) average fixed costs are higher than the price of the product;
c) the price of the product is below the minimum of average variable costs;
d) the price of the product is below marginal cost;
e) the total income does not cover the total costs of the firm.
The correct answer is d).
The firm will produce at its optimum output if price is equal to marginal cost. If the firm continues to produce, the price will exceed marginal cost and the firm will begin to incur additional losses. Therefore, either the total profit of the firm will begin to decline, or its losses will begin to increase. If the price of the product is below the minimum average cost (a) or the average fixed cost is above the price (b) or the total revenue does not cover the total cost (e), the firm will be unprofitable. If the price of a product is below average variable cost (c), then the firm must leave the market.
Production in modern microeconomics refers to the activity of using factors of production in order to create a product or service and achieve the best result. In the process of production, factors of production are used: labor, capital, land, etc. It is possible to single out the constituent parts of each factor and consider them as independent factors. For example, in the “labor” factor, the labor of managers, engineers, workers, etc. can be singled out.
AT economic theory allocate primary factors of production, which, in accordance with the theory of factors of production (it is associated with the name of the French economist Jean B. Say) create a new value. These include labor, capital, land, and entrepreneurial ability. Secondary factors do not create new value. In modern production, the role of energy and information is increasing, they have signs of primary and secondary factors.
The production function expresses the technological relationship between the final output and the costs of production factors and. It is implicitly written as follows:
where is the form of the function; - the maximum output that can be obtained with the technology used and the available number of production factors (s).
In models of the production process, in production functions, two main factors are taken into account: labor and capital. This allows you to analyze the most important connections and dependencies in the production process without simplifying their real content. In the production function, output, labor and capital costs are measured in natural units (output in meters, tons, etc., labor costs in man-hours, capital costs in machine hours, etc.).
An example of a production function that explicitly represents the relationship between output and inputs of production factors is the Cobb-Douglas function:
where is the technology efficiency;
Private elasticity of output with respect to labor;
Private elasticity of output with respect to capital.
The function was derived by mathematician C. Cobb and economist P. Douglas in 1928 on the basis of statistical data from the US manufacturing industry. This now well-known function has a number of remarkable properties. Below we analyze the economic meaning of its parameters. The Cobb-Douglas function describes an extensive type of production.
If factors of production are used, then the production function has the form:
where is the amount of the i-th factor of production used.
The properties of the production function are as follows.
1. Factors of production are complementary. This means that if the costs of at least one factor are equal to zero, then the output is equal to zero: The exception is the function
According to such a function, only labor or only capital can be used, and output will not be zero.
- 2. The property of additivity means that it is possible to combine the factors of production and. But pooling is only worthwhile if the output after pooling exceeds the sum of outputs before the pooling of factors of production.
- 3. The property of divisibility means that the production process can be carried out on a reduced scale if the following condition is met
At the same time, if, then we have constant returns to scale; if - increasing returns to scale; if so, there are diminishing returns to scale. With a constant return, the average cost of the firm does not change, with increasing returns they decrease, with decreasing returns they increase.
The isoquant (or the constant product curve - (isoquant) is a graph of the production function. The points on the isoquant reflect the many combinations of production factors, the use of which provides the same output.
Isoquants characterize the production process in the same way as indifference curves characterize the consumption process. They have a negative slope, are convex with respect to the origin. An isoquant (Fig.), which lies above and to the right of another isoquant, represents a larger volume of output (products). However, unlike indifference curves, where the total utility of a set of goods cannot be accurately measured, isoquants show real output. The set of isoquants, each of which represents the maximum output obtained by using factors of production in various combinations, is called the isoquant map.
The real isoquant with output is shown in Figure 1.1 a in three-dimensional space. Its projection is marked with a dotted line and transferred to Fig. 1.1 b. If the noted combinations of factors of production are used, but a more advanced technology is used, then the output will be equal. But the projection of an isoquant with such an output will be the same as that of an isoquant with a smaller output. Economists place an isoquant with a large output on the plane (Fig. 1.1 b) above and to the right of the isoquant with a smaller output.
On fig. a the relationship between output and costs is broken: the output is obtained with more labor and capital than. Below it will be shown how the applied technology and its parameters influence the location of the isoquant.
Technology efficiency (a parameter in the Cobb-Douglas function) can be represented graphically as follows (Fig.). At the points and the release is the same. On fig. b isoquant represents more efficient technology, since the cost per unit of production is lower here than on the isoquant in Fig. a.
1.1. The enterprise, its internal and external environment
Economic agents are divided into two groups: producers and consumers. The former are called enterprises or firms.
A firm (it.: “signature on paper”) is an economic agent (economic unit) that is engaged in economic, industrial, commercial activities and has economic and administrative independence stipulated by law.
The concept of "firm" is somewhat broader than the concept of "enterprise", since it can be used in relation to one or several enterprises united organizationally, technologically, and finances.
The main features of the company are:
- Brand name on state language country in which the company is registered. It can be complete and abbreviated, translated into other languages.
- From the date of registration, the company acquires the status legal entity. As a legal entity, it operates on the basis of state legislation, its founding documents (charter, founding agreement), has its own reporting, seal, stamp and product details; may open branches and representative offices; acts as a plaintiff and defendant in court, arbitration.
- A trade mark is a designation placed directly on a product or on its packaging. A legally registered trademark is a trademark. A trademark can be expressed in fonts, graphics, or a special symbol. The trademark performs the function of guaranteeing the quality of goods and advertising. The procedure for acquiring the right to a trademark, its execution and protection is established by the legislation of the country.
- The image of the company and its style, achieved with the help of a logo - a special font for writing the name of the company, slogan, motto, anthem, special printing symbols in advertisements. The main task of the corporate image and style is to make products recognizable and different from the products of other companies.
In contrast to the market order, which assumes the spontaneous nature of relations, firms are based on the hierarchical principle of organizing economic activity. In a market economy, there are indirect methods of control, in a firm - direct ones; the market economy excludes dictatorship, firms assume unity of command and are based on administrative forms of management.
The activities of the company can be viewed from two sides: individual and public.
In terms of individual goals- its activity is aimed at maximizing profits. Hence, it is interested in the highest possible prices for its products, low prices for resources. On the other hand, the entrepreneur does public function: the creation of products, the study of the needs of society, their satisfaction.
The desire of an entrepreneur to succeed breeds competition. It requires a high return from the entrepreneur, the ability to quickly respond to the needs of society and scientific and technical progress. The entrepreneur always operates in conditions of uncertainty, instability and risk.
Protective measures are used to reduce and manage risk.
One of the methods - diversification(diverse): production of several types of products. Risk can be reduced with self-insurance – For this, a special reserve fund is created. One way is hedging(hedge - to enclose) - insurance against possible losses due to fluctuations in the price of goods on the market through the purchase of futures contracts.
Each entrepreneur interacts with the environment, on the functioning of which his success and degree of risk depend. The internal environment consists of relations between the owners of capital, managers and employees.
The external environment includes relations:
- with other entrepreneurs. Although there is competition, the bankruptcy of some enterprises can cause a chain of bankruptcies;
- with exchanges - the organizational centers of the market economy;
- with the monetary system - through it the movement of financial resources is carried out;
- with insurance companies;
- with the Ministry of Finance, to which taxes are paid;
- with agencies such as:
- Central Issuing Bank;
- Export-import bank;
- State Pension Fund etc.
1.2. Forms of business organization
Depending on the main purpose of the enterprise are divided into commercial and non-commercial. In cases where private commercial or state enterprises cannot ensure the satisfaction of individual and social needs, private non-profit enterprises are created and operate. These include voluntary charity organisations, environmental societies, organizations helping the disabled, consumer associations, various unions, etc., created, as a rule, in the field of social services. The establishment of such enterprises is the result of private initiative. Their resources are formed from private donations, state subsidies, membership fees, voluntary work of members of these organizations. They usually receive tax breaks. Making profit from such enterprises is not the goal.
By type and nature of activity distinguish between industrial, transport, agricultural, financial and other enterprises.
Enterprises are divided into small, medium, large and extra large.
Role small businesses in a market economy is characterized by:
- flexibility, the ability to quickly respond to changing market conditions;
- multiplicity;
- constant support for competition due to their multiplicity and flexibility, low production costs due to the lack of expenses for the administrative apparatus, etc.;
- fast update.
Medium firms, unlike small firms, are not as numerous. They tend to capture certain segments of the market and stick to a "niche" specialization.
Although the majority of enterprises in all countries are small and medium, the leading role in the economy, despite their relatively small number, belongs to large enterprises.
Large enterprises have both advantages and disadvantages. The advantages of large firms are as follows:
- only large firms have access to mass and serial production;
- they have financial opportunities to master the achievements of scientific and technical progress, create new industries, and conduct scientific research;
- large firms are characterized by stability, as a rule, they are not physically liquidated, but only change owners;
- they have economies of scale.
By type of ownership distinguish between private, state, municipal and cooperative enterprises.
State enterprises can be both commercial and non-commercial. The state (or municipality) acts here as the organizer of production and founder. Usually, state-owned enterprises operate in areas of economic activity that do not attract private business due to excessively large initial investments, investments with a long payback period, and the social significance of their products. The state takes over this production in order to better meet social needs and stimulate scientific and technological progress.
The share of state-owned enterprises in the total industrial output fluctuates in different countries from 20 to 25%. Most of the state-owned enterprises are concentrated in the extractive industries, public transport, road construction, etc.
have a special status unitary enterprises- commercial organizations that are not endowed with the right of ownership of the property assigned to them. Their property is state or municipal property and cannot be divided into shares, shares. According to the nature of the rights on the basis of which indivisible property is assigned to unitary enterprises, enterprises based on the right of economic management and enterprises based on the right of operational management are distinguished. The difference between them is that the former are more independent: they are not liable for the debts of the owner, and the owner is not liable for the debts of the enterprise. Unitary enterprises of the second type are formed only at the federal level. The state is responsible for the obligations of these enterprises.
Production cooperatives based on a private-collective form of ownership. A cooperative is a voluntary association of citizens on the basis of membership for joint economic activities. The owners of the means of production in such enterprises are also workers. Therefore, their income consists of two sources: wages and profits.
The main share of goods and services in developed countries is produced by enterprises owned by private individuals. Private enterprise can be organized in three main legal forms: individual enterprise where the owner of the capital is one person; partnerships on shares (partnerships), where the capital of several persons is combined; joint-stock company (corporation), where the share of each is confirmed security- share.
By ownership of capital allocate national, foreign and joint (mixed) enterprises.
In business practice various countries also developed join types, which differ depending on the goals of the association, the nature of the relations between their participants, the degree of independence of the enterprises included in the association: cartels, syndicates, pools, trusts, concerns, industrial holdings, conglomerates, financial and industrial groups, consortiums.
1.3. Production function and its properties. Total, average and marginal product of a variable factor
Production is the process of converting inputs into finished products. The task of the company is to use resources in the most efficient way, to get the greatest return from them. It is characterized production function. It shows the maximum possible output that can be obtained with given resources:
Q=f(x 1 , x 2 , x 3 , … x n),
where x 1 , x 2 , x 3 , … X n are types of resources.
Production function properties:
The manufacturing process takes place over time. Based on this, two periods can be considered: short-term and long-term.
short term- this is such a period during which producers are able to change some part of the resources used. It is too short to change the production capacity of the enterprise, but sufficient to change the degree of its utilization. Factors of production (labor, raw materials, auxiliary materials, etc.) that can be changed within a short period are called variables (variable). All fixed factors are fixed.
Long term- this is a period when the company can change all input resources and technology, reorganize, modernize, fundamentally expand or reduce production. In this period, all factors of production are variable.
result production process is a product. In the framework of the simplest economic analysis, the general (cumulative), average and marginal product of a variable factor is studied.
Total variable factor product(Total product - TP) is the volume of output produced with a certain amount of a given factor and other constant factors of production.
In the practice of management, such a trend has been noticed, which is formulated as the law of diminishing returns on factors of production or the law of diminishing marginal productivity. Its essence lies in the fact that an increase in the use of one of the factors with a fixed value of the others leads to a consistent decrease in the return on its use.
Average product of variable factor AP V- attitude TP V to the used amount of the variable factor, or: how much output is produced per unit of the variable factor:
In this regard, research marginal product of the variable factor MP V- the increase in the total product obtained as a result of applying an additional unit of this factor.
Rice. 1. General ( TP), average ( AP L) and limit ( MP L) variable factor product.
In this case, the variable factor is
the amount of labor (labor - labor)
It can be proved that the enterprise must increase any variable factor (the number of labor force) while the others remain unchanged until its average and marginal product are equal, on the graph - up to L 3 . The remaining funds must be used either to increase other factors, or in an alternative way (for example, put in a bank at interest).
Thus, such an analysis makes it possible to determine the optimal volume of production and the optimal combination of production factors.
1.4. Curves of equal product (isoquants) and lines of equal costs (isocosts)
Producers are also consumers, using resources: capital and workers. In this case, indifference curves are also used to study their behavior - isoquants (isoquant) or lines of equal product and budget lines – isocosts (isocost) or equal cost lines.
Rice. 2. Isoquants representing different levels release.
To– production capital (equipment); L- number of workers
For a firm, isoquants are equal utility curves, but unlike indifference curves, they show real output.
The set of isoquants, each of which shows the maximum output achieved by using certain combinations of resources, is called isoquant map. The further the isoquant is located from the origin, the greater the volume of production it represents.
On the isoquant, the increase in the use of one factor ( L) is offset by a decrease in the use of another factor ( To). From how many units of one factor ( To) can be abandoned to increase the second factor ( L) per unit, shows marginal rate of technical replacement - MRTS:
Usually, MRTS decreases as you move along the isoquant.
On isoquants, one can see the intensity of the use of various resources in a certain variant of their combination. production method BUT- capital intensive method AT- labour intensive.
In the analysis of isoquants, natural indicators of the resources used and output are used. But the most cost-effective combinations depend on resource prices.
With a price ratio p L /p K can be portrayed equal cost line or a price line - isocost (or budget line).
Rice. 3. Lines of equal costs (isocosts)
The isocost equation:
C=p K K+p L L.
An increase in the company's capabilities (its budget) or a decrease in prices shifts the isocost to the right. Conversely, if prices change, the slope of the isocost changes.
1.5. manufacturer's optimum. Returns to scale
The equilibrium (optimum) of the producer is characterized by the point of contact of the isocost and the isoquant - the point e - the total amount of costs for the production of this output is minimized.
Rice. 4. Optimum manufacturer
Here is the equality:
When prices change, first, the firm's profitability changes; second, the firm can purchase more of the cheaper resource. One can consider decomposing the overall effect of price changes into a substitution effect and an income effect.
Expanding production, the company is faced with the concept "returns to scale". It shows how much the volume of production increases with an increase in the use of factors of production.
If output increases in proportion to the increase in factors of production, this indicates constant returns to scale.
If output grows faster than the amount of inputs used, then increasing returns to scale, i.e. resources are saved. With large production scales, there are relatively less costs for management, electricity, etc.
If output grows more slowly than the amount of resources used, then we have diminishing returns to scale, i.e., an increase in output requires a greater increase in the resources used. This may be due to handicapped management of large-scale production, coordination between links is disrupted.
In the case of increasing returns to scale, the enterprise must increase production, since this leads to relative economies (per unit of output).
Diminishing returns indicate that the effective size of the enterprise has already been reached and a further increase in production is impractical.
Rice. 5. Returns to scale.
a) constant returns to scale (O a=ab=bs );
b) diminishing returns to scale (O a<аб<бс);
in) increasing returns to scale (O a>ab>bs )
Based on the analysis carried out, the following conclusions can be drawn:
- Analysis of output using isoquants makes it possible to determine the technological efficiency of production (option a or b).
- The intersection of isoquants with isocosts characterizes not only technological, but also economic efficiency, i.e., it allows you to choose a technology depending on prices (labor-saving, capital-saving, etc.).
- Analysis of the line of growth and returns to scale reveals the concept of the effective size of the enterprise.
1.6. Costs and results: total, average and marginal values of revenue and costs
Having produced a certain amount of products and sold it, the company receives revenue (income). It is necessary to distinguish between total (cumulative) revenue, average and marginal.
Total (cumulative) revenue(Total revenue - TR) is the amount of revenue received by the company from the sale of all goods produced. At a constant price, it is equal to:
Average revenue (AR) is the revenue per unit of product sold:
marginal revenue(Marginal revenue - MR) - an increase in income that arises due to an infinitesimal increase in output (usually by one):
Production costs are primarily considered in the accounting sense, that is, as monetary costs for the acquisition of resources for production. These are explicit or external costs.
However, resources can be used in different ways, producing either one or the other product. Therefore, it is important to assess in advance how to use limited resources economically. For such an analysis, the category "opportunity costs" or opportunity cost. These are implicit or internal costs. They are determined by the value of the resources owned by the enterprise (own buildings, own labor, own capital). Capital can be deposited in a bank at interest, own premises can be rented out, etc. For example, buying a bakery costs $300,000. This money can be deposited in the bank and receive interest. At 15% per annum, this is equal to 15 thousand dollars. Consequently, the buyer refuses 15 thousand dollars. This is included in the opportunity cost.
Based on this, distinguish accounting and economic profit. Accounting profit equal to total revenue minus accounting (external) costs. economic profit
Taking into account time limits, production costs are divided into permanent (fixed cost) and variables (variable cost). In addition, distinguish cumulative or total (total cost), average (average cost) and marginal (marginal cost) production costs.
total costs- is the sum of the costs of acquiring the factors of production necessary for the production of a certain amount of goods. They consist of total fixed cost (TFC) and total variable cost (TVC) costs. TFC the company cannot change in the short term: the maintenance of industrial buildings, rent, administrative expenses, etc. They do not depend on the quantity of products produced and are available even when products are not produced. TVC change depending on the quantity of products produced: the cost of raw materials, fuel, etc.
TC=TFC+TVC.
Note that the S-shaped form (see Fig. 6) of total variable costs is associated with the effect of returns to scale: in the initial period of the organization of production, the company has not yet reached optimal sizes, capacities are being developed, so costs are growing faster than production volumes. In the future, there is a relative cost savings, but in the end, when the enterprise crosses the line of effective production size, total variable costs increase sharply.
Average cost of production (average cost - AC) – unit cost
AC=TC/Q.
AC are also divided into fixed and variable average costs, i.e.
AC=AFC+AVC.
A.F.C. decrease with an increase in output (for example, rent per unit of output), and AVC usually first decrease, and then, due to the law of diminishing returns of factors of production, increase.
Marginal cost (MC) is the increase in total cost due to an infinitesimal increase in production. MS are always variable costs.
The concept of marginal cost is of strategic importance to the firm. It allows you to determine those costs, the value of which the company can directly control - whether to increase production by several units or reduce.
Marginal cost usually decreases first (followed by a decrease in average cost), since it is a variable cost on the same basis of fixed costs, and then increases.
Rice. 6. General, average and marginal costs of the enterprise
conclusions
Each entrepreneur interacts with the environment, on the functioning of which his success and degree of risk depend. The internal environment consists of relations between the owners of capital, managers and employees. The external environment includes relationships: with other entrepreneurs; with exchanges; with the monetary system; with insurance companies; with the Ministry of Finance; with agencies such as the Central Issuing Bank, Export-Import Bank, State Pension Fund, etc.
Depending on the main purpose of the enterprise are divided into commercial and non-commercial. According to the type and nature of activity, industrial, transport, agricultural, credit and financial and other enterprises are distinguished. Enterprises are divided into small, medium, large and extra large. According to the forms of ownership, private, state, municipal and cooperative enterprises are distinguished. According to the ownership of capital, national, foreign and joint (mixed) enterprises are distinguished.
The production function shows the maximum possible output that can be obtained with given resources. Its properties:
- there is a limit to the increase in output that can be achieved by increasing the cost of one factor, other things being equal;
- there is a certain complementarity (complementarity) of factors of production, but without a reduction in the volume of production, a certain interchangeability is also possible.
The total product of a variable factor is the volume of output produced with a certain amount of this factor and other constant factors of production. The law of diminishing returns of factors of production or the law of diminishing marginal productivity indicates that an increase in the use of one of the factors with a fixed value of the others leads to a consistent decrease in the return on its use.
Average variable factor product – the ratio of total product to the amount of variable factor used, or: how much output is produced per unit of variable factor.
The marginal product of a variable factor is the increase in total product resulting from the application of an additional unit of this factor.
Isoquants are lines of equal product. On an isoquant, an increase in the use of one factor is offset by a decrease in the use of another factor. How many units of one factor can be abandoned to increase the second factor by one, shows the marginal rate of technical replacement. The set of isoquants, each of which shows the maximum output achieved by using certain combinations of resources, is called an isoquant map. The further the isoquant is located from the origin, the greater the volume of production it represents.
A firm's budget lines, or isocosts, are equal cost lines. An increase in the company's capabilities (its budget) or a decrease in prices shifts the isocost to the right. And vice versa. If prices change, the slope of the isocost changes.
The equilibrium (optimum) of the producer is characterized by the point of contact of the isocost and isoquant - the total amount of costs for the production of this output is minimized.
Expanding production, the company is faced with the concept of "returns to scale". It shows how much the volume of production increases with an increase in the use of factors of production. If output increases in proportion to the increase in factors of production, this indicates constant returns to scale. If output grows faster than the amount of resources used, then there is an increasing return to scale, i.e., resources are saved. If output grows more slowly than the amount of resources used, then there is diminishing returns to scale, i.e., an increase in output requires a greater increase in the use of resources.
Analysis of output using isoquants makes it possible to determine the technological efficiency of production. The intersection of isoquants with isocosts characterizes not only technological, but also economic efficiency, i.e., it allows you to choose a technology depending on prices (labor-saving, capital-saving, etc.). Analysis of the line of growth and returns to scale reveals the concept of the effective size of the enterprise.
Total (cumulative) revenue is the sum of the revenue received by the firm from the sale of all goods produced.
Average revenue is the revenue per unit of product sold. Marginal revenue is the increase in income that arises from an infinitesimal increase in output (usually by one unit).
Accounting profit is equal to total revenue minus accounting (external) costs. Economic profit is equal to accounting profit minus implicit (internal) costs.
Total cost is the sum of the costs of acquiring the factors of production required to produce a given quantity of goods. They consist of total fixed and total variable costs. The firm cannot change fixed costs in the short term: the maintenance of industrial buildings, rent, administrative expenses, etc. They do not depend on the quantity of products produced and are available even when products are not produced. Variables change depending on the amount of production: the cost of raw materials, fuel, etc.
Average production costs – costs per unit of output. They are also divided into fixed and variable average costs. Marginal cost is the increase in total cost caused by an infinitesimal increase in production.
Questions for self-examination
- What organizational forms of the enterprise exist, what are the criteria for their division?
- What are the advantages and disadvantages of a particular organizational form of an enterprise?
- What are the methods of protection in conditions of risk?
- What characterizes the production function and what are its properties?
- How is the long term different from the short term?
- What is invested in the concepts of "total", "average" and "marginal" product of a variable factor of production?
- What is the law of diminishing returns on factors of production?
- What is meant by the terms "isocost" and "isoquant"?
- How is the optimal enterprise determined?
- What does the concept of "returns to scale" mean and what types of it exist?
- What conclusions can be drawn from the analysis of the enterprise's optimum?
- What is invested in the concepts of "total", "average" and "marginal" revenue?
- How is economic profit different from accounting profit?
- What is the essence of the concepts of "general", "average" and "marginal" costs?
- How are the costs of the enterprise classified taking into account time boundaries?
- What is the meaning of the concept of marginal cost?
Literature
Main
- Economic Theory: Textbook / Ed. ed. acad. V. I. Vidyapin, A. I. Dobrynin, G. P. Zhuravleva, L. S. Tarasevich. - ed. correct and additional - M.: INFRA-M, 2005. - S. 217-231.
- Economics: principles, problems and politics: Proc. allowance. V. 2 / K. R. McConnell, S. L. Brue. - M.: Respublika, 1996. - S. 12-29.
- Pavlova IP Microeconomics: Electronic textbook. allowance. - St. Petersburg: RIC MBI, 2006.
- Pavlova I. P. Microeconomics. Basic summary: workbook. - St. Petersburg: RIC MBI, 2006.
Additional
- Nureev R. M. Course of microeconomics: Textbook for universities. - 2nd ed. M.: Norma, 2005. - S. 80-95.
- Galperin V. M., Ignatiev S. M., Morgunov V. M. Microeconomics: Textbook: in 2 vols. T. 1 / Ed. V. M. Galperin. - 1998. - S. 39-65. Title of the presentation
As a result of studying this chapter, the student should:
know
The concept of the production function and its properties, the relationship between the volume of output, the quantity and prices of production factors, the cost function and its properties, the patterns of behavior of the firm when prices are set or the firm has the ability to set prices itself;
be able to
solve the optimization problem of maximizing the profit of the company, describe the reaction of the company to market incentives in the short and long term;
own
Methods for solving problems of minimizing costs for a given level of output and finding the volume of output that maximizes profit.
Production function and its properties
Production is the process of converting factors of production into products. The reality that the firm faces in this case is the problem of technological admissibility.
sti. Technology determines and limits the possibilities of combining factors of production to produce products.
The production possibilities set is the most general way to describe a firm's technology. production function characterizes the maximum possible volume of production that can be obtained using a given combination of resources.
If with the help of many factors only one product is produced (and in what follows we will consider firms that produce a single product from many factors), we will denote the output by y, and the volume of the i-th factor by xi, so for P factors, the entire vector of factors will be denoted as. At the same time, it is required that
The production function is built for this technology. An improvement in technology that increases the maximum possible output for any combination of factors is represented by a new production function.
Although production functions are different for different types of industries, they all have common properties.
The production function is continuous, strictly increasing and strictly quasi-concave. Continuity ensures that small changes in factor inputs lead to small changes in output. The condition of strict increase ensures that the volume of output increases with an increase in the costs of any of the factors. Strict quasi-concavity ensures the complementarity of factors of production, which means that the production of a given product cannot be carried out without any costs of factors of production.
The listed (desirable) properties of the production function are quite consistent with its definition, since they concern only the input-output ratio.
Let us give examples of the most successfully constructed and therefore often used in practice production functions. In this case, for simplicity, we will consider a two-factor one-product production function of the form
1. Cobb-Douglas production function.
The first successful experience in constructing a production function as a regression equation based on statistical data was obtained by American scientists - mathematician D. Cobb and economist P. Douglas in 1928. The function they proposed initially had the form
( 4. 1)
where Y- volume of output; To- value production assets(capital); L- labor costs; - number
parameters (scale number and elasticity index). Due to its simplicity and rationality, this function is still widely used and has received further generalizations in various directions. The Cobb-Douglas function will sometimes be written in the form
It is easy to check that Y(0,0) = 0 and
Moreover, function (4.1) is linearly homogeneous:
For multifactorial production, the Cobb–Douglas function has the form
To take into account technical progress in the Cobb-Douglas function, a special multiplier (technical progress) is introduced, where t is the time parameter; v is a constant number characterizing the rate of development. As a result, the function takes a "dynamic" form:
where optional
2. The CES production function (with constant elasticity of substitution) is
( 4. 2)
where is the scale coefficient; is the distribution coefficient; is the replacement coefficient; is the degree of homogeneity. If the conditions are satisfied, then the function (4.2) satisfies the inequalities and
Taking into account technological progress, the CES function is written
The name of this function follows from the fact that for it the elasticity of substitution is constant.
3. Production function with fixed proportions. This function is obtained from (4.2) and has the form
4. The input-output production function (the Leontief function) is obtained from (4.3) with
( 4.
4)
Here is the number of costs of the form to, required to produce one unit of output, and at-release.
5. Production function of the analysis of methods of production activity. This function generalizes the input-output production function to the case when there are some number r of basic processes (modes of production activity), each of which can proceed with any non-negative intensity. It has the form of an "optimization problem"
where is the output at a unit intensity of the j-th basic process; – intensity level; - the number of costs of the type k, required at a unit intensity of the method j.
As can be seen from (4.5), if the output produced at a unit intensity and the costs required per unit of intensity are known, then the total output and total costs are found by adding the output and costs, respectively, for each basic process at the chosen intensities. Note that the problem of maximizing the function po in (4.5) under given inequality constraints is a model for the analysis of production activity (maximization of output with limited resources).
6. A linear production function (a function with mutual substitution of resources) is used in the presence of a linear dependence of output on costs:
(4.6)
The volume of output will increase with the growth of the use of the variable factor in production, but this growth has certain limits within the framework of a given technology. If the production function is differentiable, then its partial derivative is called marginal product i- th factor of production and shows the change in output when using an additional unit of the i-ro factor.
The graphical representation of the production function is isoquant- a curve representing an infinite number of combinations of factors of production that provide the same output. Let's denote this set by . For a given vector of production factors X isoquant passing through a point X, is a set of vectors of factors of production, each of which allows to produce the same amount of output as X, namely
An analogue of the marginal rate of substitution in the theory of consumption in the theory of the firm is marginal rate of technological substitution(marginal rate of technical substitution, MRTS). It measures the extent to which one factor can be replaced by another without changing output. Formally, MRTS is defined as the ratio of marginal products
(4.7)
The MRTS of any two factors of production, generally speaking, depends on the amount of all factors involved. In empirical work, however, it is often assumed that factors of production can be broken down into a relatively small number of types, with the degree of substitution between factors of the same type differing from the degree of substitution between factors of different types. Production functions with this property are called separable, and there are at least two main types of separability.
Let be the number of factors of production and assume that this set can be divided into disjoint subsets. A production function is said to be non-strictly separable if the MRTS between two factors in one group is independent of the factors in the other group:
for all,
where and are marginal products i th and j-th factors.
When , a production function is called strictly separable if the MRTS between two factors from different groups does not depend on factors outside these groups:
for all
Isoquants (as well as indifference curves) can have different configurations (Fig. 4.1).
Rice. 4.1. Types of isoquants: a - isoquant, when the factors are completely interchangeable; b- isoquant, in which the substitution is incomplete; c - isoquant, in which the factors are not interchangeable
The shape of the presented isoquants is determined by elasticity of substitution. For the production function f(x), the flexibility of substitution between the tth and j-th factors at the point X defined as
where and are the marginal products of the i-th and j-th factors.
If the production function is quasi-concave, then the elasticity of substitution cannot be negative. The closer it is to zero, the more difficult it will be for factors to be replaced; the larger it is, the "easier" is the substitution between them. On fig. 4.1a elasticity is infinite; in fig. 4.16 elasticity is finite, but greater than zero; in fig. 4.Ie elasticity is zero.
All production functions with constant elasticity of substitution (including the Cobb-Douglas and Leontief functions) are included in the class of homogeneous first-degree production functions, which plays an important role in theoretical and applied research. Homogeneity of the first degree additionally structures the production function; functions homogeneous of the first degree are always concave (Shepard's theorem).
Example 4.1
Consider a production function with constant elasticity of substitution y=(Χχρ X2pI17p at 0 ≠ p< ]. Чтобы рассчитать эластичность замещения, заметим, что In(X2Zx1) = In(X2) In(X1)1 поэтому, если взять полный дифференциал числителя σ, мы получим
Calculating the partial derivatives of the function, dividing them by each other and taking the logarithms, we get
Taking the total differential, we find the denominator σ:
Dividing (a) by (b), we get the elasticity of substitution, which is a constant, hence the abbreviation
CES - constant elasticity of substitution.
For CES functions, the degree of substitution between factors is always the same regardless of the level of output or ratio of factors. This limits the range of technologies described by such functions. At the same time, with the help of different values of the parameter p, and hence different values of the parameter σ, it is possible to specify technologies with very different (but everywhere constant) elasticity of factor substitution. The closer p is to one, the greater σ; if p = 1, then σ is infinite, the production function is linear, and its isoquants are similar to those shown in Fig. 4.1 a. Other popular production functions can also be considered as special cases of some CES functions.
