Option 11.
PRODUCTION FUNCTION OF THE FIRM, ISOQUANT AND ISOCOST.
2. Properties of isoquants. Substitution of factors of production.
3. Isocost and equilibrium conditions of the firm.
In the cobweb model, the demand function: Q D = 200 - P, and the supply function: Q S = 0.5P - 10.
The goods are sold within five days. Determine the equilibrium price of the good. Find the volumes of supply and demand, as well as the price by day of the week, if on the first day the price was equilibrium, and on the second day the demand increased by 30 units. goods?. Record your results in a table:
What is the equilibrium price after the increase in demand?
1. The production function of the company, its construction.
2. Properties of isoquants. Substitution of factors of production.
In order to organize the production of products at the enterprise, it is necessary to ensure the interaction of production factors.
Thus, the factors of production for the production of a television set include: industrial premises, machine tools, machinery, equipment, labor of workers, a piece of land on which industrial buildings and structures are built, etc.
Depending on the speed with which the amount of resources involved in production can change, they are divided into fixed and variable. Those of them that remain unchanged for a certain period of time form constant factors of production, and those whose number changes form variable factors of production.
Everything production resources, involved in the production process, are available in limited quantities. As a result, the volume of production of goods and services is limited by the amount of available resources. Therefore, society as a whole and each commodity producer in particular is always faced with the task of their most efficient use. Thus, the volume of goods produced is determined by the availability of the necessary resources. Moreover, various options for their use allow the producer to receive more or less goods or services. Therefore, the enterprise should be interested in ensuring the fullest use of labor, material and financial resources and their optimal combination.
The ratio between the volume of output and the volume of factors of production involved reflects the production function.
The production function indicates the possible maximum output (Q) for a certain combination of production factors within the framework of using a particular type of technology:
Where Q is the volume of output, L is the mass of attracted work force(labor); K - the amount of capital used (means of production).
At the same time, in modern conditions, technology is considered as a completely independent factor of production. Then the production function takes next view:
Where the new symbol M stands for production technology.
The influence of the economic order. It is clear that any enterprise operates in specific economic conditions, is directly affected by the national economic system. Therefore, it is not without meaning if, in the analysis of the production function, the economic conditions of management are perceived as a separate specific factor of production. It is believed that the symbol f is used to denote it in the production function formula.
The production function allows:
Determine the share of participation of each of them in the creation of goods and services.
By changing the ratio of factors, one can find such a combination of them that will achieve the maximum volume of production of goods and services.
Track how output changes with an increase or decrease in the use of certain factors of production by one unit, and, thus, identify the production capabilities of the enterprise.
Determine the economic feasibility of the production of a particular product.
Note that the production function, as a rule, is calculated for a specific technology.
For various types of industries (cars, agricultural products, confectionery etc.) the production function will be different, but they all have the following properties in common:
* there is a limit to the increase in production that can be achieved by increasing the cost of one resource, all other things being equal;
* there is a certain mutual complementarity of production resources and their interchangeability (substitution). The complementarity of resources means that the absence of one or more of them makes the production process impossible - production stops. At the same time, the factors of production are interchangeable to a certain extent. The lack of one of them can be compensated by an additional amount of the other, i.e. resources can be combined with each other in the production process in various proportions;
* a differentiated assessment of the influence of each of the factors on the dynamics of output is given in relation to certain periods of time.
The production function can be expressed graphically as an isoquant - a curve that reflects the various combinations of resources that can be used to produce a given volume of output. For example, the production of 1 ton of potatoes (Q) can be achieved by using a different combination of the amount of living labor (L) and technical means- capital (K).
As the main properties of the production function, we point out that:
1) for each branch of production, its own production function is formed;
2) within a certain technology, different combinations of the main factors of production may be allowed;
3) a radical change in technology inevitably causes a transition from one production function to another;
4) the analysis of the production function involves the search for such a variant of the organization of production, which ensures maximum economic efficiency.
Conclusion: the technological mode of production is reflected through a combination of production factors.
production grid.
The production function draws our attention to three important things:
1) the greater the volume of involved factors of production, the greater the volume of output;
2) the same output can be provided with different combinations of factors of production;
3) reducing the scale of application of one factor, it is necessary to increase the volume of attraction of another factor of production.
All these provisions are confirmed by the production grid (Table 1).
Horizontally, Table 1 shows the amount of labor involved in production, and vertically, the amount of capital.
By moving diagonally down and from left to right and increasing the number of factors of production, we increase the volume of output from 20 to 115 units.
Table 1. Change in output with a change in the volume of production factors involved (production grid)
Moving diagonally from left to right and up, the output (Q=75) remains constant
Isoquant. Such a relationship between a fixed volume of output and the ratio of two factors - labor and capital - will be reflected in a special graph. As a result, we get a line, which is called an isoquant (Fig. 2)
| Q=75 | ||||||
| 0 | 1 | 2 | 3 | 4 | 5 | L |
Rice. 2 Construction of an isoquant with an output of 75 units.
On fig. the isoquant corresponding to the production of 1 ton of potatoes is shown. It shows that there are many options for using resources to produce a given amount of potatoes. In one case, more manual labor (L) can be used - 70 man-hours and only 2 machine hours (K) (point A), in the other - 40 man-hours Li and 3 K (point B), in the third - 20 person-h L to 6 h K (point C), etc.
An isoquant map is used to determine the maximum output that can be achieved with each combination of factors.
Isoquant analysis can be used to determine the marginal rate of technological substitution, i.e. the possibility of substituting one resource for another in the process of their use. This possibility depends on the production function. There are functions in which resources are easily replaced, and there are also those where resources have rigid, unchanging proportions.
The Marginal Rate of Technological Substitution (MPTS) expresses the number of units of a given resource that can be replaced by a unit of another resource while maintaining the same output.
Let us assume that the production technology of one car provides for the use of 1000 hours of labor and 500 hours of work of machines and equipment. The ratio of labor to capital in this case will be 2 hours of labor to 1 hour of machine work (point A).
In order to mechanize and automate production, the enterprise is moving to the use of more capital-intensive production process, i.e. the production of one car will require less living labor and more materialized labor (machines, equipment). In this example, the marginal rate of technological substitution of labor for capital is determined by the amount of capital that can replace each unit of labor without causing an increase or decrease in the production of cars. The marginal rate of technological substitution at any point of the isoquant is equal to the slope of the tangent at that point, multiplied by -1:
MPTS = - DK / DL (const Q),
where DK - reduction or increase in the resource of capital;
DL - reduction or increase in labor resource;
Q is the volume of production.
The curvature of the isoquant helps the manager to determine exactly how much labor savings will be required during implementation. new technology production. At point B, it takes only 500 hours of labor and 1,000 hours of machinery to produce a car. The ratio of capital to labor here is only 0.5 hours of labor for every hour of operation of machinery and equipment.
Isoquant - a line that reflects the combination of factors of production that can be used to produce a fixed volume of output for a specific period of time.
An isoquant is a graphical form of expressing a two-factor production function. It has an objective character, as it reflects real economic processes.
Law of the isoquant: the more one factor of production is used, the less another factor is used.
Special configurations of the isoquant. Under certain circumstances, the isoquant can take the form of a straight line. A linear isoquant assumes that the replacement of one factor by another is carried out in a proportion that is unchanged throughout the isoquant.
If it is possible to organize production, limited to the use of only one type of economic resource (the situation of absolute substitutability), then in this case the isoquant will touch the axis of the opposite factor of production.
The solid nature of the line means that each option always has alternative options for combining factors of production.
The concave isoquant reflects the fact that we have to deal with a flexible production function, when the reduction in the use of one factor of production is compensated only with more high pace increase in the volume of application of another factor (i.e., the ratio between the volume of labor and capital is constantly changing).
In conditions when the release of a fixed volume of products is possible only with a single combination of factors of production, we have to admit that we are dealing with a rigid production function. Under this combination of circumstances, the isoquant takes the form of a right angle.
3 Isocost and firm equilibrium conditions
Isocost - a line showing combinations of factors of production that can be bought for the same total amount of money. The isocost is also known as the line of equal costs. The isocosts are parallel lines because it is assumed that the firm can purchase any desired number of factors of production at constant prices. The slope of the isocost expresses the relative prices of factors of production. Each point on the isocost line has the same total cost. These lines are straight because factor prices are negatively sloped and parallel.
Combining isoquants and isocosts, one can determine the optimal position of the firm. The point at which the isoquant touches (but does not cross) the isocost indicates the cheapest combination of factors required to produce a given volume of product. The figure shows a method for determining the point at which the cost of producing a given volume of production of a product is minimized. This point is located on the lowest isocost, where the isoquant touches it.
Firm equilibrium conditions.
It should be emphasized that the division of costs into fixed and variable can only be said in relation to the short-term period of the firm's operation. In other words, based on the analysis of the types of costs and their dynamics, we can distinguish between the short-term and long-term periods of the firm's operation. In the short run, fixed costs remain unchanged, the firm can change the volume of output only by changing the value of variable costs. In the long run, all costs become variable, that is, this is a sufficiently long time interval for the firm to change its production capacity. Thus, in the presence of unemployment and the availability of workers of appropriate qualifications in the labor market, it is easy to increase the volume of production at the expense of the mass of living labor. A similar situation may occur when additional resources of raw materials or energy are used. Naturally, in this case it is necessary to take into account the specifics of production. Thus, an increase in the volume of production can be easily obtained by attracting additional workers. But a completely different situation develops when it is necessary to expand production capacities, areas industrial premises etc. Here required time is measured in months, and sometimes, say, in heavy engineering or metallurgy, in years. In the short term, it is not possible to bring new production capacities into operation, but it is possible to increase the degree of their utilization. Within the long term, it is possible to expand the production capacity. Of course, the scope of these periods for different industries are different. The division into two periods is of great importance in determining the strategy and tactics of the firm in maximizing profits.
In the same industry, there are not identical, but completely different firms with different scales, organization and technical base of production, and hence with different levels of costs. Comparing the average cost of a firm with the price level makes it possible to assess the position of this firm in the market.
Three possible positions of the firm in the market are shown below. If the price line R only touches the average cost curve AC at the minimum point M , then the firm is only able to cover its minimum costs. Dot M in this case is the point of zero profit.
It should be emphasized that speaking of zero profit, we do not mean that the firm does not receive any profit at all. As already shown, production costs include not only the costs of raw materials, equipment, labor, but also the interest that firms could receive on their capital if they invested it in other industries.
If the average cost is below the price, then the firm at a certain volume of production (from Q 1 before Q 2 ) receives an average profit higher than the normal profit, i.e. excess profit . Finally, if the average cost of a firm at any level of production is higher than the market price, then the firm suffers losses and will go bankrupt unless it is reorganized or withdraws from the market.
The dynamics of average costs characterizes the position of the firm in the market, but in itself does not determine the supply line and the point of optimal production volume. Indeed, if the average cost is below the price, then on this basis we can only assert that in the interval from Q 1 before Q 2 there is a zone of profitable production, and with the volume of production Q 3 , which corresponds to the minimum average cost, the firm receives the maximum profit per unit of product. However, does this mean that the point Q 3 is the point of optimal output where the firm reaches its equilibrium. The manufacturer, as you know, is not interested in profit per unit of output, but in the maximum of the total mass of the profit received. The average cost line does not show where this maximum is reached. In this regard, it is necessary to consider the so-called marginal costs, i.e. incremental cost associated with producing an additional unit of output in the cheapest possible way. Marginal cost is obtained as the difference between production costs n units and production costs n -1 units:
MS=TC
n
-TS
n
-1
,
gross total costs. 
The evolution of marginal cost is shown below.
The marginal cost curve is independent of fixed costs because fixed costs exist whether or not an additional unit of output is produced. First, marginal cost is reduced, remaining below average cost. This is explained by the fact that if the costs per unit of production decrease, therefore, each subsequent product costs less than the average costs of previous products, i.e. average cost is higher than marginal cost. A subsequent increase in average cost means that marginal cost becomes higher than the previous average cost. Thus, the marginal cost line intersects the average cost line at its minimum point M .
The production of an additional unit of output, generating additional costs, on the other hand, brings additional income, proceeds from its sale. The value of this additional, or marginal income (revenue) is the difference between the gross proceeds from the sale n And n -1 units of production: MR = TR n - TR n -1 . In conditions of free competition, as is known, the manufacturer cannot influence the level of the market price, and, therefore, sells any quantity of his products at the same price. This means that under conditions of free competition, the additional income from the sale of an additional unit of output will be the same for any volume, i.e. marginal revenue will be equal to price: MR = P .
Having introduced the concepts of marginal cost and marginal revenue, we can now define more precisely the firm's equilibrium point, or the point where it stops production, having achieved the maximum mass of profit possible at a given price. It is obvious that the firm will expand the volume of production, while each additional unit produced will bring additional profit. In other words, as long as marginal cost is less than marginal revenue, the firm can expand production. If marginal cost exceeds marginal revenue, the firm will incur losses.
It is shown below that as production increases, the marginal cost curve ( MS) goes up and crosses the horizontal limit line 
income equal to the market price R 1, at the point M corresponding to the volume of production Q
1
. Any deviation from this point results in losses for the firm, either in the form of direct losses with more output, or as a result of a reduction in the mass of profits with a decrease in output.
Thus, the equilibrium condition of the firm, both in the short run and in the long run, can be formulated as follows: MS= MR. Any profit-seeking firm seeks to establish a level of production that satisfies this equilibrium condition. In a perfectly competitive market, marginal revenue is always equal to price, so the firm's equilibrium condition becomes MS=R .
The ratio of marginal cost and marginal revenue is a kind of signal system that informs the entrepreneur about whether the optimum production has been reached or whether further profit growth can be expected. However, it is impossible to accurately determine the amount of profit received by the firm on the basis of the dynamics of marginal costs, since, as already noted, they do not take into account fixed costs.
The total profit earned by a firm can be defined as the difference between gross revenue ( TR) and gross costs ( TS). In turn, gross revenue is calculated as the product of the quantity of products and the price ( TR = Q * AC). Thus, only by combining the earlier analysis of marginal cost and marginal revenue with an analysis of the dynamics of average costs, we can accurately determine the amount of profit received.
Let's consider three possible market situations.
When the marginal revenue line just touches the average cost curve, gross revenue is exactly equal to gross cost. The profit of the firm will be normal, since the price of its products is equal to the average cost.
If at some interval the line of price and marginal revenue is located above the average cost curve, then at the equilibrium point M the firm will receive a quasi-rent, i.e. profits above the normal level. With optimum production Q 2 average cost will be From 2, therefore, the gross cost will be the area of the rectangle OC 2 LQ 2 . Gross revenue (rectangle OP 2 MQ 2 ) will be larger, and the area of the shaded rectangle C 2 P 2 ML will show us the total mass of the resulting excess profits.
The third figure shows a different situation: the average cost at any level of production exceeds the market price. In this case, even with the optimal production volume ( MS=R) the firm incurs losses, although they are less than with other outputs (the area of the shaded rectangle P 3 C 3 LM is minimal precisely at the volume of production Q 3 ).
Let's take a closer look at this last situation. No one is immune from losses in a market economy. Therefore, if for one reason or another (for example, unfavorable market conditions). If the firm is not making a profit, it must minimize its losses. If we consider the behavior of the firm in the short term, when it still remains at this market, what is preferable for her - to continue to work and produce products or to temporarily stop production? In which case will the losses be less?
Note that when a firm produces nothing, it incurs only fixed costs. If it produces a product, then fixed costs variables are added, but at the same time the firm receives some income from sales. Therefore, in order to understand when a firm is minimizing losses, it is necessary to compare the price level not only with average costs ( AC), but also with average variable costs ( AVC). Consider the situation shown below:
Market price R 1 below the minimum average cost, but above the minimum average variable cost. With optimum production Q
1
the value of the average production costs will be the segment Q
1
M, the value of average variable costs is the segment Q
1
L. Therefore, the segment ML are the average fixed costs. If the firm continues to operate, then its gross revenue (rectangle OP
1
EQ
1
) will be less than the total cost (rectangle OC
T
MQ
1
), but variable costs will be covered (rectangle OC v LQ
1
) and part of the fixed costs. The amount of loss will be measured by the area of the rectangle P
1
C
1
ME. If the firm stops production, then the losses will be the entire value of fixed costs (rectangle C v C
T
ML). Thus, as long as the price is above the minimum average cost, it is more profitable for the firm in the short run to continue producing products, since in this case losses are minimized. If the price is equal to the minimum average variable cost, then it makes no difference to her whether to continue production or stop it. If the price falls below the minimum average variable cost, then production must be stopped.
It is known that when the price changes, the firm will change the volume of production, moving along the curve MS. Summing up the individual supply curves of all firms in a single industry, we obtain the aggregate industry supply curve. As the price rises gradually, the various firms in the industry expand their production and their offerings. The change in the market price for any product will occur until the aggregate demand for the industry's products is equal to the aggregate industry supply. This equality is achieved at a certain level of price, which then tends to maintain this level for a short period.
The solution of the problem
Let's determine the equilibrium price of the goods on the first day, for this we equate the demand function to the supply function Q D =Q S ;
P=140 - equilibrium price
Find the volume of supply and demand on the first day
Q D \u003d 200-140 \u003d 60 units.
Q S \u003d 0.5 * 140-10 \u003d 60 units.
Finding the volume of demand on the second day
Q S \u003d 60 + 30 \u003d 90 units.
So the equilibrium price after an increase in demand is
P= (Q S +10)/0.5
The production function reflects the relationship between resource inputs and output. It is characterized by an isoquant. isoquant shows a different combination of factors of production for the release of the same amount of output. The isoquant curve has a negative slope and resembles on kind of indifference curve. But utility, as a characteristic of an indifference curve, cannot actually be measured, while isoquanta is measurable (in the number of units, weight measure, etc.). Each of the combinations of factors of production (there are 5 in total) is a separate technological method (Table 11.4). The total volume of production increases as labor intensity increases at a fixed cost of capital. Output also rises when the cost of capital increases at fixed labor costs.
Tab. 11.4
The results of output with various combinations of factors of production
The set of combinations of factors can increase or decrease in total. The isoquant map is a set of isoquants, each of which shows the maximum output achieved using certain combinations of factors (Figure 11.5). The isoquant curve located, according to the graph, to the right and above, shows a higher level of output (Q 3), and located to the left and below, a lower level of output (Q 2).
The law of diminishing returns applies to labor and capital. "The slope of the isoquant is defined as the ratio of the marginal product of capital to the marginal product of labor (based on Fig. 11.5). This ratio expresses MRTS - marginal rate of technological substitution:
MRTS LK = - (MP K / MP L).
As capital is replaced by labor, labor productivity begins to decline, and vice versa, when labor is replaced by capital, capital productivity or capital productivity decreases.
If the firm's budget and unit prices of resources (labor and capital) are known, then a line of equal costs can be drawn. This line is expressed as isocost, each point of which determines the ratio of units of two types of factors of production that require the firm the same amount of costs for their use. In its appearance, the isocost resembles a budget line; the angles of the line can also change, its shifts are parallel to the right or left, but from the standpoint of the manufacturer's budgetary capabilities (Fig. 11.6).
Parallel isocost shifts Rice. 11.6
Producer equilibrium position
Rice. 11.7
Producer equilibrium occurs when he chooses resources for production, and graphically - at the point of contact of the isoquant and isocost (Fig. 11.7, at point E). This means a combination of labor and capital in which the firm produces the maximum number of units of output with the available purchased limited resources.
The long-term strategy of the firm involves the choice of the required scale of production and the size of the firm. If, with a change in factors of production by L times (L>0), the volume of output increases by more than L times, then such a process expresses positive, economies of scale. Graphically, the distances between the equilibrium points shifting to the right
isoquants and isocosts decrease. If, with a change in factors of production by L times (L>0), the volume of output increases by L times, then such a process expresses a constant effect on the scale of production. Graphically, the distances between the isoquant and isocost equilibrium points shifting to the right are the same. If, with a change in factors of production by L times (L>0), the volume of output increases less than s L times, then the taxi process expresses negative effect of the scale of production. Graphically, the distances between the isoquant and isocost equilibrium points shifting to the right increase.
A positive effect may be the result of increasing the productivity of production factors through the introduction of advanced technologies, finding a market segment for goods and services with increased demand and developing new, more competitive product models. Constant economies of scale usually preclude noticeable innovation in production. The negative effect of scale is the result of the inefficient work of the company, its weak adaptation to the dynamically developing market conditions.
Production costs and the rule of least
costs
Based ultimate goal of its activities, any firm must know how much profit it will receive, for this it must study the demand, determine the selling price of its products, compare its planned income with the costs to be incurred. costs or expenses express all that is necessary for the manufacturer to produce a given, planned product in order to generate income and profit. In microeconomics, the company's costs for resources and factors of production are of particular importance. In this regard, there is a classification of production costs.
Understanding of costs by economists is based on taking into account the limited resources and the possibility of their alternative use. The economic costs acquire a double meaning. Firstly, economic costs aimed at minimizing them in order to maximize profits. Second, the economic or opportunity cost of producing a certain economic good is mentally equated with the best possible cost of other possible costs. For example, the financial cost of producing or purchasing an additional 100 computers is equivalent to the opportunity cost of 20 home theater systems that have to be abandoned.
Economic costs can be internal and external. External or explicit costs- these are cash costs in favor of suppliers from the outside, aimed at paying for the used factors of production. All explicit costs to the firm are ultimately reduced to reimbursement of basic revolving funds, remuneration of organizers of production and marketing. External costs are considered and how accounting costs. Internal or Ridiculous Costs- all kinds of opportunity costs aimed at using the firm's own resources. They are equal to cash payments that could be spent to use these resources. Accounting for explicit and implicit costs allows the firm to more accurately assess benefits, revenues and profits.
In the short run, all costs can be either fixed or variable. Fixed costs (FC) are costs that are independent of changes in output. They must be paid even with zero production. Fixed costs may include: payment of loan obligations, rent payments, insurance premiums, salaries of the administration, maintenance of security, payment of the most necessary minimum services of energy, communications, communications, etc. Variable costs (VC) - These are costs, the magnitude of which depends on changes in the volume of production. These include the costs of renewable wages of employees, the maintenance and reproduction of fixed and working capital of the company. Total costs (Total costs -TS) - is the sum of fixed and variable costs for any given volume of production:
TC=FC+VC.
An increase in output necessitates an increase in the cost of producing an additional unit of output, defined as marginal cost (MC):
MS=TC/Q,
The tabular and graphic form of the types of costs clearly illustrates the types of costs and their interaction (table and Fig. 11.8). According to the graph, FC has a horizontal view, since their value is unchanged, and VC and TC are parallel to each other by the value of FC and have an upward view with a positive slope.
Tab. iris. 11.8
| TR | FC | VC | TC | MC | AC |
| 353,333 | |||||
| 288,75 | |||||
25(38). Isocost. Equation and slope of the isocost. Isocost shift and isocost slope change.
The same amount of output can be obtained using different technologies. The firm solves the problem of choosing a technology at which costs are minimal. TC = P L *L+P K *K (total cost = labor cost + capital cost). All combinations of resources that have the same cost are combined into one line. Isocost is a curve of equal costs. 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 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 TS, the TO isocost rotates (price decreases - to the right, increase - to the left)
26(39). Optimal combination of production factors. Company growth line.
Producer equilibrium is achieved when the isoquant and the zocost have one in common, i.e. touch each other. Pl / Pk \u003d MRL / MRK; MPl / Rl \u003d Mrk / Rk. - all resources used have the same value of 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, while the ratio of the marginal product of each factor to the unit price of each factor will not be equal for all factors involved. The firm minimizes its costs when the cost of producing an additional unit is the same, regardless of which additional factor is involved in the production process. isoquants and isocosts and draw a curve through them, then we will get a line of the trajectory of the company's development. The growth line characterizes technically possible ways expansion of production, that is, the transition from a lower to a higher isoquant. Among the possible growth lines, of interest are the isoclines 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 - a set of costs in cash in the production and sale of products. They reflect all positive and negative sides firms. The concept of a firm's costs is based on two assumptions: 1) resources are limited, so there are alternatives to using the same resource (the best one must be selected); 2) resources are evaluated 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 - the actual costs of acquiring resources at market prices. 2 approach - determines economic costs - opportunity costs - the value of other benefits that could be obtained with the best option resource use. Economic cost = explicit cost + implicit cost + 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 firm, these are the unpaid costs of the firm. These include: implicit rent, implicit rent, etc. Economic costs include normal profit - the profit that an entrepreneur receives for working in this industry. This profit is included in the costs. The division of costs into accounting and economy involves the division of profits into accounting and economy. Profit=TR-TC(total revenue-costs). EKp \u003d TR-EI (saving costs). Bp \u003d TR-BI (accounting for their maintenance). If the accountant's profit is greater than normal, then resources are used inefficiently. In the best use case, booked profit = profit economy
In the long run, the firm can change the number of all applied factors, so the manufacturer needs to determine the optimal combination of resources used, providing maximum output. To solve this problem, consider two new economic categories: isoquant (curve of equal output or equal product) and isocost (line of equal costs).
isoquant - this is a curve, the points of which reflect various combinations of input factors that provide the same output.
Rice. 2.24. Isoquant map
Assume that the firm uses only two factors - labor and capital. Then the isoquant ( Q 1 ) will look like this (Fig. 2.24):
If several isoquants are placed on one graph, then we get isoquant map . Equal output curves (by analogy with indifference curves, see subsection 2.2) have the following properties:
1) isoquants have a negative slope: when moving from a point A exactly B a decrease in the amount of capital must be compensated by an increase in labor costs to maintain the same volume of production;
2) isoquants do not intersect;
Q 2 > Q 1 .
The substitution of one factor of production for another while maintaining a constant output reflects the slope of the tangent to the isoquant. The absolute value of this coefficient is called the marginal rate of technological substitution ( MRTS) It is determined by the formula:
Marginal rate of technological substitution of labor for capital represents the amount by which capital must be reduced by the use of one additional unit of labor at a fixed output (always counted as a positive value and is similar to the marginal rate of substitution used in consumer choice theory). The more capital is replaced by labor, the less productive labor becomes, and the more capital is used.
more efficient. Conversely, the more labor is replaced by capital, the less productive capital becomes and labor more productive.
The entrepreneur buys the factors used in the market and, when choosing a variant of their combination, he must take into account their market prices, as well as the size of his budget.
Isocost - this is a straight line, each point of which shows different combinations of two variable factors involved in production at the same cost for their acquisition (Fig. 2.25, line C 1 ).
2.25. Isocost map
The isocost equation is:
(2.21)
where C- the budget of the producer or the cost of acquiring factors of production; r– price of capital; w- labor cost
where is the angle of inclination of the isocost to the abscissa axis.
The properties of isocosts are similar to those of the budget line (see subsection 2.2): negative slope, points of intersection with the axes, angles of the line, changes in the producer's budget and prices of production factors.
If there are many combinations of the use of factors of production to achieve a certain volume of output, then the question inevitably arises: which combination of their set will be the most optimal, i.e. to achieve a given volume of output at minimum cost?
Rice. 2.26. Optimal combination of production factors used
To determine the optimal combination of production factors used, it is necessary to combine the isoquant map with the isocost (Fig. 2.26). This shows that the isocost at the point E touches the isoquant. This means that the cost of the entrepreneur to acquire production factors will be minimal. Other combinations of factors (for example, points A And B) are not optimal, since at the same costs for their acquisition (points A, B, E belong to the same isocost) provide a smaller output (points A And B lie on an isoquant Q 1 , and the point E- on the isoquant Q 2 ). The combination of factors corresponding to the point F(which belongs to the same isoquant as the point E, and, therefore, provides the same output Q 2 ) is not available to the manufacturer, since it does not lie on the isocost.
Hence the point E – This is the equilibrium point of the producer, which corresponds to the combination of factors of production that provides the maximum output at the minimum cost of acquiring production resources.
It should also be noted that at the point E the condition called cost minimization rules using factors of production. This condition has the following form:
Thus, in order to minimize costs (for a given volume of production), it is advisable for a firm to replace one factor with another until the ratio of the marginal product of each of the factors to the price of this factor is equal for all factors involved. In other words, equation (2.23) shows that, at minimum total cost, each additional monetary unit of input costs adds the same amount of output.
The production function can be graphically represented as a special curve - an isoquant.
Product isoquant is a curve showing all combinations of factors within the same output. For this reason, it is often referred to as an equal output line.
Isoquants in production perform the same function as indifference curves in consumption, so they are similar: they also have a negative slope on the graph, have a certain proportion of factor substitution, do not intersect with each other, and the farther they are from the origin, the greater the result of production reflect:
A,b,c,d - various combinations; y, y 1, y 2, y 3 are isoquants of the product.
Isoquants can have different kind:
- linear - when it is assumed that one factor is completely replaced by another;
- in the form of an angle - when a strict complementarity of resources is assumed, outside of which production is impossible;
- a broken curve expressing the limited possibility of replacing resources;
- smooth curve - the most general case of the interaction of factors of production
The shift of the isoquant is possible under the influence of the growth of attracted resources, technical progress and is often accompanied by a change in its slope. This slope always determines the marginal rate of technical substitution of one factor for another (MRTS).
where MRTS is the marginal rate of technical substitution of one factor for another.
Properties of an isoquant:
1. An isoquant, like an indifference curve, is a continuous function, not a set of discrete points.
2. For any given volume of output, its own isoquant can be drawn, reflecting various combinations of economic resources that provide the producer with the same output (isoquants describing a given production function never intersect).
3. Isoquants do not have areas of increase (If there were an area of increase, then when moving along it, the amount of both the first and second resource would increase).
Isocost.
Isocost- a line that limits the combination of resources to the cash costs of production, therefore it is often called the line of equal costs. FROM its help determines the budgetary possibilities of the manufacturer.
The manufacturer's budget constraint can be calculated:
C = r + K + w + L,
where C is the manufacturer's budget constraint; r is the price of capital services (hourly rent); K - capital; w is the price of labor services (hourly wages); L - labor.
Even if an entrepreneur does not use borrowed funds, but own funds, this is still a cost of resources, and they should be considered. The factor price ratio r/w shows the slope of the isocost:
Isocost and its shift
K - capital; L - labor.
An increase in the entrepreneur's budgetary possibilities shifts the isocost to the right, and a decrease to the left. The same effect is achieved in conditions of unchanged costs with a decrease or increase in market prices for resources.
The combination of resources that provides the minimum level of the firm's total costs is called optimal and lies at the point of contact of the isocost and isoquant lines:
34. The concept of the optimum of the manufacturer.
The production function reflects different ways of combining factors to produce a certain amount of output. The information that a production function carries can be represented graphically using isoquants.
isoquant is a curve on which all combinations of production factors are located, the use of which provides the same output (Fig. 11.1).
Rice. 11.1. Isoquant plot
In the long run, when a firm can change any factor of production, the production function is characterized by such an indicator as the marginal rate of technological substitution of production factors (MRTS)
,
where DK and DL are changes in capital and labor for a single isoquant, i.e. for constant Q.
The firm is faced with the problem of how to achieve a certain level of production at minimum cost. Assume that the price of labor is equal to the rate wages(w) and the price of capital equals the rent for equipment (r). Production costs can be represented as isocosts. Isocost includes all possible combinations of labor and capital with equal gross costs
Rice. 11.2. isocost chart
We rewrite the equation for gross costs as an equation for a straight line, we get
.
It follows from this that the isocost has a slope equal to
It shows that if a firm forgoes a unit of labor and saves w (c.u.) to acquire a unit of capital at a price of r (c.u.) per unit, then gross production costs remain unchanged.
The equilibrium of the firm occurs when it maximizes profit at a certain volume of production with an optimal combination of production factors that minimize costs (Fig. 11.3).
On the graph, the equilibrium of the firm reflects the point of contact T of the isoquant with the isocost at Q 2 . All other combinations of factors of production (A, B) can produce less output.
Rice. 11.3. consumer equilibrium
Given that the isoquant and the isocost have the same slope at T, and that the slope of the isoquant is measured by the MRTS, the equilibrium condition can be written as
.
The right side of the formula reflects the utility for the producer of each unit of the factor of production. This utility is measured marginal product labor (MP L) and capital (MP K)
The last equality is the producer's equilibrium. This expression shows that the producer is in equilibrium if 1 ruble invested in a unit of labor is equal to 1 ruble invested in capital.
35. The concept of returns to scale.
The economies of scale are related to the change in the cost of a unit of output depending on the scale of its production by the firm. considered in the long term. Reducing the cost per unit of output with the consolidation of production is called economies of scale. The type of the long-run cost curve is associated with the effect of scale in production.
Companies of all sizes can take advantage of economies of scale by expanding their operations. The most common methods are purchasing (obtaining volume discounts), management (using the specialization of managers), finance (obtaining less expensive loans), marketing (spreading advertising costs for a larger range of products). The use of any of these factors reduces the long-term average cost (eng. Long Run Average Costs LRAC) shifting the short-run average cost curve down and to the right on the graph. Short-run average total cost SRATC).
Sections of the production curve with positive returns to scale and one (last) section with negative returns to scale.
Formal definition
Let the parameter K- unit of capital, parameter L- unit of labor force, parameter a- increase / decrease in a-times.
We can say that for the production function at:
positive returns to scale
constant returns to scale
diminishing returns to scale
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