Production means activity to use factors of production (resources) in order to achieve the best result. If the volume of resource use is known, then the result is maximized and vice versa, if the result that needs to be achieved is known, then the volume of resources is maximized.

Under costs refers to everything that a company (manufacturer) purchases for further use in order to obtain the desired result.

Release refers to any good (product or service) produced by a firm for sale. The activities of a company can mean both production and commercial activities.

Within the framework of the theory of the firm In order to simplify the presentation of activity, it is generally accepted that the firm produces one good.

That's why The economic activity of a firm is described by a production function that includes variables for the production of one type of good or service:

Q = f (F 1, F 2, F 3, ... F n), where

Q - maximum production volume at given costs;

F 1, F 2, F 3, ... F n - the number of factors used.

Costs include all factors of production used (labor, materials, equipment, level of technical and organizational knowledge; when considering agricultural production, another factor is taken into account - land).

In microeconomic analysis it is assumed that the level of organizational and technical knowledge is fixed, and all material factors are combined into one factor - capital. Therefore, the production function includes two factors on which output depends: labor and capital.

Hence, production function characterizes the technical relationship between the amount of resources used and the maximum volume of output per unit of time.

The production function describes a set of technologically efficient production methods, each of which is characterized by a specific combination of resources necessary to obtain a unit of output at a given level of technology. As a technological relationship, the production function can only be determined empirically by changing actual indicators.

The production function has a number of features or properties:

1) factors of production are complementary;

2) the absence of one of the factors makes production impossible;

3) the production function used at the macro level is called the function Cobb-Douglas:

Q = f (k*K a *L b), where

Q - maximum output volume;

K - capital costs;

L - labor costs;

a, b - elasticity of output with respect to the costs of the relevant factors (capital and labor); k is the coefficient of proportionality or scale in the industry.

4) the production function is continuous and has no time limits, and therefore indicates the continuity of the production process.

Types of production functions:

Production functions can be static or dynamic.

Static production functions have the following form:

Y = f (x 1 ,x 2 ,…x n)

They don't include includes an indicator of time, i.e. do not contain time as a factor changing the main production characteristics of the dependence being studied.

Among the static of production functions, the most common are linear functions (y = a 0 + a 1 x 1 + a 2 x 2) and the Cobb-Douglas function.

Dynamic production functions have the following form:

y = f (t, x i (t) ...x n (t)), where:

x i (t) - represents the dynamics of changes in a certain production factor depending on time;

t - is a temporary independent variable that implicitly reflects the impact of all unaccounted factors on the performance of the indicator y.

Consider the graphical representation production function. The graph of the two-factor function Q = f (L,K) is an isoquant, which is a line of constant level of output. Those. isoquant - is an equal product curve or a set of possible combinations of labor and capital factors that achieve the same output.

Rice. 1.6. Two-factor production function

Isoquant map is a set of isoquants, each of which shows the maximum volume of output using a certain combination of factors of production.

Rice. 2.6. Isoquant map

The properties of isoquants include:

1) negative slope;

2) concavity to the origin;

3) never intersect;

4) show different levels of production.

1. Production means:

1) the process of creating material wealth;

2) the process of transforming production resources into benefits;

3) the process by which the problem of scarcity of goods is solved;

4) the process of creating goods that meet market requirements.

2. The production function reflects:

1) any functional connection between input factors of production;

2) functional relationship between technology and output volume;

3) optimal combination of production factors;

4) the ability of the enterprise to carry out profitable production.

3. Technological efficiency is:

1) the best way to reduce production costs;

2) application of the most advanced technology for given conditions;

3) the best way to replace workers with machines in production;

4) the best combination of production factors to ensure a given volume of output.

4. Long term versus short term:

1) avoids excessively intensive use of equipment;

2) makes it possible to more widely use a two-shift operating mode;

3) narrows the possibilities for reorganizing production;

4) expands the enterprise’s capabilities in achieving technological efficiency.

5. A variable factor is understood as a factor of production:

3) whose productivity changes during the production process;

4) whose performance varies depending on the technology.

6. Which of the following can be classified as a variable factor:

1) railway rolling stock;

2) hydroelectric turbine;

3) the area of ​​the sales floor of a retail store;

4) number of breeding livestock.

7. A constant factor is understood as a factor of production:

1) the value of which can be changed within a short-term period;

2) the value of which can be changed within the long-term period;

3) whose performance can be changed during the production process;

4) whose performance does not change depending on the technology.

18. Which of the following indicators characterizes the value of the production function:

1) total product from a variable factor;

2) average product from a variable factor;

3) marginal product from a variable factor;

4) average product from a constant factor.

9. The action of the law of diminishing marginal productivity of a factor indicates that:

1) the immutability of technology limits the possibilities for increasing output;

2) the marginal product of a variable factor is always decreasing;

3) in the long term, an increase in the use of a factor leads to a decrease in its productivity;

4) in the short term there are restrictions on increasing output.

10. When the average product of a variable factor increases and its marginal product decreases, we can say that:

1) the law of diminishing returns has ceased;

2) the total product of production began to decline;

3) more efficient technologies began to be used in production;

4) production has not reached maximum output.

11.Effective use of a variable factor in production is achieved when:

1) the marginal productivity of its use is the same in all production processes;

2) most of it is used in the most efficient production process;

3) its average productivity is the greatest;

4) its average productivity is higher than its marginal productivity.

12. It is optimal to use such an amount of variable factor that:

1) the highest marginal productivity of the factor is achieved;

2) the highest average factor productivity is achieved;

3) maximum production output is achieved;

4) the average productivity of the factor is higher than the marginal productivity.

13. When the average product from a variable factor increases and its marginal product decreases, then a further increase in the use of the variable factor leads to:

1) reducing the efficiency of its use;

2) increasing the efficiency of its use;

3) violation of the optimal ratio of production factors;

4) reduction in overall production efficiency.

14. Which of the following definitions correctly characterizes the concept of “isoquant”:

1) a line showing all combinations of factors of production that provide equality in factor productivity;

2) a line showing all changes in factor productivity;

3) a line showing the ratio of average factor productivity in the short and long term;

4) a line showing all possible combinations of production factors that provide a given volume of output.

15.The maximum rate of technological substitution is:

1) an indicator of the proportion in which the ratio of average and marginal productivity of factors changes;

2) an indicator of the proportion in which one factor should be replaced by another while maintaining the same volume of output;

3) an indicator reflecting the degree of technological complexity of substituting production factors in the short term;

4) an indicator reflecting the degree of technological complexity of replacing production factors in the long term.

16. The optimal combination of production factors is achieved when:

1) the marginal rate of technological substitution is maximum;

2) the marginal products of production factors are equal;

3) a stable excess of average productivity over the maximum is ensured;

4) the positive effect of scale is completely exhausted.

17. Economies of scale mean:

1) the nature of the change in the relationship between the increase in production factors and the change in output volumes;

2) the nature of the change in the relationship between the increase in production factors and the change in their productivity;

3) the nature of changes in output when more efficient technology is used;

4) the nature of the change in the ratio between the volume of short-term and long-term output.

18. If the volume of output increases in a proportion greater than the increase in factors of production, then in this case the following occurs:

1) neutral economies of scale;

2) decreasing economies of scale;

3) constant economies of scale;

4) positive economies of scale.

19. If the marginal rate of substitution of factors of production is zero, then we can say that:

1) a reduction in a factor by one does not cause changes in the volume of output;

2) technology does not allow the replacement of one factor by another;

3) the transition to new technology does not give any positive effect;

4) there is a neutral type of scale effect.

20. If technology remains unchanged, then what can be said about the comparative productivity of a factor of production for the short-term and long-term periods:

1) it will be higher in the short term;

2) it will be higher in the long term;

3) it will be the same;

4) the type of period does not affect the productivity of the factor.

21.The average product of a resource is called:

1) the ratio of the volume of resource used to the total product;

2) additional products produced by increasing a given factor of production;

3) the ratio of the total product to the volume of resource used;

4) additional income received from the sale of an additional unit of production.

22. The enterprise has doubled the amount of all resources. At the same time, output increased by 1.5 times. It means that:

1) economies of scale are decreasing, but labor productivity has increased;

2) economies of scale are increasing, and labor productivity has increased;

3) economies of scale are decreasing and labor productivity has decreased;

4) economies of scale remain unchanged, but labor productivity has decreased.

23. If, with unchanged output, the marginal product of labor decreases, then it can be argued that:

1) the average product of labor is growing;

2) the average product of capital decreases;

3) the average product of capital is growing;

4) MRTS L ,K increases.

24. An enterprise uses capital K and labor L in such a combination that their marginal products are: MP K = 10, MP L = 16. Factor prices are equal, respectively: Pk = 3, P L = 4. What will the company do:

1) use more labor and less capital;

2) use less labor and more capital;

3) use more labor and more capital;

4) use less labor and less capital.

25. An enterprise increases the use of labor and capital in equal proportions, while the elasticity of output with respect to labor increases, and the elasticity of output with respect to capital does not change. It means that:

1) MRTS L,K decreased;

2) the marginal product of labor has decreased;

3) MRTS L,K increased;

4) the production function is characterized by constant returns to scale.

26. An enterprise that has monopoly power in the product market, but does not have a monopoly in factor markets, will hire:

1) more labor than competitive enterprises, but pay lower wages;

2) less labor and pay lower wages compared to competitive enterprises;

3) more work and pay higher wages;

4) less labor and pay the same wages as competitive enterprises.

27. If an enterprise increases resource costs by 10%, and production volume increases by 15%, then in this case:

1) there is a negative effect of scale of production;

2) the law of diminishing returns applies;

3) there is a positive effect of production scale;

4) the long-run average cost curve shifts upward.

28. An enterprise that is a monopoly in the labor market, but does not have monopoly power in the product market, will:

1) hire less labor and pay lower wages compared to competitors;

2) hire more labor and pay higher wages;

3) hire less labor and pay the same wages as competitors;

4) hire more labor than competitors, but pay lower wages.

29. Derived demand for a production resource is determined by:

1) demand for other factors of production;

2) the type of market supplying the factor of production;

3) demand for the product supplied by the enterprise;

4) marginal productivity of the production factor;

30. When an enterprise acquires a production resource in a market that is characterized by imperfect competition, then, other things being equal, the enterprise will:

1) purchase a resource at a price below its marginal cost for the resource;

2) purchase a resource at a price higher than its marginal cost for the resource;

3) purchase a resource at a price equal to its marginal cost for the resource;

4) purchase a resource at a price below its marginal cost and in larger quantities.

31.Unlike other markets for productive resources, the mechanism for establishing market equilibrium in the land market has the specific feature that:

1) buyers face an inelastic supply curve;

2) the rules for concluding transactions when purchasing land are regulated by the state;

3) buyers face a lack of information;

4) land sellers strategically interact with each other.

32. Price of land:

1) is directly dependent on the interest rate;

2) determined by the quality of the land;

3) depends on the price of substitute factors;

4) represents a capitalized annuity;

33. If the state increases the land tax, then the consequence of this, other things being equal, will be:

1) increasing the ground rent rate;

2) rent growth;

3) increase in land price;

4) reduction in income of the land owner.

34. Monopsony is a type of market structure, the distinctive feature of which is that:

1) many sellers are opposed by one buyer;

2) many buyers are opposed by one seller;

3) market demand is completely inelastic;

4) market demand is perfectly elastic.

35. The law showing that an increase in the costs of one resource, while the use of other resources and technologies remains unchanged, brings less marginal income, is called the law:

1) proposals;

2) demand;

3) diminishing marginal utility;

4) diminishing marginal productivity.

36. The elasticity of demand for labor is higher:

1) the lower the share of labor costs in the enterprise’s costs;

2) the lower the price of the finished product;

3) the higher the price elasticity of demand for finished products;

4) the less the possibility of replacing labor with capital in this process.

37. Let us assume that the enterprise acts as a monopsonist in the labor market. In equilibrium, the wages of its workers are:

1) equal to the marginal product of labor in monetary terms;

2) less than the marginal product of labor in monetary terms;

3) greater than the marginal product of labor in monetary terms;

4) any of the listed options is possible;

38. The enterprise’s demand for employee labor is described as L = 200 -0.3W, where L is the number of employees hired, W is the monthly wage rate. The minimum wage established by the state is 600 den. units per month. Under these conditions, the maximum number of workers that an enterprise can hire is:

39. If the rent from a land plot of 10 hectares amounted to 120 thousand den. for the year. units, and the bank interest rate is 20%, then the price of this land plot will be equal to:

1) 120 thousand den. units;

2) 240 thousand den. units;

3) 500 thousand den. units;

4) 600 thousand den. units

40. An investor invested 30 thousand money in the project. units, expecting to recoup it in 3 years. The annual income is expected to be constant and the bank interest is expected to be 10%. What level of annual income for the project is minimally acceptable for an investor:

1) 10 thousand den. units;

2) 12 thousand den. units;

3) 14 thousand den. units;

4) 16 thousand den. units

41. If a landowner receiving a rent of 2400 den. from his plot of land of 4 hectares. units per year, decides to sell it, then the price of land at a bank interest rate of 12% will be:

1) 20,000 den. units;

2) 24,000 den. units;

3) 28800 den. units;

4) 50,000 den. units

42. An investor invested 100 thousand money in the project. units, expecting to recoup it in 2 years. It is expected that the annual income will be constant and the bank interest will be 20%. Then the minimum acceptable level of annual income for an investor is:

1) 55 thousand den. units;

2) 60 thousand den. units;

3) 65 thousand den. units;

4) 70 thousand den. units

43. To produce a certain product, 2 factors are required: labor and land. In which of the following cases is cost minimization achieved?

The original basis of life is social production. Before engaging in science, art, or politics, people must have a minimum means of subsistence: a roof over their heads, clothing, food. And therefore, if we want to touch the complex tangle of social relations, reveal economic connections, social processes and determine the direction and trends in their movement, we first of all need to consider social production as the source of all well-being.

Production is not the only factor that determines the wealth of countries and peoples. Economic development is influenced by natural resources, climate, natural fertility of the land, knowledge and experience accumulated by people, population size and other factors. However, society can obtain a certain result only if it uses the effect inherent in these factors in the production process.

Under production understands the process of human influence on objects and forces of nature and their adaptation to satisfy certain needs. Three components interact in it: human labor power, objects of labor and means of labor.

Under labor force is understood as the totality of physical and spiritual abilities that the body possesses and which are realized during the labor process. As social production develops, the nature and content of the labor force changes. In the early stages of the development of society, the main role was played by a person’s physical ability to work. As production develops, especially in the conditions of the modern scientific and technological revolution, increasingly high demands are placed on a person’s mental abilities, his intellectual level, scientific and technical education, qualifications and other qualities.

Labor power acts as a personal factor of production, and man is its carrier, the worker is the main productive force.

Subject of labor- this is everything that human labor is aimed at, which forms the material basis of the future product. If at the dawn of civilization the subject of labor was exclusively the substance of nature, then with the development of production, science and technology, among the objects of labor, production products, which are called raw materials, occupy an increasing place.

Means of labor- these are things or complexes of things with the help of which a person processes objects of labor and influences them. These include various tools, mechanisms, means of communication, means of communication, land, etc. As production develops, the means of labor develop, improve, and become more complex.

Objects of labor and means of labor in the aggregate act as a material factor of production, as means of production.

Production cannot be imagined as a mechanical connection of its elements. This is a complex system of interaction between labor and the means of production, i.e. with its material basis. The methods of combining production factors determine the system of production relations prevailing in society. The content of production relations is determined by the level of development of the productive forces, and the nature of their manifestation is determined by the way the worker connects with the means of production, i.e. relations of ownership of the means of production.

Certain types and types of property always dominate in society: private, collective, small labor, state, mixed, etc. At the same time, they change, develop under the influence of changes in the material conditions of production and are in different combinations, in constant connections. If property relations cease to change, then the productive forces are constrained in their development, and technical and social progress is hampered. Property relations determine the ownership of the produced product, the form of its distribution, the nature of exchange and the level of consumption of different groups of people. Often the concept of property comes down to the ownership of certain property, capital (plant, factory, house, bank account, etc.). This is not entirely true.

The amount of property of the city mayor is determined not by his bank account and personal property, but by the opportunities that his position actually gives him.

Every society is based on several universal economic conditions. Some fundamental problems retain the same significance in the modern economy as they had in the Ancient World. Any society, regardless of what stage of civilization it is at, always faces three main and interrelated problems:

1. What should be done, i.e. Which of the mutually exclusive goods and services must be produced and in what quantity? What would you like to have immediately, what can you wait to get, and what should you give up altogether? Sometimes the choice can be very difficult.

2. How will goods be produced, by whom, using what resources and technology, in what types of enterprises? There are different options for producing the entire set of goods and each of them separately. For various projects, you can build an industrial and residential building, use land, produce cars, etc. The decision to produce can be made at the level of the state or a private firm.

3.For whom are the produced goods intended, in what proportions will they be distributed among people, families, and who will benefit from them? Since the number of goods and services created is limited, the problem of their distribution arises. The solution to this problem determines the goals of society and the incentives for its development.

These three questions are basic and common to all economic systems, to all farms. At different stages of its development, society uses different approaches and tools to identify and take into account production and personal needs and to distribute material and human resources among activities that produce the necessary products, services and ideas.

The economy of a modern state is divided into industries. It includes manufacturing sectors and non-production activities. The concepts of “production” and “non-production” spheres are the largest structural characteristics of the economy.

Non-production sphere(or service sector) includes activities that do not create a material (material) product. As a rule, the following non-production sectors are distinguished:

· Department of Housing and Utilities;

· non-production types of consumer services for the population;

· health, physical education and social welfare;

· public education;

· finance, credit, insurance, pensions;

· Culture and art;

· science and scientific service;

· control;

· public associations.

Manufacturing sector(“real sector” - in modern terminology) is a set of industries and activities, the result of which is a material product (goods). The branches of material production usually include industry, agriculture, transport, and communications.

The division into industries is determined by the social division of labor. There are three forms of social division of labor: general, private, individual.

General division of labor is expressed in the division of social production into large spheres of material production (industry, agriculture, transport, communications...).

Private division of labor manifests itself in the formation of various independent branches within industry, agriculture and other branches of material production. For example, in industry there are:

· electric power industry;

· fuel industry;

· ferrous metallurgy;

· non-ferrous metallurgy;

· chemical and petrochemical industry;

· mechanical engineering and metalworking;

· forestry, wood processing and pulp and paper industries;

· construction materials industry;

· light industry;

· food industry.

In turn, each of them consists of highly specialized industries. For example, non-ferrous metallurgy includes copper, lead-zinc, tin and other industries.

Unit division of labor takes place in an enterprise, institution, or organization between people of different professions and specialties.

The most important branch of production is industry, which consists of many industries and industries that are interconnected.

Under industry sector is understood as a set of enterprises that produce products of a homogeneous economic purpose and are characterized by the commonality of processed raw materials, the uniformity of the technical base (technological processes and equipment), and the professional composition of personnel.

Under production understands the process of human influence on objects and forces of nature and their adaptation to satisfy certain needs. Three components interact in it: human labor power, objects of labor and means of labor.

Under labor force is understood as the totality of physical and spiritual abilities that the body possesses and which are realized during the labor process. Labor power acts as a personal factor of production, and man is its carrier, the worker is the main productive force.

Subject of labor- this is all that human labor is aimed at, which forms the material basis of the future product. If at the dawn of civilization the subject of labor was exclusively the substance of nature, then with the development of production, science and technology, among the objects of labor, production products, which are called raw materials, occupy an increasing place.

Means of labor- these are things or complexes of things with the help of which a person processes objects of labor and influences them. These include a variety of tools, mechanisms, means of communication, means of communication, land, etc. As production develops, the means of labor develop, improve, and become more complex.

Objects of labor and means of labor in the aggregate act as a material factor of production, as means of production.

Production can be “extensive” or “intensive”. Extensive is carried out mainly due to the quantitative increase in the means of production already used, and intense- due to their qualitative renewal (as a result of the mass development of more efficient technology and production organization).

There is a distinction between “individual” and “social” production. Under " individual» production refers to activities on the scale of the main production unit (firm). Public production covers the entire system of production connections between firms, which acquires an additional element - the so-called “production infrastructure” (industries and enterprises that do not produce the products themselves, but ensure their technological movement - transport, communications, warehouses).

Division of labor- this is the totality of all currently existing types of labor activity. Typically, three levels of division of labor are distinguished: within an enterprise (“single”), between enterprises (“private”), and also on a societal scale (“general” - industrial and agricultural, mental and physical, skilled and unskilled, manual and machine).

The dual content of the division of labor means that production is characterized by the “law of socialization of labor”: the deeper the specialization of labor, the higher its cooperation. The socialization of labor is an objective law, for it follows from the division of labor objectively inherent in production.

The deepening of the specialization of labor knows no limits (“subject-by-subject” - “detailed” - “operational”), therefore, the socialization of labor is limitless.

The main result of production activities is "public wealth"(all values ​​accumulated by the country), the annual part of the increase of which is denoted by the concept "total social product"(SOP).

How is the sum of products everyone enterprises SOP was named "gross social product"(GP), and as the sum of only final products - final social product"(KOP). Measured at market prices, the CPC is known as "gross national product" (GNP). This means that GNP shows the actual volume of market consumption of goods by the population.

Characterizes the relationship between the amount of resources used () and the maximum possible volume of 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 achieved by increasing one resource and keeping other resources constant. If, for example, in agriculture we increase the amount of labor with constant amounts of capital and land, then sooner or later a moment comes when output stops growing.

2. Resources complement each other, but within certain limits their interchangeability is possible without reducing output. Manual labor, for example, can be replaced by the use of more machines, and vice versa.

3. The longer the time period, the more resources can be revised. In this regard, instantaneous, short and long periods are distinguished. Instantaneous period - a period when all resources are fixed. Short period- a period when at least one resource is fixed. A long period - a period when all resources are variable.

Typically in microeconomics, a two-factor production function is analyzed, reflecting the dependence of output (q) on the amount of labor () and capital () used. Let us recall that capital refers to the means of production, i.e. the number of machines and equipment used in production and measured in machine hours (topic 2, clause 2.2). In turn, the amount of labor is measured in man-hours.

Typically, the production function in question looks like this:

A, α, β are specified parameters. Parameter A is the coefficient of total productivity of production factors. It reflects the impact of technological progress on production: if a manufacturer introduces advanced technologies, the value A increases, i.e. output increases with the same quantities of labor and capital. Options α And β are the elasticity coefficients of output for capital and labor, respectively. In other words, they show by how many percent output changes when capital (labor) changes by one percent. These coefficients are positive, but less than one. The latter means that when labor with constant capital (or capital with constant labor) increases by one percent, production increases to a lesser extent.

Construction of an isoquant

The given production function suggests that the producer can replace labor with capital and capital with labor, leaving output unchanged. For example, in agriculture in developed countries, labor is highly mechanized, i.e. There are many machines (capital) per worker. On the contrary, in developing countries the same output is achieved through a large amount of labor with little capital. This allows you to construct an isoquant (Fig. 8.1).

Isoquant(equal product line) reflects all combinations of two factors of production (labor and capital) for which output remains unchanged. In Fig. 8.1 next to the isoquant the corresponding release is indicated. Thus, output is achievable using labor and capital or using labor and capital.

Rice. 8.1. Isoquant

Other combinations of labor and capital volumes are possible, the minimum required to achieve a given output.

All combinations of resources corresponding to a given isoquant reflect technically efficient production methods. Mode of production A is technically effective in comparison with the method IN, if it requires the use of at least one resource in smaller quantities, and all others not in large quantities in comparison with the method IN. Accordingly, the method IN is technically ineffective compared to A. Technically inefficient production methods are not used by rational entrepreneurs and are not part of the production function.

From the above it follows that an isoquant cannot have a positive slope, as shown in Fig. 8.2.

The dotted line reflects all technically inefficient production methods. In particular, in comparison with the method A way IN to ensure the same output () requires the same amount of capital, but more labor. It is obvious, therefore, that the way B is not rational and cannot be taken into account.

Based on the isoquant, the marginal rate of technical substitution can be determined.

Marginal rate of technical replacement of factor Y by factor X (MRTS XY)- this is the amount of a factor (for example, capital) that can be abandoned when the factor (for example, labor) increases by 1 unit, so that output does not change (we remain at the same isoquant).

Rice. 8.2. Technically efficient and inefficient production

Consequently, the marginal rate of technical replacement of capital by labor is calculated by the formula

For infinitesimal changes L And K it amounts to

Thus, the marginal rate of technical substitution is the derivative of the isoquant function at a given point. Geometrically, it represents the slope of the isoquant (Fig. 8.3).

Rice. 8.3. Limit rate of technical replacement

When moving from top to bottom along an isoquant, the marginal rate of technical replacement decreases all the time, as evidenced by the decreasing slope of the isoquant.

If the producer increases both labor and capital, then this allows him to achieve greater output, i.e. move to a higher isoquant (q 2). An isoquant located to the right and above the previous one corresponds to a larger volume of output. The set of isoquants forms isoquant map(Fig. 8.4).

Rice. 8.4. Isoquant map

Special cases of isoquants

Let us recall that these correspond to a production function of the form . But there are other production functions. Let us consider the case when there is perfect substitutability of factors of production. Let us assume, for example, that skilled and unskilled loaders can be used in warehouse work, and the productivity of a qualified loader is N times higher than unskilled. This means that we can replace any number of qualified movers with unqualified ones in the ratio N to one. Conversely, you can replace N unqualified loaders with one qualified one.

The production function then has the form: where is the number of skilled workers, is the number of unskilled workers, A And b— constant parameters reflecting the productivity of one skilled and one unskilled worker, respectively. Coefficient ratio a And b— the maximum rate of technical replacement of unqualified loaders with qualified ones. It is constant and equal N: MRTSxy= a/b = N.

Let, for example, a qualified loader be able to process 3 tons of cargo per unit time (this will be coefficient a in the production function), and an unskilled loader - only 1 ton (coefficient b). This means that the employer can refuse three unqualified loaders, additionally hiring one qualified loader, so that the output (total weight of the processed cargo) remains the same.

The isoquant in this case is linear (Fig. 8.5).

Rice. 8.5. Isoquant with perfect substitutability of factors

The tangent of the isoquant slope is equal to the maximum rate of technical replacement of unskilled loaders with qualified ones.

Another production function is the Leontief function. It assumes strict complementarity of production factors. This means that factors can only be used in a strictly defined proportion, violation of which is technologically impossible. For example, an airline flight can be carried out normally with at least one aircraft and five crew members. At the same time, it is impossible to increase aircraft hours (capital) while simultaneously reducing man-hours (labor), and vice versa, and keep output constant. Isoquants in this case have the form of right angles, i.e. the maximum rates of technical replacement are equal to zero (Fig. 8.6). At the same time, it is possible to increase output (the number of flights) by increasing both labor and capital in the same proportion. Graphically, this means moving to a higher isoquant.

Rice. 8.6. Isoquants in the case of strict complementarity of production factors

Analytically, such a production function has the form: q =min (aK; bL), Where A And b— constant coefficients reflecting the productivity of capital and labor, respectively. The ratio of these coefficients determines the proportion of use of capital and labor.

In our airline flight example, the production function looks like this: q = min(1K; 0.2L). The fact is that capital productivity here is one flight per plane, and labor productivity is one flight per five people or 0.2 flights per person. If an airline has an aircraft fleet of 10 aircraft and has 40 flight personnel, then its maximum output will be: q = min( 1 x 8; 0.2 x 40) = 8 flights. At the same time, two aircraft will be idle on the ground due to a lack of personnel.

Let us finally look at the production function, which assumes that there are a limited number of production technologies to produce a given quantity of output. Each of them corresponds to a certain state of labor and capital. As a result, we have a number of reference points in the “labor-capital” space, connecting which we obtain a broken isoquant (Fig. 8.7).

Rice. 8.7. Broken isoquants with a limited number of production methods

The figure shows that product output in the amount of q 1 can be obtained with four combinations of labor and capital corresponding to the points A, B, C And D. Intermediate combinations are also possible, achievable in cases where an enterprise jointly uses two technologies to obtain a certain total output. As always, by increasing the quantities of labor and capital, we move to a higher isoquant.