Whatever the company does, it in any case works for the result. And this result is produced can be both real and immaterial. At a machine-building plant, machines act as a product of production, at a candy factory - candies, in medical field- the number of patients served, at the university - the number of graduates.

Various resources are used in the production of products. These are money, equipment, land, fossils, human labor. Labor is also a product. It is divided into general, average and marginal. The marginal product of labor is the additional expansion of production resulting from an increase in one unit. The rest of the factors of production remain unchanged.

What is the marginal product of labor?

The volume of products manufactured by the company, of course, depends directly on the number of employees. The average product of labor shows the efficiency (productivity) of the work of the team as a whole. For example, 24 masters made 10 tables in an hour, and 12 masters of another salon made the same number of products in the same period of time. So their work is more efficient.

What does the marginal product of labor actually represent?

The marginal product of labor is equal to the increase in the volume of output divided by the variable resource. In other words, this indicator makes it clear how much productivity increases due to the use of a new variable resource in the same unit of time. For example, a new resource may be a new workforce, equipment, or technology.

How many workers to hire

For any firm seeking to successful work and development, it is important to determine how many people are needed to maximize effective work. It would seem that the more employees, the higher the volume of production? Not at all.

When the average marginal product of labor reaches its maximum, it becomes equal to the value of the marginal product. This means that an increase in the number of employees will lead to a decline in production. This equality can be determined by a special calculation that takes into account at least two variable resources - labor and capital.

What does wages depend on?

With a fair and correct calculation, the head of the company can determine the highest possible payment for the work of hired employees, while maintaining the growth of the profits of his enterprise. Wage and marginal product of labor are interdependent concepts. When the enterprise maintains the optimal ratio of variable resources and the number of labor resources involved, then there is an increase in productivity. Accordingly, this leads to stable wages. If the enterprise does not have enough variable resources (for example, the same amount of capital invested in production), then attracting new units of labor will eventually lead to decreasing productivity, which subsequently affects the wages of the staff as a whole.

Everything in close connection from formulas and calculations

Considering that the marginal product of labor is additionally produced products by attracting an additional labor unit, it is also necessary to take care of investing additional capital in production. A simple example: if a company invests in the purchase of 100 tons of meat for the production of sausages, and 100 employees of the company produce products, then with an increase in staff by 50 additional jobs, the company will reduce its profit due to the need to pay additional wages to new employees.

And the number of products produced is the same. It turns out that with an increase in the number of employees, it is necessary to increase the purchase of raw materials. Therefore, increase the invested capital. But so that the marginal product of labor and the capital invested in production have the proper ratio. That is, the additional amount of output produced should bring income to the company in excess of the invested capital costs.

Of course, any employee dreams of getting more salary at work. Money is needed primarily to satisfy material needs. By working more, a person gets more income. This is ideal. But over time, when income increases so much that it covers all basic needs, there comes a period when the worker prefers leisure rather than work. And no longer aspires to more productivity in the course of performing their duties. Thus, when wages rise, the income effect conflicts with the substitution effect.

Not to your own detriment

Determining the optimal amount of attracted labor resource, it is necessary to take into account all available indicators. This includes the number of employees, and total costs, and marginal costs, and overall productivity. When hiring a new employee, the head of the company looks at how much the revenue from his work is commensurate with the costs that are inevitable with the need to hire him.

And here there are such concepts as the marginal product of labor in monetary terms and the marginal product of labor in physical terms. First of all, labor costs are taken into account. This is a cost to the business. And this wage should be competitive. Otherwise good employees will look for other firms where their work will be appreciated. At the same time, the head of the company is not entitled to establish wages for labor that exceed the revenue that the labor of the employee brings, or equal to it.

Features and need for modernization

As long as the profit of the enterprise exceeds the cost of labor, the head of the company can invite new employees to work and receive additional profit. The marginal product of labor will increase. But there is another way: without expanding the staff, the company invests additional costs in the modernization of production.

Upgrading equipment, increasing labor productivity due to this, the company provides itself with profit growth.

Marginal product of labor in monetary terms shows how much the total income of the firm has increased when using the same labor units using progressive modern equipment. With the correct calculation, the cost of equipment will pay off in a certain period of time and will begin to bring net profit. And this is more profitable than attracting new employees, the costs of which remain unchanged or even grow.

Ratio of labor to capital income

So the marginal product of labor is the surplus product. It is obtained using additional labor units. And the marginal product of capital is the additional goods and services received as a result of additional investment Money. And the company is interested in purchasing new technologies until the marginal product equals the real cost of capital. The company will receive economic profit when it pays for all stages of production, there will also be “money from above”. More broadly, the national income as a whole is then distributed among the income of workers, the income of the owners of capital, and economic profit.

One of the American senators - Paul Douglas - in 1927 thought about a strange phenomenon. The indicator of national income has not changed for years, working and businessmen alike enjoy the results of increased production and a progressing economy. The senator wanted to know the reason for the constancy of the shares of production factors and turned to the famous mathematician Charles Cobb for calculations. This is how the famous Cobb-Douglas production function was born, confirming that the ratio of labor to capital income is unchanged. And the shares of factors of production depend only on the share of labor in income, but do not depend on the number of factors themselves and the level of development of the industrial industry.

Flexibility of the production process

A competent manager will always find the perfect combination of production factors in order to increase profits and reduce the costs of the enterprise. Recall that the marginal product of labor is closely related to the amount of capital used. With an increase in the output of goods and services, the marginal product will increase, and vice versa - with a decrease in output, it also falls.

It is not enough just to increase the number of services and goods produced. It is more important that these goods are in demand and sold. The value of the marginal product of labor is equal to the income from the marginal product of labor for any amount of resource used. Search and find markets for the sale of goods, be able to negotiate and implement competitive goods and services - this is the task of the head of the company and his assistants.

Decreasing productivity

There is such a thing as the "law of diminishing productivity". It is brought to the rank of "law", because it is characteristic of all industries without exception. That is, this is what happens: a gradual increase in any of the factors of production per unit initially brings profit, but then from a certain moment it begins to decrease. Thus, at first there is an increase in the value of the marginal product of labor, and then this value is reduced. Why it happens?

At a time when labor costs are low and capital is still unchanged, the head of the firm decides to increase the units of labor. And this results in increased profits. But when there are many workers, and the invested capital remains the same, some of the workers work inefficiently, and then the profit of the enterprise falls.

A simple example: 10 people work on the potato harvest. But then the eleventh worker comes, but the volume of production does not change with his arrival, since the land is the same, the harvest is almost the same. In this case, as a rule, without reducing the staff, the company introduces technological improvements, and the volume of output grows again. That is, on the same land plot, you can grow a richer crop using the latest technologies. Then the cost of wages for the eleventh employee will be justified by the increased profits of the company.

Work only with profit

So, the marginal productivity of labor and the marginal product of labor are interrelated concepts. And they mean an increase in the volume of production due to the use of an additional unit of labor. The head of the company takes into account all factors of production when compiling short-term and long term plans. He tries to be flexible in improving production processes, observing the dynamics of all indicators.

The hiring of new employees will also occur gradually, as will the increase in invested capital, if the possibilities of reduction have been exhausted. production costs. And the main indicator of the correct decisions of the head of the company and his assistants, managers, is the growth of the company's profit. And since the marginal product of labor is, in fact, profit, this indicator is the main one.

The firm will hire 4 workers. Let's justify our decision.

The use of 3 workers will give a profit increase of 400 - 300 \u003d 100 rubles. In the case of hiring 4 workers, the marginal product in the monetary form of the 4th worker (300 rubles) exactly corresponds to the amount of his earnings, i.e. MRP L = MRC L . Hiring the 5th is unprofitable, because. the marginal product in cash is 200 rubles, and the marginal cost associated with hiring the 5th worker is 300 rubles (the fifth worker will have to pay 300 rubles), in this case the company will incur losses in the amount of 300 - 200 \u003d 100 rubles. Therefore, if MRP > MRC, then the firm, in order to maximize profits, should increase the amount of the variable factor, and vice versa.

And only in case MRP = MRCThe firm will earn the maximum profit.

For example, consider the equilibrium situation of a firm presenting a demand for labor under perfect competition (Fig. 8.3).

Rice. 8.3. Equilibrium in the labor market

The firm, hiring an additional worker, commensurates the amount of revenue from the use of his labor with the cost of hiring an additional worker ( w). Negative slope MRP L is associated with the law of diminishing marginal productivity of the factor, its location is determined by the level of marginal productivity of the factor ( MR L) and the price of manufactured products ( R). Dot E is the equilibrium point of the firm in the factor market, since right in it MRP L =w e. This means that at the wage level (w e), the firm should hire L e workers. In this way, ifMRP L = w e provide an optimal level of employment.

When the number of workers is less than Le, when MRP L > w e the firm should increase the number of workers. When the number of workers is greater than Le, when MRP L < w e, the firm should reduce their number.

Any firm operating on two variable, partially interchangeable factors faces the problem of selecting the combination of inputs for each given volume production, and it seeks to minimize costs for each given volume of production.

To identify all possible combinations of factors in the production of a given volume of products, we construct an isoquant and an isocost.

isoquant - this is a curve, any point on which shows different combinations of two variable factors that provide the same output (Fig. 8.4).

All possible technologically efficient combinations of two factors corresponding to a certain volume of production are on the curve. For example, the release of 90 units of production (Table 12.1) can be obtained with the following combinations of labor and capital: 3 units. TO and 4 units. L; 4 units TO and 2 units. L. All combinations will be on the isoquant with a volume of 90 units. But if a less efficient technology is used, then the use of 3 units. TO and 4 units. L will give a production volume equal, for example, to 85 units. products.

Other combinations of two factors, for example, 6 units. TO and 4 units. L; 2 units TO and 6 units . L, will give an output equal to 106 units. products, and will be on the isoquant with the corresponding output located above this curve (Fig. 8.5).

Isoquants never intersect. Each isoquant corresponds to a certain amount of output, the farther the isoquant from the origin, the more output it will provide.

An isoquant is a graphical form of expressing a production function. Therefore, it has the same characteristics as the production function:

1) isoquant shows the maximum output for each individual combination of factors;

2) isoquants are concave and become flatter as one moves from top to bottom along them. As we move down the isoquant, more and more units of labor are required to replace each unit of capital, resulting in a decrease in the marginal productivity of labor and an increase in the marginal productivity of capital;

3) isoquants have a negative slope, since in order to maintain the same volume of output with a decrease in the use of one factor, it is necessary to increase the use of another.

For example, the change in capital to the change in labor will look like this:

MRTS KL = -  K/  L.

By reducing the use of one factor, such as capital (  K), the firm reduces output by  Q = MP K ·(-  K). But in order to stay on the same isoquant, the decrease in the amount of capital used must be compensated by the increase in labor used (  L) on the  Q = MP L ·  L.

Therefore, in order for the output to remain unchanged, the equality must hold:

MP L ·  L + MP K ·  K=0

or MP L ·  L=MP K ·(-  K).

It follows that,

MP L / MP K = -  K /  L = MRTS KL .

In this way, the marginal rate of technological substitution of factors of production is equal to the inverse ratio of their marginal products (productivity).

As you move down the curve MRTS KL decreases (therefore, the curve has a convex shape towards the origin). This is explained by the fact that as capital is replaced by labor (reduction of the factor TO and increasing the amount of factor L) the marginal product of capital ( MR TO) increases, and the marginal product of labor ( MR L) decreases (the numerator decreases and the denominator increases). Consequently, the marginal rate of technological replacement of capital by labor decreases. And vice versa.

On the other hand, equality MP L / MP K = -  K /  L says that at any point of the isoquant, the marginal rate of substitution of one resource for another is equal to the slope of the tangent to the point lying on the isoquant . MRTS KL is the slope of the isoquant.

Isoquants have a different form depending on the degree of interchangeability of resources (Fig. 8.6).

a) Absolutely b) Complimentary c) Partially

interchangeable (mutually complementary) interchangeable

Rice. 8.6. Isoquant forms

Isoquants, in the form of straight lines (Fig. 8.6 a), characterize the ideal interchangeability of factors, that is, one factor can be completely replaced by another. In this case, production can be carried out even with the help of a single factor. For example, the sale of drinks can be carried out by sellers, or maybe by vending machines. In this case, the marginal rate of technological substitution is constant at all points of the isoquant ( MRTS KL = cons’ t). Then the production function looks like:

Q= α ∙K+β ∙ L.

Isoquants in the form of a right angle (Fig. 8.6 b) reflect the patterns of production with fixed proportions of factors. In this case, the production technology is such that the factors used complement each other and substitution between them is impossible ( MRTS KL =0 ). In order to carry out the production process, both factors must be applied in the same strictly defined proportion, for example, 1 car and 2 drivers (1 unit of production). TO and 2 units. L). A prerequisite for the transition to a new isoquant is not only an increase in two factors, but also compliance with a given proportion in the use of resources. If there is an increase in one factor without changing the other, then the transition is impossible. For example, a combination of 3 cars and 2 drivers makes no economic sense, just like a combination of 1 car and 6 drivers. The transition to a higher isoquant in this case is possible with a combination of 3 cars and 6 drivers.

In this case of complementary factors, the production function has the form (the "input-output" formula or V.V. Leontiev's formula):

Q= f(K, L) = min{ α TO,βL} .

This means that the volume of output will be equal to the minimum of the values ​​that will be obtained by substituting the quantitative values ​​of variable factors into the function.

Let α=3, β= 2, TO=1, L=2, then the output will be equal to 3, since Q= min(3(1),2(2)). Then the volume will be equal to 3 and 4.

In the case of partially interchangeable factors (Fig. 8.6 c), production can be carried out with the obligatory use of two factors. Their combinations can be different depending on the given production function (Cobb-Douglas formula):

Q=A∙K α ∙ L β .

A firm operating with two variable factors faces the problem of choosing the optimal combination of inputs for each given output. A profit maximizing firm will seek to choose the cheapest combination of inputs. Thus, the problem is reduced to minimizing the costs of the firm for each given volume of production.

Just as the same amount of output can be obtained with different combinations of factors, different combinations of them can give the same level of costs. The line that reflects different combinations of factors of production that give equal total costs is calledisocostal (Fig. 8.7).

Let's graph the total costs:

TS = R TO ∙K+R L ∙ L,

where TS- total costs equal to the sum of fixed and variable; R TO- the price of a unit of capital; TO- amount of capital; R L- the price of a unit of labor; L - the amount of labor.

Rice. 8.7. Isocost

The isocosta is constructed as follows. If we assume that everything is spent only on the acquisition of capital, then it is possible to acquire the maximum TS/R TO units If everything is spent only on the acquisition of labor, then we can acquire the maximum TS/R L units By connecting these boundary points, we get the isocost (Fig. 8.7).

Any point on the isocost shows a combination of two factors in which the total costs (total costs) for their acquisition are equal. The isocost is described by the equation:

TC= P TO ∙K+R L ∙ L,

.

The angle of inclination of the isocost is equal to the marginal rate of technological substitution:

.

Thus, the slope of the isocost is equal to the ratio of the prices of the factors used, multiplied by (-1). If a firm increases the amount of one factor, then it must reduce the use of another. In order to keep the total cost of acquiring factors unchanged, the following condition must be met:

-  K /  L = P L / P K .

Insofar as, The isocost is both an equal cost line and a firm's budget constraint line., then the equation can look like:

B= P TO ∙K+R L ∙ L,

where IN- the company's budget for the purchase of factors; R TO- the price of a unit of capital; TO - amount of capital; R L – unit price of labor; L- the amount of labor.

For example, the company's budget for the purchase of factors is 1000 rubles, and the price of 1 unit of capital is 500 rubles, and the price of 1 unit of labor is 250 rubles. In this case, the firm can purchase 2 units of capital or 4 units of labor (Figure 8.8).

A change in the size of the budget causes a shift in the isocost to the left (decreased) or to the right (increased) (Fig. 8.9 a). A change in the price of factors of production leads to a change in the slope of the isocost (Fig. 8.9 b). But cases of simultaneous changes in both the budget and prices for factors of production are possible.

The task of the entrepreneur is to choose such a combination of factors that ensures the production of the required quantity of products at the lowest cost. The optimal ratio of factors will be when the combination of these resources lies on the isocost, and the slope of the isocost is equal to the slope of the isoquant, i.e.

.

This equality says that the minimum costs are achieved when the cost of an additional unit of output does not change from the use of any additional factors.

To determine the optimal combination, let's overlay the isoquant map on the isocost (Fig. 8.10). Isocost with budget constraints IN 1 (or costs FROM 1 ) does not allow reaching the required output, since it does not have a point of contact with the isoquant. We see the intersection of the isocost with isoquants at points BUT, IN And D. points IN And D indicate excessively high costs ( IN 3 ) to achieve a given output volume Q. Dot BUT is optimal, since it is this combination of factors that allows you to produce volume Q at a lower cost ( IN 2 ).

In order to increase or decrease the volume of production, the firm must change the ratio of factors until the marginal rate of substitution of factors ( MRTS KL) will not be equal to the slope of the isocost ( P L /P K). From this follow the following conclusions:

1) the factor of production is used until its marginal productivity, expressed in monetary units, becomes equal to its market price, which is the limiting limit of the factor's application;

2) the optimal combination of a factor is achieved when the ratio of the marginal productivity of the factors is equal to the ratio of their market prices;

3) the ratio of prices and marginal productivity of factors of production determines the demand for each of them.

In the short run, if the price of any factor rises, then the firm will reduce its use and increase the cheaper one. However, a change in the use of factors of production leads to a change in production costs. And any restriction on the use of any factor will lead to an increase in costs and will not allow the company to achieve the optimal combination of factors. However, in long term the firm has more opportunities to combine factors for each given output, because the costs in the long run are lower than the costs in the short run.

Having determined the optimal ratio of factors for the volume Q, you can do the same for volumes Q 1 , Q 2 etc. As a result, we get a certain map of cost-optimal options for the implementation of production (Fig. 8.11). Combination of factors at a point BUT will give the least cost for volume Q 1 , at the point IN with volume Q 2 , at the point FROM with volume Q 3 . Connecting all points of optima for different volumes of production ( BUT, IN, FROM) we get a curve called growth trajectory.

When making decisions about changing production volumes, the firm will move along this curve.

The direction of the trajectory depends on the ratio of factor prices and their marginal productivity. For most producers, a shift towards capital due to a shift to more capital-intensive technologies is most likely (Figure 8.12a). If the technology requires a constant ratio of factors, then a linear development trajectory will be observed (Fig. 8.12 b). If in rare cases the use of a large amount of labor is required, then a downward trajectory of development takes place (Fig. 8.12 c).

As mentioned above, at the point of contact, the slopes of the isoquant and isocost are equal. The slope of the isocost is P L /P K, and the isoquants are MRTS KL . .

MRTS KL = MP L / MP K = -  K /  L,

but - K/L = P L / P K . Then MP L / MP K = P L /P K, i.e:

-cost minimization rule.

a) Capital-intensive b) Mixed c) Labor-intensive

Rice. 8.12. Various forms technology development trajectories

From the point of view of rational economic behavior, this means that a more expensive factor of production is replaced by a cheaper one. For example, capital is more expensive than labor ( MP L / P L  MP K / P K), then the firm minimizes costs by replacing capital with labor. If labor is more valuable than capital MP L / P L  MP K / P K), labor is replaced by capital.

Let's illustrate this simple example. Let the firm use 4 units. labor and 9 units. capital. The price of labor ( P L) = 100 rubles, the price of capital ( P K) = 100 rubles. Marginal product of the 4th unit. labor ( MP L) = 12, and the 9th unit. capital MP K = 6.

According to the cost minimization rule, the equality must hold:

MP L / P L = MP K / P K .

In our case, 12/100  6/100, 0.12  0.06.

This is not equal. Consequently, this combination is not optimal, since the last ruble spent on acquiring an additional unit of labor gives an increase in output of 0.12 units, and the last ruble spent on acquiring an additional unit of capital gives an increase in output of only 0.06 units. In this situation, the firm should replace a relatively expensive factor (capital) with a relatively cheap factor (labor), that is, increase the amount of labor and decrease the amount of capital. This substitution is carried out until the ratios of marginal product to price for the two factors are equal. For example, for the 6th unit. labor and the 7th unit. capital, the marginal products will be equal to ( MP L =10, MP K = 10).

Then 10/100 = 10/100 - in this case, the firm minimizes costs.

Cost minimization is a necessary but not sufficient condition for profit maximization. The difference between cost minimization and profit maximization is as follows. Upon reaching the optimal combination of factors for any volume of output, the prices of factors and their marginal productivity are accepted. When formulating the conditions for maximizing profits, the marginal product of the factor in monetary terms, which reflects the demand for products produced with their help, is also taken into account. This is due to the derivative nature of the demand for factors.

The firm's profit is maximized if MRP L = MRC L .

Under conditions of perfect competition, this rule is formulated as follows: profit maximization is achieved when the marginal product of a factor in monetary terms is equal to its price. If the firm uses two variable factors - labor and capital, then profit maximization will be ensured at such a volume of production when MRP L = P L And MRP K = P K ,

or MP L / P L= 1 and MP K / P K = 1.

11.3. Profit maximization when using an economic resource

Let's consider a certain firm "Orion", which produces goods X using resource A. As it is established, acting in any market structure, the firm maximizes profit by releasing such a volume of production at which its marginal revenue equals marginal cost: MC = MR. Since Orion produces product X using resource A, it is logical to assume that the firm will hire this resource until the marginal revenue received by adding an additional unit of the resource is equal to marginal cost associated with hiring that unit of resource. Let's pay attention to the following: the categories of marginal revenue (MR) and marginal cost (MC) were defined as changes, respectively, in total revenue (TR) and total cost (TC) associated with the production and sale of an additional unit of goods. Since we are interested in the change in TR and TC associated with hiring an additional unit of resource, we need to introduce two new terms:

monetary marginal product (MRP)- change in the total revenue of firms due to the sale of units of goods produced using an additional unit of the resource:

marginal resource cost (MRC)- change in the total production costs associated with the attraction of an additional unit of the resource:

It can be proved that the condition for profit maximization by a firm is the use of such an amount of a resource that satisfies the condition:

If the firm is not able to influence the prices of resources, i.e. buys resources in a perfectly competitive factor market, then the MRC values ​​will be the same for all hired units of the resource and will amount to the price of a unit of the resource P a . Profit maximization in this case is achieved if P a = MRP.

This means that at any price of the resource P a, the firm can determine the amount of the resource used, i.e. QD of the resource under which the condition is fulfilled: P a = MRP. Then the firm can find a correspondence between the price of the resource P a and QD of the resource or determine the demand for the resource. The resource demand curve is the MRP curve and the supply curve is the MRC curve.

In the long run, when all resources are variable, by producing any amount of output using several resources, say A and B (for example, labor and capital), the firm can minimize the cost per unit of output if the condition

where MPC and MPL are the marginal products of capital and labor;
PC and PL are unit prices of capital and labor.

Equality (8) allows you to find the ratio of resources that provide the company with minimal costs for a given volume of output, but it does not guarantee that in this case the company receives the maximum possible profit. It was proved above that using one resource, say A, the firm maximizes profit when the value of the marginal product in monetary terms is equal to the marginal cost of the resource:

Using only two resources, such as labor and capital, a firm maximizes profit when each resource satisfies this rule, i.e. MRP L=MRC L And MRP C = MRC C . Then, in a generalized form, the profit maximization condition when using two resources can be represented as:

If the firm is not able to influence the prices of resources, then MRC equals the price of the resource and equality (9) takes the form:

Note that, in contrast to equality (8), where a proportional ratio of MP and P is assumed (i.e., the firm can minimize costs if MP L / P L = MP C / P C = 3), the profit maximization condition means that the value of the MRP of the resource is equal to the marginal cost of the resource (resource price) and MRP L / P L =MRP C / P C = 1.

(Materials are given on the basis of: V.F. Maksimova, L.V. Goryainova. Microeconomics. Educational and methodological complex. - M.: Publishing Center of the EAOI, 2008. ISBN 978-5-374-00064-1)

As a starting point in the analysis of production costs, the thesis was considered that the production of any product or service is based on the costs of economic resources. In this regard, questions arise:

What will the profit maximization condition of a firm using some resource R look like? At what cost of this resource (Q R) will the firm's profit be maximized?

If several types of resources are used in the production of this good - R 1 , R 2 , R 3 , ..., R n -1 , R n , then what should be their combination in order to provide the company with the opportunity to produce this product at the lowest cost?

What should be the combination of R 1 , R 2 , R 3 , ..., R n -1 , R n for the firm to get the maximum profit?

Any firm maximizes profit by producing such a volume of output at which its marginal revenue (MR) equals marginal cost (MC). The values ​​of marginal revenue and marginal costs depend on the dynamics of gross income (TR) and gross costs (TC), respectively. How do TR and TC change when an additional unit of a resource is introduced into production? Let's introduce two new terms - "marginal product in monetary terms" and "marginal cost of a resource".

Marginal product in monetary terms (MRP) represents the change in total revenue (TR) of the firm due to the production and sale of units of goods produced when using each additional unit this resource:

where Q R is the amount of resource R involved in the production of a given good (some product X).

Marginal resource cost (MPC) reflect the change in the total costs of the company (TC) in connection with the involvement in the production of an additional unit of the resource in question:

(2)

Any firm, in order to maximize profits, must use additional units of any resource as long as each subsequent unit of this resource gives a greater increase in the total income of the firm compared to the increase in its gross costs. Then profit maximization condition is the use of such a quantity of a given resource in which the marginal product in monetary terms will be equal to the marginal cost of the resource: MRP = MRC. This identity, in addition to the logical justification, is also explained mathematically.

So, initial condition our mathematical proof will be the equality MR = MC, the components of which are calculated as follows:

where Q X is the change in the volume of production of some product X. Next, the indicator of marginal product (MP) is determined:

Now we use a technique common in mathematics - we multiply both the numerator and denominator in the expressions mrp and MRC by the same value, namely by Q x . It is clear that the quotient of division in formulas will not change as a result of such transformations. We get:

Thus, MRP = MR x MP, i.e., the product of the firm's marginal revenue and the marginal product of a given unit of resource, and the marginal cost of a resource can be obtained by multiplying the firm's marginal cost by the marginal product too: MRC = MC x MP. In expressions (3) and (4), the second factors are the same. On the other hand, at the beginning of our proof, we took MR = MC, which means that the values ​​of the first factors in these expressions are equal and equal. Hence, we can state that the identity MRP = MRC really reflects the profit maximization condition for the manufacturing enterprise.

If a firm using in production this species resource, unable to influence its price (i.e., buys resources in a perfectly competitive market for factors of production), then the marginal cost of the resource for all hired units of this resource will be the same and equal to the price of the resource (Р R). The profit maximization condition in this case will take the form: MRP = MRC - P R , or MRP = P R . The significance of the provisions presented here will become apparent in the analysis of the demand for an economic resource.

The above statements are valid for a single resource. However, the production costs of the firm include the costs of attracting many types of resources, without the use of which it is impossible to carry out production. As a tool for analyzing this issue, economic science uses the concept of "production function". production function reflects the relationship between a certain volume of manufactured products (Q x) and the quantitative costs of resources (QR 1 , QR 2 ,QR 3 , ..., QR (n -1) ,QR (n)) required to create this product X: Q x= f(Q R 1 , Q R 2 ,Q R 3 , ..., Q R (n -1) ,Q R (n))

Any production function reflects a specific technology, showing what contribution to the creation finished products contributes each of the resources involved in manufacturing process. Using the production function, you can determine the maximum possible output for a given cost of resources. On the other hand, it allows us to find out what is the minimum required amount resources for the production of a given volume of output. The production function helps to determine the various combinations of resources used, providing the possibility of achieving the same result, i.e. the same value Q x . This raises two basic questions: what should be the combination of resources to produce any given level of output at the lowest cost, and what combination of resources will maximize the firm's profits?

To answer the first question, let's recall that we consider the level of its performance, in particular the MP indicator, as the main indicator of the effectiveness of the use of any resource. In quantitative terms, the efficiency of using any resource is determined not only by its marginal productivity, but also by the market price of this production factor (PR) and will be described by the expression: MP i / PR i , where MP i is the marginal product i-th resource; R Ri is its price.

In this case, any firm will always give preference to the resource for which the ratio of MP and R R will be higher. Involving an increasing amount of this resource in the production process, the company will face the problem of reducing the efficiency of its use, with the price of the resource unchanged, due to the law of diminishing marginal productivity; its mp will begin to decrease, which means that the quotient of the division MP / P R will also decrease. Obviously, the firm will continue to increase the volume of use of the resource under consideration only until its relative efficiency is equal to the relative efficiency of other resources, i.e. until the equality

(5)

In other words, the cost of producing any volume of output is minimized if the marginal product for each monetary unit of the cost of each input used is the same. This principle is called least cost rules.

The presented identity (5) makes it possible to find such a combination of resources that will provide the firm with the production of a given volume of output at minimal cost, but does not guarantee maximum profit. Above, it was proved that the firm maximizes profit if the equality mrp = mrС is observed. If the firm uses only two resources - A and B, the maximum profit is achieved if: MRP A \u003d MRC A and MRP B \u003d MRC B, i.e. when

In other words, when the following expression occurs:

If the firm is not able to influence the prices of economic resources and has to purchase each next unit of the resource at the price prevailing in the market (p r), then mrc = P R , and the above condition is transformed:

where P A and P in are the prices of resources A and B, respectively.

This example considers the situation for two types of resources. If the obtained results of the study are “expanded” for all the resources used by the firm, we get the following expression, called profit maximization rule:

This equation characterizes the situation when the firm not only minimizes costs, but also maximizes profits. In its form, it is more rigorous than identity (5), and requires not just the proportionality of the marginal product and the price of the resource, but the equality of the numerator and denominator.

Marginal product and its monetary value

marginal product MR (marginal product) is called additional products produced with the help of an increment of a given factor of production:

Change overall size the firm's revenue from the use of an additional unit of a resource. It is assumed that the amount of all other resources used remains unchanged.

Marginal product in monetary terms MRP (marginal revenue product) is the additional income received from the sale of an additional unit of production:

Marginal product in money terms equals the change in total revenue divided by the change in the amount of resource used.

The optimal ratio of resources: the rule of minimizing costs and maximizing profits

The marginal cost of resources MRC (marginal resource cost) - additional costs for acquiring an additional unit of a resource are called:

According to the resource use rule, the producer acquires additional resources until the value of the marginal product in monetary terms is equal to the marginal cost of resources:

The cost minimization rule is as follows: the cost of producing a certain volume of output becomes minimal if the ratio of the marginal product of one factor of production to its price is equal to the ratio of the marginal product of another factor of production to its price:

MP1/P1= MP2/P2,

where 1 and 2 are factors of production.

The profit maximization rule can be formulated as follows: the firm's profit becomes maximum if the ratio of the marginal product in monetary terms of one factor of production to its price is equal to the ratio of the marginal product in monetary terms of another factor of production to its price, while both ratios are equal to one:

MRP1/P1= MRP2/P2=1.

Conclusion

IN market economy factors of production act as commodities. This means that they, like ordinary goods, are subject to purchase and sale in the respective factor markets. The buyers in these markets are entrepreneurs as representatives of enterprises (firms) that are in need of such factors of production as capital, labor and land. Accordingly, manufacturers of means of production, the working population, land owners can be sellers in such markets.

The factors of production can be divided into two types: the personal factor - workers - and the material factor - the means of production. For the coordinated functioning of the factors of production, it is necessary to use them in the correct quantitative ratios. It is necessary to find such a ratio of these factors, which will allow to extract the greatest benefit from their use. That is, it is necessary to determine such a combination of factors of production, in which the costs of the enterprise would be minimal, and the efficiency of production would be maximum. This combination is constantly changing as a result of changes in the prices of factors of production.