The nature of the managerial decisions taken depends on the assessment of the period under consideration. The short period involves the solution of operational (tactical) tasks, and the long-term -- conceptual (strategic). In this regard, in the short term, models of the production function are used, which characterize the dependence of the volume of output on the volume of variable factors, while all the others remain unchanged.

Consider an example. Let 200 units of a certain product be produced using a certain set of factors. Let us begin to increase one of the factors, for example, the labor force, by increasing the number of workers, which was originally equal to 100, by adding 20 workers in succession. Other factors are left unchanged. The results of production in the form of the number of units of the production product and other indicators are presented in the following table:

As can be seen from the table, output (income) with an increase in one of the resources grows disproportionately to the increase in this resource, but at a lower rate, that is, there is a decrease, a decrease in the increase in output, and thereby profitability. Similarly, it behaves, that is, decreases, and productivity, the return of this type of resource, represented in the example considered by the output per employee. The observed dependence reflects the essence of the law of diminishing returns, returns.

The reason for the diminishing returns effect is fairly obvious. After all, all resources, factors of production "work" in a complex, so it is necessary to observe a certain ratio between them. Increasing one factor with a fixed value of others in conditions when the factors were initially coordinated with each other, we generate a disproportion. The number of employees no longer corresponds to the amount of equipment, the amount of equipment - to production areas, the number of tractors - to the area of arable land, etc. Under these conditions, an increase in one type of resource does not cause an adequate increase in the result, income. The return of the resource is reduced.

Consider a one-factor model. This means that only one of the resources is variable, and all the others do not change. In this case, the following parameters are entered.

Total product (TR) -- the amount of production obtained from the use of the entire volume of the resource.

Average product (AR) -- the amount of production obtained from the use of a unit factor. AP can be determined by the formula AP = TP: F,

Marginal product (MP) -- the amount of output obtained from the use of an additional unit of resource. It is defined as the ratio of the increment in the total product? TP = TP 1 - TP 0 to the increment in the amount of the factor used (F = F 1 - F 0): MP = ?TP: ?AF.

The change in these indicators occurs in accordance with the law of diminishing returns (or diminishing productivity) ". It says that as the investment in the production of any product of one of the variable resources increases (with all the others unchanged), the return on this resource, starting from a certain period , falls.

The operation of this law can be illustrated using the graphs presented in Fig. 1, where it is possible to single out separate sections characterizing the change in the indicators of the total, average and marginal products. The segment OA determines the growth of productivity or returns. With an increase in the cost of a variable resource from zero to h, the indicators of the total product (TP), average product (AP) and marginal product (MP) increase. This means that an increase in investment in the production of a given resource will increase not only the total output, but also the output per unit of this resource.

Segment AD illustrates the operation of the law of diminishing returns. In this case, marginal product decreases. However, the dynamics of the total and average products in this segment is not the same. Since this is where the law of diminishing returns begins, the marginal product begins to decrease, reaching its maximum value at point A. However, both the total and the average products still increase, i.e. each subsequent unit of the resource provides a product increase that is less than the previous one. But this increase will give an increase in the total product and will still be sufficient for the average product to also increase, although the growth rates of both (TR) and the other (AR) indicators will noticeably decrease.

At point B, the average product reaches its maximum value, and starting from this point, it decreases in the same way as the indicator of marginal product. At the same time, the total product continues to grow, reaching its maximum value at point C.

This means that an increase in a unit of resource provides such an insignificant increase in product (smaller than the increase in resource) that the product per unit of resource begins to decline.

Rice. one.

Finally, the segment CD is a segment of the absolute decline in production, when each additional unit of the resource does not bring an increase in the product, but leads to its reduction. In this case, the marginal product takes on a negative value and all indicators TP, AR, MP decrease.

It must be borne in mind that there is a clear geometric relationship between the graphs of all indicators. The indicator of the average value (average product) reaches its maximum value when it becomes equal to the indicator of the marginal value (marginal product). This is explained by the fact that the growth of the average value is possible only when an additional volume greater than the average value itself is added to it, otherwise there will be no growth. Conversely, a decrease in the average value is possible only when a smaller additional value is added to it. Thus, the average value increases when the limit value is greater than the previous average value, and decreases otherwise.

Therefore, the maximum average value (or its minimum) will be achieved in the case of equality of the limiting and average values. It is this point that will determine the maximum production efficiency (maximum product per unit cost). The value of the resource F 1 corresponding to this volume of output (with АР = MP) is of great importance for the tactical short-term development of the firm.

The geometric relationship between the total and average products is that on the graph of the total product, the average product at any point is given by the steepness - the slope of the line from the origin to this point. It is obvious that point B corresponds to the greatest steepness of such a line.

The locus of marginal product at any point on the output curve is determined by the slope of that curve at that point. In turn, the slope of the output curve is equal to the slope of the tangent through the given point. It is at point C that the slope of the tangent is greatest.

The law of diminishing returns applies to a certain technology and, accordingly, to a short period of time. However, in the long term, technology changes, and as a result of the action of scientific and technological progress, changes are determined by technological improvements.

It means that:

firstly, with the same amount of resources used, a larger output can be achieved;

secondly, the beginning of the law of diminishing returns is moved to the region of a larger value of the variable resource;

thirdly, the maximum possible use of the variable factor provides a greater volume of production with more advanced technologies. On the chart, all this will mean an upward shift in the total product curve (Fig. 2).

The law of diminishing returns is sometimes called the law of increasing costs. This means that performance and cost indicators are mutually inverse. In other words, one can determine, for example, how much output will be produced by one hour of labor (productivity or average product of labor) or how much labor is needed to produce a unit of output (labor intensity or average cost). Therefore, it would be logical to move from the analysis of product indicators to the analysis of cost indicators.

Rice. 2. The impact of scientific and technological progress on the law of diminishing returns

I. ECONOMIC THEORY

10. Production function. Law of diminishing returns. scale effect

production function is the relationship between a set of factors of production and the maximum possible volume of product produced using this set of factors.

The production function is always concrete, i.e. intended for this technology. New technology - new productive function.

The production function determines the minimum amount of input needed to produce a given amount of product.

Production functions, no matter what kind of production they express, have the following general properties:

1) An increase in production due to an increase in costs for only one resource has a limit (you cannot hire many workers in one room - not everyone will have places).

2) Factors of production can be complementary (workers and tools) and interchangeable (production automation).

In its most general form, the production function looks like this:

where is the volume of output;
K- capital (equipment);
M - raw materials, materials;
T - technology;
N - entrepreneurial abilities.

The simplest is the two-factor model of the Cobb-Douglas production function, which reveals the relationship between labor (L) and capital (K). These factors are interchangeable and complementary.

where A is a production coefficient showing the proportionality of all functions and changes when the basic technology changes (in 30-40 years);

K, L- capital and labor;

Elasticity coefficients of output for capital and labor inputs.

If = 0.25, then a 1% increase in capital costs increases output by 0.25%.

Based on the analysis of the coefficients of elasticity in the Cobb-Douglas production function, we can distinguish:
1) a proportionally increasing production function, when ( ).
2) disproportionately - increasing);
3) decreasing.

Let us consider a short period of a firm's activity, in which labor is the variable of two factors. In such a situation, the firm can increase production by using more labor resources. The graph of the Cobb-Douglas production function with one variable is shown in Fig. 10.1 (curve TP n).

In the short run, the law of diminishing marginal productivity applies.

The law of diminishing marginal productivity operates in the short run when one factor of production remains unchanged. The operation of the law assumes an unchanged state of technology and production technology, if the latest inventions and other technical improvements are applied in the production process, then an increase in output can be achieved using the same production factors. That is, technological progress can change the boundaries of the law.

If capital is a fixed factor and labor is a variable factor, then the firm can increase production by employing more labor. But on the law of diminishing marginal productivity, a consistent increase in a variable resource, while the others remain unchanged, leads to diminishing returns of this factor, that is, to a decrease in the marginal product or marginal productivity of labor. If the hiring of workers continues, then in the end, they will interfere with each other (marginal productivity will become negative) and output will decrease.

The marginal productivity of labor (marginal product of labor - MP L) is the increase in output from each subsequent unit of labor

those. productivity gain to total product (TP L)

The marginal capital product MP K is defined similarly.

Based on the law of diminishing productivity, let's analyze the relationship between total (TP L), average (AP L) and marginal products (MP L) (Fig. 10.1).

There are three stages in the movement of the total product (TP) curve. At stage 1, it rises at an accelerating rate, since the marginal product (MP) increases (each new worker brings more production than the previous one) and reaches a maximum at point A, that is, the growth rate of the function is maximum. After point A (stage 2), due to the law of diminishing returns, the MP curve falls, that is, each hired worker gives a smaller increment in the total product compared to the previous one, so the growth rate of TP after TS slows down. But as long as MP is positive, TP will still increase and peak at MP=0.

Rice. 10.1. Dynamics and relationship of the total average and marginal products

At stage 3, when the number of workers becomes redundant in relation to fixed capital (machines), MR becomes negative, so TP begins to decline.

The configuration of the average product curve AR is also determined by the dynamics of the MP curve. At stage 1, both curves grow until the increment in output from newly hired workers is greater than the average productivity (AP L) of previously hired workers. But after point A (max MP), when the fourth worker adds less to the total product (TP) than the third, MP decreases, so the average output of four workers also decreases.

scale effect

1. Manifested in a change in long-term average production costs (LATC).

2. The LATC curve is the envelope of the firm's minimum short-term average cost per unit of output (Figure 10.2).

3. The long-term period in the company's activity is characterized by a change in the number of all production factors used.

Rice. 10.2. Curve of long-run and average costs of the firm

The reaction of LATC to a change in the parameters (scale) of a firm can be different (Fig. 10.3).

Rice. 10.3. Dynamics of long-term average costs

Stage I: positive effect of scale	An increase in output is accompanied by a decrease in LATC, which is explained by the effect of savings (for example, due to the deepening of the specialization of labor, the use of new technologies, the efficient use of waste).
Stage II: constant returns to scale	When the volume changes, the costs remain unchanged, that is, an increase in the amount of resources used by 10% caused an increase in production volumes also by 10%.
Stage III: negative scale effect	An increase in production (for example, by 7%) causes an increase in LATC (by 10%). The reason for the damage from the scale can be technical factors (unjustified gigantic size of the enterprise), organizational reasons (growth and inflexibility of the administrative and management apparatus).

The costs incurred by the enterprise in the production of a given volume of output depend on the possibility of changing the amount of all resources employed. The quantities of many resources used - living labor (i.e. human labor), raw materials, fuel, energy - can be changed fairly quickly. Other resources require more time to master - for example, the capacity of an enterprise, that is, the area of its production premises and the number of machines and equipment in it, can only be changed over a long period of time. In some heavy industries, changing production capacity can take several years.

Since different times are spent on changing the amount of resources used in the production process, it is necessary to distinguish between short-term and long-term periods. short term- during which the enterprise cannot change its production capacities, but at the same time sufficient to change the degree of intensity of use of these fixed capacities.

The production capacity of the enterprise remains unchanged within the short run, but the volume of production can be changed by using more or less living labor, raw materials and other resources. Existing production capacities can be used more or less intensively within the short term.

long term is a period of time long enough to change the quantities all employed resources, including production facilities. From an industry perspective, the long run also includes enough time for incumbents to break up and exit the industry, and for new businesses to emerge and enter the industry. If the short-term period is a period of fixed capacities, then the long-term period is a period of varying capacities.

When analyzing production costs, it is important to take into account the effect law of diminishing returns which says that, starting from a certain moment, the successive addition of units of a variable resource (for example, labor) to an unchanged fixed resource (for example, land) gives a decreasing additional, or marginal, product per each subsequent unit of a variable resource.

Let's illustrate the operation of the law graphically (see Fig. 1).

For example, in the production room there is equipment - turning, milling and other machines. If the company hired one or two workers, the total output would be low, since the workers would have to perform many operations, moving from machine to machine. In this case, time would be lost (used irrationally), and the equipment would be idle. Production would be inefficient due to the excess of capital over labor.

These difficulties would disappear as the number of workers increased. In this case, the equipment would be used more fully, and the workers would specialize in individual operations. However, a further increase in the number of workers gives rise to the problem of their surplus. Now the workers have to stand in line to use the machine, there are workers to be underutilized. Ultimately, the continued increase in the number of workers in the enterprise would lead to the filling of all free space with them and to a stop in the production process.

Therefore, on the graph in Fig. 1, we observe that the total volume of production first grows, reaching the point Nopt, and then begins to decline, despite the increase in the amount of labor, that is, workers in the shop.

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1 .
2 .
3 . Tests
4 . Whell
Lliterature

1 . Law of diminishing returns. Total, Average and Marginal Product Curves (Analytical and Graphical Interpretation)

The essence of the law of diminishing returns is that additional costs produce less and less additional output. The law expresses the relationship between the costs and the results of these costs. However, it should be borne in mind that the law of diminishing returns is valid when one factor of production changes and the others remain unchanged. For example, income will change when an additional number of workers are involved in the production process. Moreover, the additional amount of output received from an additional unit of labor will decrease. But this is with the invariance of other factors (equipment, technology).

At the same time, if a large number of all resources are simultaneously involved in the production process (labor - the population has grown, new lands have been developed, advanced technologies, etc.), the return will increase. The increase in returns occurs on the basis of an increase in the scale of production.

The maximum value of the physical volume of the product produced by a certain value of the variable factor with the same technological process represents the total (gross or total) product TP (total product). If we assume that the variable factor is the labor force (L), and the constant factor is capital (K), then the increase in the total product of labor will be under the influence of the labor force additionally involved in the labor process. Economics / Ed. A.I. Arkhipova, A.N. Nesterenko, A.K. Bolshakov. - M: Prospect, 2002. - S. 112.

The total product calculated per unit of the variable factor used in production is the average product AP (average product).

AP = TP / L = Q / L.

The average product measures the performance of a variable factor. If the variable factor is the labor force, then the value of the average product is the productivity of labor.

The change in the value of the total product as a result of a change in the unit of the variable factor used in production expresses the marginal product MP (marginal product). Marginal product measures the productivity of an additional unit of a variable factor. If the variable factor is the labor force, then the productivity of the additional factor is called the marginal productivity of labor. The marginal product expresses the change in the total product (dQ) in terms of infinitesimal increments of the variable factor (dL). In this way,

MPL = dQ / dL, or Q / L.

The law of diminishing marginal productivity shows that: starting from a certain period of time, an increase in the volume of use of one resource while the volume of another remains unchanged leads to a decrease in the marginal product of a variable factor.

The rule of substitution of factors of production is that the ratio of increments of two resources is inversely related to the value of their marginal products.

Factors of production are divided into variables and constants. Variables include labor, raw materials, fuel, electricity, etc. The firm can easily change the number of these factors (for example, hire additional workers, use raw materials and fuel more economically).

Constant factors include buildings, heavy specialized equipment. In order to change these factors, a long period of time is required for the firm to change the volume of all the factors of production used. In the long run, all factors of production become variable. Therefore, the concept of "constant factors" is typical only for a short period.

If a firm reduces or increases production over a short period of time, then the change in output will not be proportional to changes in the number of variable factors. For example, land and capital in agriculture are constant factors in the short run. During the fall season, a farmer harvests a piece of land planted with a particular crop in the spring, meaning the size of the agricultural area cannot be changed. Agricultural buildings and implements remain constant. However, the farmer may, with a good harvest, hire additional workers. Most importantly, even if all workers are working with the same efficiency, each additional worker will add a different amount of output to the total output. Labor productivity, measured by the average product, first increases as the number of workers increases, then reaches a maximum, and finally, there comes a point when the average output begins to decrease.

The dynamics of productivity is determined by the ratio between constant and variable factors. With a low level of workload of constant factors, an additionally hired worker provides a significant increase in the total volume of production.

Further attraction of additional workers leads to the fact that the constant amount of land and capital is no longer enough for all workers to work with full efficiency. With an increase in the number of workers, the total output may increase, but the output per worker will gradually decrease.

There is a definite relationship between marginal and average products. The average product is calculated by dividing the total product by the number of workers. If we represent the aggregate, average and marginal products graphically (Fig. 1.1), then we can see that the marginal product line intersects the average product line at the maximum point of the latter. When the marginal product curve is above the average product curve, the average product increases. If the marginal product curve is below the average product curve, then the average product decreases. Nureev R.M. Microeconomics course. - M.: Norma-Infra-M, 2004. - S. 226.

At the same time, the value of the marginal product depends on the change in the total product.

Figure 1.1 - Total, average and marginal products of a variable resource (L) (fictitious values)

Thus, these quantities are dependent on each other. Similarly, we can consider this value depending on other factors of production.

2 . Interest rate, its types and role. Factors affecting the interest rate

Capital is a resource that has a long service life and is used to produce more economic goods. An entrepreneur, when purchasing capital goods (machines, machine tools, etc.), must correlate the costs of their purchase and operation with the expected income from their use. Semenikhina V.A. Microeconomics. - Novosibirsk: Siberian Institute of Finance and Banking, 2003. - P. 215.

The demand for capital services is the demand for free cash that a firm needs to upgrade or purchase capital equipment. Cash is used by the entrepreneur in the investment process.

There are two ways to determine the profitability of an investment: by discounting, comparing the demand price DP, which is equal to the present present value of PV, with the supply price of capital SP, or by comparing the expected return on capital P" with the interest rate r.

The firm receives the maximum profit provided that the marginal revenue and marginal cost per unit of capital are equal, i.e. MRPk = MRCk.

The marginal income of capital depends on the marginal income of a unit of capital MRk and the additional unit of output MPk obtained as a result of using a unit of capital: MRPk = MPk MRk.

Under conditions of perfect competition, the interest rate is formed on the market, none of the lenders or borrowers can influence its value. The interest rate balances the demand and supply of savings, as well as the marginal cost of capital (MRCk = i).

The equilibrium in the capital market looks like this (Fig. 2.1).

In the said picture:

S - money supply curve;

Di is the investment demand curve;

rE - equilibrium interest rate;

QE is the equilibrium value of investments and savings.

Figure 2.1 - Capital market

If an entrepreneur takes on a loan, then he necessarily compares the loss that he will incur due to the payment of interest, and the benefit that the acquisition of capital represents for him.

Savings serve as a source of borrowed funds. Economic practice shows that people who save, firstly, compare current consumption with the future, and, secondly, compare the most efficient ways of distributing savings. The main role in this distribution is played by the percentage value.

The interest rate is the price paid to the owners of capital for the use of funds borrowed from them for a certain period of time. Despite the fact that the share of this percentage in the total amount of factor incomes of the population is insignificant, many people have deposits in banks and receive income from this. Kurakov L.P. Economic theory. - M.: Press service, 2000. - S. 56.

For the subject of demand for capital, interest acts as a cost, for the subject of supply of capital - as income. The interest rate depends on the demand and supply of borrowed funds; in reality, there is a wide range of rates. When making investment decisions, it is not the nominal interest rate (at current prices) that is taken into account, but the real one (cleared from inflation). Those. the real interest rate rr is the nominal rate rn minus the inflation rate i. rr = rn - i. These are the types of interest rates.

The interest rate is defined as the ratio of the amount of interest to the amount of loan capital. If the loan is granted for several years and without the condition of annual interest payment, then the total amount at the time of repayment of the loan is determined by the formula for calculating compound interest. For example, in January 2006, a loan of 5,000 rubles was granted. for five years at a rate of 25% per annum. Under these conditions, the total amount of capital by January 1, 2011 will be: 5,000 (1 + 0.25) 5 = 15,000 rubles.

In this case, the nominal loan interest rate is used, i.e. excluding inflation.

Banks often act as intermediaries in the movement of loan capital. In this regard, it is necessary to distinguish between depositary and loan interest rates.

Depository interest rates are used in the calculation and payment of interest on bank deposits. Contributors receive the accrued amounts.

Loan interest rates are the standard fee for using a bank loan. The rate of this interest depends on the degree of risk, urgency (increases with the length of the term), the size of the loan.

The factors on which the loan interest rate depends are shown in Figure 2.2.

Figure 2.2 - Factors affecting the loan interest rate

Wanting to maximize profit, each entrepreneur chooses a project that provides a rate of return greater than the market lending interest rate. Accordingly, the owners of capital are the more willing to refuse current consumption, the higher the depositary interest rate. Thus, the market interest rate plays an important role in regulating economic processes. Through the market rate is the rational use of limited monetary resources. They are directed to the most efficient, profitable industries. At the same time, the market rate stimulates people's savings, promotes investment, without which it is impossible to establish large-scale production and receive stable profits. McConnell K.R., Brew S.L. Economics: principles, problems and politics. Per. from English. - M.: Infra-M, 1999. - S. 337.

An important tool in determining the effectiveness of investment is such a tool as discounting.

Discounting is the procedure for calculating today's value of amounts that can be received in the future at the current rate of interest. Discounting allows you to compare the value of today's costs and future income. If the present value of the expected net income exceeds the cost of investment, the firm decides to invest. In the second method, the firm will invest if the expected return on capital is equal to or greater than or equal to the interest rate.

To make an investment decision, based on the net present value, the present value of the expected returns is calculated and compared with the investment. Hence, if the net present value is greater than zero, then the investment can be made. The present profit with a positive net present value exceeds the investment.

Thus, firms always compare costs with results, since profit is their main goal.

3 . Tests

1. Opportunity cost:

a) include explicit and implicit costs, including normal profit;

b) include explicit costs, but do not include implicit ones;

c) include implicit costs, but do not include explicit ones;

d) include neither explicit nor implicit;

e) exceed the explicit and implicit costs by the amount of normal profit.

Opportunity costs are opportunity costs, so they are implicit costs.

2. The supply curve of a competitive seller in the short run is:

a) marginal cost curve;

b) the price line of the goods;

c) the decreasing part of the average cost curve;

d) the rising part of the average cost curve;

e) the portion of the marginal cost curve above average variable cost.

The competitive seller's supply curve graphically coincides with the marginal cost curve in the ascending section, i.e. above average variable costs.

4 . Task

Suppose a monopolist can sell 10 units. goods at a price of $100 per unit, but selling 11 units. will cause the price to drop to $99.5. What is the marginal revenue for increasing sales from 10 to 11 units?

Marginal revenue is calculated using the following formula:

where MR is marginal revenue;

TR - increase in total income;

Q - increase in the number of goods sold.

We get:

MR = (1199.5 - 10100) / (11 - 10) = $94.5.

Answer: 94.5 dollars.

Literature

1. Kurakov L.P. Economic theory. - M.: Press service, 2000. - 498 p.

2. McConnell K.R., Brew S.L. Economics: principles, problems and politics. Per. from English. - M.: Infra-M, 1999. - 665 p.

3. Nureev R.M. Microeconomics course. - M.: Norma-Infra-M, 2004. - 542 p.

4. Semenikhina V.A. Microeconomics. - Novosibirsk: Siberian Institute of Finance and Banking, 2003. - 235 p.

5. Economics / Ed. A.I. Arkhipova, A.N. Nesterenko, A.K. Bolshakov. - M: Prospect, 2002. - 250 p.

Law of diminishing marginal returns of factors of production. Marginal return of resources Law of diminishing marginal return

10. Production function. Law of diminishing returns. scale effect

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