8.4.1. Producer Equilibrium Analysis using isoquants has obvious disadvantages for the producer, since it only uses natural indicators resource costs and product output. In production theory, the producer's equilibrium is determined by the symmetrical

4. Returns to scale of production The production function allows us to determine the various ratios of the two most important factors of production for production: labor and capital. Through this, the organization has the opportunity to judge not only its own potential,

Consumption is impossible without constant production goods and services. In the economic cycle, firms are responsible for the production of economic goods that form their supply on the market.

In order to produce food, medicine, cars, clothing, and other goods and services, raw materials, materials, machines, equipment, a plot of land or premises, specialists and workers of relevant specialties are needed. The goods necessary to organize the production process are called factors of production or economic resources.

Factors of production include labor ( work force), land, capital, entrepreneurial abilities, information. The process of combining these factors in order to obtain new goods and services demanded by consumers is production.

To organize the production process economic resources required in a certain quantity. At the same time, the company strives to maximize output volumes. Output is any economic good produced by a firm for sale.

The dependence of the maximum volume of product output on the costs of the factors used is called the production function:

where Q is the maximum volume of output at given costs and the achieved level of technology; TO- capital costs; L- labor costs; N- land costs, etc.

The introduction of more advanced technologies leads to changes in the production function.

Although a combination of factors must be used to produce a particular product, production function has a number of common properties.

First of all, the factors of production are complementary. This means that the production process with the existing technology is possible only with a set of certain factors. The absence of at least one of the necessary resources (for example, raw materials or components) will make it impossible to produce the product produced by the company.

In addition, when organizing production activities, there is a certain interchangeability factors. One factor can be replaced by another (for example, manual labor - with certain equipment), which, however, does not mean the possibility of completely eliminating any economic resource from the production process.

Different combinations of factors of production produce different volumes of output. Moreover, with an increase in the scale of application of one of the factors, while others remain unchanged, there is a certain limit to the growth of production volumes. This is the law of diminishing marginal productivity or law of diminishing returns, characteristic of a production function with one variable factor. An example is the desire of a farmer to increase the production of vegetables through the active use of mineral fertilizers. Initially, the volume of production will grow quite quickly, then the rate of product growth will begin to gradually decrease. Finally, a moment will come when a further increase in the amount of fertilizer used will have a negative effect, and the overall output will decrease.

In order to reflect the influence of a variable factor on the production process and its results, the concepts of total, average and marginal product should be introduced.

Total product (GR)- This total economic good produced with the help of a variable factor (x).

Average product (AG)- this is an attitude total product to the amount of variable factor consumed:

Marginal product (MP)- the amount of additionally produced product obtained as a result of an increase in a variable resource by one unit:

The law of diminishing returns is relative. First of all, it operates in the short term, when at least one of the factors of production remains unchanged. In addition, its manifestation is closely related to the introduction of new technologies, the use of which changes the proportions between the economic resources used in the production process.

Now consider the option when a firm uses two variable factors of production (labor and capital) to produce a constant volume of a product, for example, men's shirts. Given a certain combination of these two factors, 500 shirts are produced. With this technology, the same volume of products can be produced using various quantities labor and capital, while the change in the scale of use of variable factors occurs in the opposite direction. At the same time, the total production volume remains at the same level. This dependence can be represented using isoquants(Fig. 6.1).

An isoquant, or equal product curve, reflects all possible combinations of two factors that can be used to produce a given amount of product.

As the scale of variable factors used increases, it becomes possible to increase total output. The isoquant reflecting the production of a larger volume of product will be located to the right and above the previous isoquant.

Rice. 6.1.

Number of factors used X And at can constantly change, and the maximum output of the product will decrease or increase accordingly. Consequently, many isoquants may arise corresponding to different volumes of output, which form isoquant map(Fig. 6.2).

The negative slope of isoquants is explained by the fact that an increase in the use of one factor for a certain volume of product output will always be accompanied by a decrease in the amount of another factor.

Rice. 6.2.

Isoquants have a concave shape relative to the origin. Their slope characterizes the degree of interchangeability of production factors and is determined by different marginal productivity of factors. This means that the same increment in the use of one resource will be replaced by a decreasing amount of another resource. The value reflecting the necessary quantitative changes in one factor depending on the change in the scale of another factor by one unit with a constant output volume is called the marginal rate of technological substitution ( MRTS xy). It is measured by the ratio of the change in factor y to the change in factors. Since the substitution of factors occurs in the inverse ratio, and we are interested in the absolute value MRTS^, That

Accordingly, effective interchangeability of resources is possible only within the zone of technological substitution (AD). Moreover, in the upper part of the isoquant the value MRTS xy will be the most significant, i.e. to change the factor x by one unit, significant changes in the factor are required u. As you move down the isoquant, the value MRTS xy will decrease (Fig. 6.3).

Isoquants can have different kind depending on the degree of interchangeability of factors. In the first case (Fig. 6.4) isoquants are presented, reflecting the partial interchangeability of resources. In this case, the production process requires the mandatory use of two factors, but their combinations may be different. This form of isoquants is considered standard and is more common than others.

Rice. 6.3. Change MRTS xy when moving down an isoquant

Rice. 6.4.

In the second case, the isoquant reflects the situation of absolute interchangeability of goods (Fig. 6.5).

Rice. 6.5.

A similar situation occurs in cases where a kiosk selling drinks and confectionery is replaced by a machine that performs the corresponding functions. Wherein MRTS= const.

The third case occurs under the condition of severe complementary resources, when MRTS^ = 0 (Fig. 6.6).

Rice. 6.6.

This production function assumes the presence of a single possible combination of production factors. For example, for digging a pit under Vacation home a company may use an excavator with one excavator operator. Increasing the number of machines without increasing the number of workers (and vice versa) is economically meaningless. A transition to a higher isoquant (Q a or Q 2) is possible only if the proportion remains unchanged 1:1, for example, two excavators and two workers or three excavators and three workers.

When purchasing factors of production, a firm is limited in its choice. It can use economic resources in a certain combination that does not go beyond its financial capabilities. This situation is described using isocosts, which is the manufacturer's budget constraint line. It is also called the firm's equal cost line. Total costs firms can be determined by the formula

where C is the company’s budget; RhiRu- prices of factors x and y; Qx and Qy are the number of factors of production purchased by the company.

If the financial capabilities of the manufacturer expand, then, with constant prices for production factors, the isocost will move up and to the right:

Graphically, isocosts look similar to a consumer's budget line. At constant prices for economic resources, they represent parallel lines with a negative slope. The larger the company's budget, the farther the isocost is from the origin (Fig. 6.7).

Rice. 6.7.

In the event that the financial capabilities of the company remain unchanged, and the prices of the resources used in the production process change, the real budget of the manufacturer and the scale of the factors of production purchased by it also change. Accordingly, the isocost changes its position (Fig. 6.8).

Rice. 6.8.

A cotton- when the factor price changes at

The firm's task is to make the most efficient use of its budget for factors of production, with the help of which it can maximize output and profit. If you combine the isoquant map with the isocost, you can determine the producer's equilibrium (Figure 6.9).

Rice. 6.9.

For given budgetary possibilities, the isoquant, in relation to which the isocost occupies a tangent position, will ensure the maximum volume of output, and the point of tangency between the isoquant and isocost (?) will be the producer’s equilibrium point. In it, the manufacturer will get the desired result.

An isoquant implies a smaller volume of output. This means that the company's finances will not be fully utilized, which is contrary to the rational behavior of the manufacturer. An isoquant will require a larger use of resources that is not consistent with the financial capabilities of the firm.

In order to determine the prospects for the development of an enterprise in the long term, it is necessary to imagine how the volume of production of the product and, accordingly, the costs of purchasing two variable factors will increase. The task for the manufacturer at each stage of production growth remains the same: it is necessary to optimize the costs of factors x and y and“link” them with your budgetary capabilities (Fig. 6.10).

By connecting the tangent points of the isoquants with isocosts, we obtain the expansion trajectory economic activity companies, or development trajectory of the enterprise’s production activities (0TO).

Lecture 4. Theory of production

1. Production function

2. Isoquant and isocost

3. Law of diminishing returns. Total, average and marginal product

4. Economic costs

1. Production function

Production in economics they call any activity involving the use of natural resources to create goods and services (tangible and intangible products). The goods necessary for organizing the production process are called means of production.

Production function shows the dependence of the maximum production volume on various factors:

Q = f(K, M, L) ,

Where Q- the quantity of products that the company will produce;

TO- fixed capital (fixed assets) in the form industrial buildings, machines, machines, equipment;

M - working capital (revolving funds) - materials, raw materials, electricity;

L- labor.

The quantitative expression of the production function can be solved using Cobb-Douglas production function. Douglas discovered that the elasticity of scale of production does not change depending on each factor, that is:

Cobb created a mathematical model of this constant elasticity of the production process with respect to each factor:

Q = 1.01  K 0.27  L 0.73,

where 1.01 is the proportionality coefficient,

K and L - capital and labor,

0.27 and 0.73 are the elasticity coefficients of capital and labor.

That is, a 73% increase in production volume is achieved through labor and 27% through capital.

In a modern interpretation, this formula looks like this:

Q = k  K   M   L  ,

where , ,  are elasticity coefficients (++=1).

2. Isoquant and isocost

An isoquant is closely related to the concept of a production function. Isoquant - a curve in which all points indicate a combination of capital and labor that will keep the volume of production constant.

Let's build an isoquant map using hypothetical data. Let the combination of 1 unit of labor and 1 unit of capital create 20 units of output, 2 units of labor and 1 unit of capital - 40 units of output, 3 units of labor and 1 unit of capital - 55 units of output, etc. according to the table.

Table 1

The output of 55 units will be achieved if we apply 3 units of labor and 1 unit of capital or 1 unit of labor and 3 units of capital. Let's construct this isoquant. You can also construct isoquants for production volumes of 75 units and 90 units. As we move along each of these curves, one factor is replaced by another.

Isoquant map

Isoquants are similar to an indifference curve with the difference that they reflect the situation not in the sphere of consumption, but in the sphere of production. Just as indifference curves located at different distances from the origin characterize different levels of utility for the consumer, so isoquants provide information about different levels of output.

How much should the volume of capital (y) be increased in order to reduce the use of living labor (x) by one person for a given volume of production - shows marginal rate of technological substitution (MRTS) xy ) .

Isocosta expresses all possible combinations of factors of production under fixed budget constraints.

Let the initial isocost be KL. If measures are taken to increase wages, the isocost will take the position KL 1. With a reduction in capital costs, that is, with increasing returns, the isocost will take the position K 1 L.

Isocosts

The manufacturer can purchase labor and capital in a certain combination that does not exceed its budgetary capabilities. Then his costs for the acquisition of capital will be P to  K, and for the purchase of labor P L  L. The total costs (C) will be:

C = P k K + P L  L

With an increase in funds for the acquisition of variable factors, i.e. as budget constraints decrease, the isocost line will shift to the right and upward.

Producer Equilibrium is to use all budget funds for two variable factors to obtain the largest volume of production, that is, to occupy the point that is as far as possible from the origin of coordinates.

Equilibrium (rational behavior) of the producer

3. Law of diminishing returns.

Total, average and marginal product

Law of Diminishing Returns is that, starting from a certain point, the subsequent addition of a unit of a variable resource (for example, labor) to an unchanged fixed resource (for example, capital or land) gives a decreasing additional or marginal product per each subsequent unit of the variable resource.

This can be illustrated by an example with the preparation of firewood. If you have one ax and one two-handed saw, then with each additional worker the output increases, but only up to a certain point. Starting from the fourth employee, returns will decrease.

Total Product (TP) - the total quantity of a product produced that changes as the use of a variable factor increases.

Average Product (AP) - the ratio of the total product to the amount of variable factor used in production:

Marginal product (MP) - the amount of additional product obtained by using an additional unit of a variable factor:

A rational entrepreneur strives to stay and remain at a stage where attracting an additional unit of a variable resource promises, although a falling, but positive volume of output. For an enterprise oriented to maximize profits, the choice of production volume is limited to AP = max and MP = 0.

As in consumption theory, the overall result of a change in the price of a resource can be decomposed into substitution effect And release effect(income effect).

4. Economic costs

Economic costs - this is what it costs to produce and sell a given product or service (including costs, losses and effects for people not associated with this production).

Costs are divided into fixed and variable. Fixed costs do not depend on the quantity of products produced. The costs of maintaining buildings, structures, and capital equipment do not change depending on whether the volume of output increases or decreases. Even if its production is completely stopped, these costs remain. Variable costs directly related to the quantity of goods produced. The costs of raw materials, supplies, etc. depend on its increase or decrease. wages. The sum of fixed and variable costs forms total costs .

To plan the volume of output, a company needs to know average and marginal costs.

AFC = FC / Q ; AVC=VC/Q; ATC = TC/Q

The costs incurred by a firm in producing each additional unit of a given product are called marginal cost :

MS =

Costs are divided into accounting and economic.

Accounting costs - these are external costs (purchase of raw materials, materials, fuel).

If we add imputed (internal, hidden) costs to accounting costs, we get economic costs.

Associated with the concept of accounting and economic costs is the concept arrived. If we subtract accounting costs from revenue, we get accounting profit.

TR - C buh = P buh

TR = P*Q, where P is price, Q is quantity

Normal profit - This is the profit the size of which keeps the entrepreneur from using his abilities and time in alternative enterprises.

If we subtract accounting (external) costs, internal (imputed) costs, and normal profit from revenue, we get economic profit.

TR - C buh – C int – P norm = P econ

ISOQUANT - a curve showing various combinations of factors of production that can be used to produce a given volume of product. Isoquants are also called equal product curves or equal output lines.

The slope of an isoquant expresses the dependence of one factor on another in the production process. At the same time, an increase in one factor and a decrease in another do not cause changes in the volume of output. This dependence is shown in Fig. 21.1.

Rice. 21.1. Isoquant

A positive slope of an isoquant means that an increase in the use of one factor will require an increase in the use of another factor so as not to reduce output. A negative slope of an isoquant shows that a reduction in one factor (at a given level of production) will always cause an increase in another factor.

Isoquants are convex in the direction of the origin, because although factors can be replaced by one another, they are not absolute substitutes.

The curvature of the isoquant illustrates the elasticity of factor substitution in producing a given volume of product and reflects how easily one factor can be replaced by another. In the case when the isoquant is similar to a right angle, the probability of replacing one factor with another is extremely small. If the isoquant looks like a straight line with a downward slope, then the probability of replacing one factor with another is significant.

Isoquants are similar to indifference curves with the only difference that indifference curves express the situation in the sphere of consumption, and isoquants - in the sphere of production. In other words, indifference curves characterize the replacement of one benefits others (MRS), and isoquants are the replacement of one factor a others (MRTS).

The further the isoquant is located from the origin, the greater the volume of output it represents. The slope of the isoquant expresses the marginal rate of technical substitution (MRTS), which is measured by the ratio of the change in output. The marginal rate of technical substitution of labor for capital (MRTS LK) is determined by the amount of capital that can be replaced by each unit of labor without causing a change in output. The marginal rate of technical substitution at any point on the isoquant is equal to the slope of the tangent at that point multiplied by -1:

Isoquants can have different configurations: linear, rigid complementarity, continuous substitutability, broken isoquant. Here we highlight the first two.

Linear isoquant– isoquant expressing perfect substitutability of production factors (MRTS LK = const) (Fig. 21.2).

Rice. 21.2. Linear isoquant

Hard complementarity factors of production represents a situation in which labor and capital are combined in the only possible ratio, when the marginal rate of technical substitution is equal to zero (MRTS LK = 0), the so-called Leontief-type isoquant (Fig. 21.3).

Rice. 21.3. Rigid isoquant

Isoquant map is a set of isoquants, each of which illustrates the maximum allowable volume of production for any given set of factors of production. An isoquant map is an alternative way of depicting a production function.

The meaning of an isoquant map is similar to the meaning of an indifference curve map for consumers. An isoquant map is similar to a contour map of a mountain: all higher altitudes are shown using curves (Figure 21.4).

An isoquant map can be used to show the possibilities of choosing among many options for organizing production within a short period, when, for example, capital is a constant factor and labor is a variable factor.

Rice. 21.4. Isoquant map

ISOCOST - a line showing combinations of factors of production that can be purchased for the same total amount of money. Isocost is also called the equal cost line. Isocosts are parallel lines because it is assumed that a firm can purchase any desired quantity of factors of production at constant prices. The slope of the isocost expresses the relative prices of factors of production (Figure 21.5). In Fig. 21.5, each point on the isocost line is characterized by the same total costs. These lines are straight because factor prices have a negative slope and are parallel.

Rice. 21.5. Isocost and isoquant

By combining isoquants and isocosts, the optimal position of the company can be determined. The point at which the isoquant touches (but does not intersect) the isocost means the cheapest combination of factors required to produce a certain volume of product (Fig. 21.5). In Fig. Figure 21.5 shows a method for determining the point at which production costs for a given volume of production of a product are minimized. This point is located at the lowest isocost where the isoquant touches it.

PRODUCER EQUILIBRIUM is a state of production in which the use of factors of production allows one to obtain the maximum volume of output, that is, when the isoquant occupies the point farthest from the origin. To determine the producer's equilibrium, it is necessary to combine the isoquant maps with the isocost map. The maximum output volume will be at the point where the isoquant touches the isocost (Fig. 21.6).

Rice. 21.6. Producer Equilibrium

From Fig. Figure 21.6 shows that the isoquant located closer to the origin of coordinates gives a smaller amount of output (isoquant 1). Isoquants located above and to the right of isoquant 2 will cause a change in a larger volume of factors of production than the manufacturer’s budget constraint allows.

Thus, the point of tangency between the isoquant and isocost (point E in Fig. 21.6) is optimal, since in this case the manufacturer receives the maximum result.

RETURN TO SCALE expresses the response of the volume of production to a proportional change in the quantity of all factors of production.

Distinguish three provisions of returns to scale.

Increasing Returns from scale - a situation in which a proportional increase in all factors of arbitrariness leads to an ever-increasing increase in the volume of product output (Fig. 21.7). Suppose that all factors of production doubled and the volume of product output tripled. Increasing returns to scale are due to two main reasons. Firstly, an increase in factor productivity due to specialization and division of labor with an increase in the scale of production. Secondly, increasing the scale of production often does not require a proportional increase in all factors of production. For example, doubling the production of cylindrical equipment (such as pipes) would require less than doubling the metal.

Constant return from scale is a change in the quantity of all factors of production, which causes a proportional change in the volume of product output. Thus, twice as many factors exactly double the volume of product output (Fig. 21.8).

Diminishing returns from scale is a situation in which a balanced increase in the volume of all factors of production leads to an ever smaller increase in the volume of product output. In other words, the volume of output increases to a lesser extent than the costs of production factors (Fig. 21.9). For example, all factors of production increased threefold, but the volume of production increased only twofold.

Rice. 21.7. Increasing returns to scale

Rice. 21.8. Constant returns to scale

Rice. 21.9. Diminishing returns to scale

Thus, in the production process there are increasing, constant and decreasing returns to scale of production, when a proportional increase in the quantity of all factors leads to an increased, constant or decreasing increase in the volume of product output.

Western economists believe that currently, in most types of production activities, constant return from scale. In many sectors of the economy increasing returns scale is potentially significant, but at some point it may give way to diminishing returns unless the process of increasing the number of giant firms is overcome, which makes management and control difficult, despite the fact that production technology stimulates the creation of such firms.

The same output volume can be obtained using different technologies. The company solves the problem of choosing a technology at which costs are minimal. TC = P L *L+P K *K (total costs=labor costs+capital costs). All combinations of resources that have the same cost are combined into one line. Isocost is an equal cost curve. The isocost equation is: K=TC\P K -(P L *L\P K) so it has an ISOCOST SLOPE.

Properties: 1) the isocost has a negative slope, because resources are interchangeable and complementary, an increase in one leads to a decrease in the other; 2) the points of intersection of the isocost with the coordinate axes show the max. Quantity of one of the resources; 3) if costs increase at constant prices for resources, then the isocost shifts or shifts (costs increase - up, costs decrease - down); 4) if the price of one of the resources changes. While maintaining a constant value of TC, the TO isocost rotates (price decreases - to the right, increases - to the left)

26(39). Optimal combination of production factors. The company's growth line.

Producer equilibrium is achieved when the isoquant and zocost have one thing in common, i.e. touch each other.Rl/Rk = MRl/MRk; МРл/Рл = МРк/Рк. - all used resources have the same value of the marginal product per unit of cash costs. - to optimize its costs, for a given volume of production, it is advisable for a company to replace one factor with another until the ratio of the marginal product of each factor to the price of a unit of each factor will not be equal for all factors involved. A firm minimizes its costs when the costs of producing an additional unit are the same, regardless of which additional factor is involved in the production process. For each volume of production there are optimal costs and if we take the tangent points isoquants and isocosts and draw a curve through them, then we get the company’s development trajectory line. The growth line is characterized technically possible ways expansion of production, that is, a transition from a lower to a higher isoquant. Among the possible growth lines, isoclines are of interest, along which the marginal rate of technical substitution of resources for any volume of output is constant.

27(40). Production costs and their structure. Accounting and economic costs. Accounting, economic and normal profit.

Costs are the totality of costs in cash for production and sales of products. They reflect all the positive and negative aspects of the company. The concept of a company's costs is based on two premises: 1) resources are limited, so there are alternatives to using the same resource (the best one must be selected from among them); 2) resources are assessed taking into account their current value and taking into account lost profits. There are 2 approaches to determining the structure and classification of costs. 1 approach – accounting. Accounting costs are the actual costs of purchasing resources at market prices. 2 approach – determines economic costs – opportunity cost- the value of other goods that could be obtained by the best option resource use. Economic costs= explicit costs + implicit costs + normal profit. Explicit costs are direct cash payments to resource owners. These are accounting costs. Implicit costs - the cost of resources that are owned by the owners of the company; these are unpaid costs of the company. These include: implicit rent, implicit rent, etc. Economic costs include normal profit - the profit that an entrepreneur receives for working in a given industry. This profit is included in costs. Dividing costs into accounting and economic costs involves dividing profits into accounting and economic costs. Profit=TR-TC(total income - costs). EKp = TR-EI (economic costs). Bp = TR-BI (maintenance accountant). If the accountant's profit is greater than normal, then resources are being used inefficiently. In the best case scenario, accountant profit = profit economy