Option 11.
PRODUCTION FUNCTION OF THE FIRM, ISOQUANT AND ISOCOST.
2. Properties of isoquants. Substitution of production factors.
3.Isocost and equilibrium conditions of the firm.
In the cobweb model, the demand function is: Q D = 200 – P, and the supply function is: Q S = 0.5 P – 10.
The product is sold within five days. Determine the equilibrium price of the product. 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 demand increased by 30 units. goods?. Record your results in the 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 production factors.
In order to organize production at an enterprise, it is necessary to ensure the interaction of production factors.
Thus, factors of production for the production of a TV include: production premises, machines, machines, equipment, labor of workers, a plot of land on which production 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 constant and variable. Those of them that remain unchanged over a certain period of time form constant factors of production, and those whose quantity changes form variable factors of production.
All 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 using them most efficiently. Thus, the volume of goods produced is determined by the availability of the necessary resources. Moreover, various options for their use allow the commodity producer to obtain a larger or smaller amount of goods or services. Therefore, the enterprise must be interested in ensuring the fullest use of labor, material and financial resources and their optimal combination.
The relationship between the volume of output and the volume of attracted factors of production is reflected by 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 specific type of technology:
Where Q is the volume of production, L is the mass of attracted work force(labor); K – volume 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 denotes production technology.
The influence of the economic order. It is clear that any enterprise operates in specific economic conditions and is directly influenced by national economic system. Therefore, it makes sense if, when analyzing production function economic conditions of management will be 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, you can find a combination of factors that will achieve the maximum volume of production of goods and services.
To trace how production output changes with an increase or decrease in the use of certain factors of production by one unit, and, thus, to identify the production capabilities of the enterprise.
Determine the economic feasibility of producing a particular product.
Note that the production function is usually calculated for a specific technology.
For various types of production (automobiles, agricultural products, confectionery etc.) the production function will be different, but they all have the following common properties:
* there is a limit to the increase in production volume that can be achieved by increasing the costs 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, factors of production are to a certain extent interchangeable. The lack of one of them can be compensated for by an additional amount of the other, i.e. resources can be combined with each other during the production process in different proportions;
* a differentiated assessment of the influence of each factor on the dynamics of product output is given in relation to certain periods of time.
The production function can be expressed graphically in the form of an isoquant - a curve reflecting 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 through the use of different combinations 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) each industry has its own production function;
2) within the framework of 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) analysis of the production function involves searching for an option for organizing production that ensures maximum economic efficiency.
Conclusion: the technological method of production is reflected through the combination of production factors.
Production grid.
The production function draws our attention to three important circumstances:
1) the greater the volume of production factors involved, the greater the volume of output;
2) the same volume of output can be achieved with different combinations of production factors;
3) by reducing the scale of use 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 in Table 1 the volume of labor involved in production is indicated, and vertically the volume of capital is indicated.
By moving diagonally down and from left to right and increasing the volume of factors of production, we increase the volume of output from 20 to 115 units.
Table 1. Change in production output with a change in the volume of production factors involved (production grid)
Moving diagonally from left to right and up, the output volume (Q=75) remains constant
Isoquant. We will reflect this relationship between a fixed output volume and the ratio of two factors - labor and capital - on a special graph. As a result, we get a line called an isoquant (Fig. 2)
| Q=75 | ||||||
| 0 | 1 | 2 | 3 | 4 | 5 | L |
Rice. 2 Construction of an isoquant for an output volume of 75 units.
In Fig. the isoquant corresponding to the production of 1 ton of potatoes is depicted. It shows that there are many options for using resources to produce a given volume of potatoes. In one case, more manual labor (L) can be used - 70 man-hours and only 2 machine-hours (K) (point A), in another - 40 man-hours L and 3 K (point B), in the third - 20 person-hour L to 6 hours K (point C), etc.
An isoquant map is used to determine the maximum output that can be achieved for each combination of factors.
Isoquant analysis can be used to determine the marginal rate of technological substitution, i.e. the possibility of replacing one resource with another in the process of their use. This capability 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 keeping output constant.
Let us assume that the production technology of one car involves the use of 1000 hours of labor and 500 hours of work of machines and equipment. The ratio of labor to capital will be 2 hours of labor to 1 hour of machine work (point A).
To mechanize and automate production, the enterprise switches to using more capital-intensive production process, i.e. the production of one car will require less expenditure of living labor and more expenditure of material labor (machinery, equipment). In this example, the marginal rate of technological substitution of capital for labor is determined by the amount of capital that can replace each unit of labor without causing an increase or decrease in the volume of automobile production. The limiting rate of technological substitution at any point of the isoquant is equal to the slope of the tangent at this point multiplied by -1:
MPTS = - DK / DL (const Q),
where DK is a reduction or increase in the capital resource;
DL - reduction or increase in labor resource;
Q - production volume.
The curvature of the isoquant helps the manager determine exactly how much labor reduction will be required during implementation. new technology production. At point B, producing a car will require only 500 hours of labor and 1000 hours of machine work. The ratio of capital to labor here is only 0.5 hours of labor for every hour of work of machines and equipment.
Isoquant is a line reflecting options for combinations of production factors 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 is objective in nature, as it reflects real economic processes.
The isoquant law: the more one factor of production is used, the less another factor is used.
Special configurations of isoquants. Under certain circumstances, an isoquant can take the form of a straight line. A straight-line isoquant assumes that the replacement of one factor by another is carried out in a proportion that is constant throughout the isoquant.
If it is possible to organize production, limiting itself to the use of only one type of economic resource (a situation of absolute substitutability), then in this case the isoquant will touch the axis of the opposite factor of production.
The continuous nature of the line means that for each option there are always alternative options for combining factors of production.
A concave isoquant reflects the fact that we have to deal with a flexible production function, when a reduction in the volume of use of one factor of production is compensated only by more fast pace increase in the volume of use of another factor (i.e. the ratio between the volume of labor and capital is continuously changing).
In conditions where the output of a fixed volume of products is possible only with a single combination of production factors, we have to admit that we are dealing with a rigid production function. With this combination of circumstances, the isoquant takes the form of a right angle.
3 Isocost and equilibrium conditions of the firm
Isocost is a line showing the combinations of factors of production that can be purchased for the same total amount of money. Isocost is also called the equal cost line. Isocosts are parallel lines because it is assumed that a firm can purchase any desired quantity of factors of production at constant prices. The slope of the isocost expresses the relative prices of factors of production. Each point on the isocost line has the same total cost. These lines are straight because factor prices have a negative slope and are parallel.
By combining isoquants and isocosts, the optimal position of the company can be determined. The point at which the isoquant touches (but does not intersect) the isocost indicates the cheapest combination of factors required to produce a certain volume of product. The figure shows a method for determining the point at which production costs for a given volume of production of a product are minimized. This point is located at the lowest isocost where the isoquant touches it.
Conditions for the firm's equilibrium.
It should be emphasized that the division of costs into fixed and variable can only be discussed in relation to the short-term period of operation of the company. 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 company’s operation. In the short run, fixed costs remain unchanged; the firm can change the volume of output only by changing the quantity 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. So, in the presence of unemployment and the presence of appropriately qualified workers on 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, one has to take into account the specifics of production. Thus, an increase in production volume can be easily obtained by attracting additional workers. But a completely different situation arises when it is necessary to expand production capacities, areas production premises and so on. Here required time is measured in months, and sometimes, say, in heavy engineering or metallurgy – in years. In the short term, it is impossible to commission new production facilities, but it is possible to increase their utilization. Within the long term, production capacity can be expanded. Of course, the scope of these periods for various industries are different. The division into two periods is of great importance in determining the strategy and tactics of the company 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 therefore with different levels of costs. Comparing the average costs of a company with the price level makes it possible to assess the position of this company in the market.
Three possible options for a company's position 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 especially emphasized that when we talk about zero profit, we do not mean that the company does not make any profit at all. As has already been shown, production costs include not only the costs of raw materials, equipment, and labor, but also the interest that firms could receive on their capital if they invested it in other industries.
If average costs are lower than price, then the firm, at certain production volumes (from Q 1 before Q 2 ) receives on average a profit higher than normal profit, i.e. excess profit . Finally, if the firm's average costs for any volume of production are higher than the market price, then this firm is suffering losses and will go bankrupt unless it is reorganized or leaves the market.
The dynamics of average costs characterize the position of the company in the market, but in itself does not determine the supply line and the point of optimal production volume. Indeed, if average costs are lower than prices, then on this basis we can only assert that in the range from Q 1 before Q 2 there is a zone of profitable production, and with production volume Q 3 , which corresponds to the minimum average costs, the company receives 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 production, but in the maximum total amount of 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. the additional costs associated with producing an additional unit of output in the cheapest way possible. Marginal costs are obtained as the difference between production costs n units and production costs n -1 units:
MS=TS
n
-TS
n
-1
,
gross total costs. 
The dynamics of marginal costs are shown below.
The marginal cost curve does not depend on fixed costs because fixed costs exist regardless of whether an additional unit of output is produced. First, marginal cost decreases, remaining below average cost. This is explained by the fact that if costs per unit of production decrease, therefore, each subsequent product costs less than the average costs of previous products, i.e. average costs are higher than marginal costs. A subsequent increase in average costs means that marginal costs become higher than previous average costs. Thus, the marginal cost line intersects the average cost line at its minimum point M .
The production of an additional unit of product, while generating additional costs, on the other hand, also brings additional income, revenue from its sale. The amount of this additional, or marginal income(revenue) is the difference between the gross proceeds from the sale n And n -1 units of production: M.R. = 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 its products at the same price. This means that in conditions of free competition, additional income from the sale of an additional unit of production will be the same for any volume, i.e. marginal revenue will be equal to price: M.R. = P .
Having introduced the concepts of marginal cost and marginal revenue, we can now more accurately determine the firm's equilibrium point, or the point where it stops production, having achieved the maximum amount of profit possible at a given price. Obviously, the company will expand its production volume until each additional unit produced brings 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 market price P 1, at point M, corresponding to the production volume Q
1
. Any deviation from this point leads to losses for the company, either in the form of direct losses with a larger volume of production, or as a result of a reduction in the amount of profit with a decrease in output.
Thus, the equilibrium condition of the firm, both in the short and long term, can be formulated as follows: MS= M.R.. Any firm seeking profit seeks to establish a volume 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 takes the form MS=P .
The ratio of marginal costs and marginal revenue is a kind of signaling system that informs the entrepreneur whether optimum production has been achieved or whether further profit growth can be expected. However, it is impossible to accurately determine the amount of profit a firm receives based on the dynamics of marginal costs, since, as already noted, they do not take into account fixed costs.
The total profit received by the firm can be determined 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 * A.C.). Thus, only by combining the previously conducted analysis of marginal costs 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 firm's profit will be normal because the price of its product is equal to 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 quasi-rent, i.e. profits above normal levels. At optimal volume production Q 2 average costs will be equal C 2, therefore, the total costs will be the area of the rectangle O.C. 2 L.Q. 2 . Gross revenue (rectangle OP 2 MQ 2 ) will be larger, and the area of the shaded rectangle C 2 P 2 M.L. will show us the total amount of excess profit received.
The third figure shows a different situation: average costs for any volume of production exceed the market price. In this case, even with optimal production volume ( MS=P) the company incurs losses, although they are less than for other production volumes (area of the shaded rectangle P 3 C 3 L.M. is minimal precisely for the volume of production Q 3 ).
Let's look at this last situation in more detail. No one is immune from losses in a market economy. Therefore, if due to one reason or another (for example, unfavorable market conditions). The company does not make a profit, then it must minimize losses. If we consider the behavior of the company in the short term, when it still remains at this market, what is preferable for her - to continue working and producing products or to temporarily stop production? In which case will the losses be less?
Note that when a firm produces nothing, it only incurs fixed costs. If it produces products, then variable costs are added to fixed costs, but the company also receives some income from sales. Therefore, in order to understand when a company minimizes losses, it is necessary to compare the price level not only with average costs ( A.C.), but also with average variable costs ( AVC). Consider the situation shown below:
Market price P 1 below minimum average cost but above minimum average variable cost. At optimal production volume Q
1
the value of average production costs will be the segment Q
1
M, the value of average variable costs – segment Q
1
L. Therefore, the segment M.L. is the average fixed cost. If the firm continues to operate, then its gross revenue (rectangle OP
1
EQ
1
) will be less than total costs (rectangle O.C.
T
MQ
1
), but variable costs will be covered (rectangle OC v LQ
1
) and part of the fixed costs. The amount of losses will be measured by the area of the rectangle P
1
C
1
M.E.. If the company stops production, then the losses will amount to the entire amount of fixed costs (rectangle C v C
T
M.L.). Thus, as long as the price is above the minimum average cost, it is more profitable for the company 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 minimum average variable cost, then production must cease.
It is known that when the price changes, the firm will change production volumes, moving along the curve MS. By summing the individual supply curves of all firms in one industry, we obtain the aggregate industry supply curve. As the price gradually increases, various firms operating in the industry expand their production and their supply. A change in the market price for any product will occur until the aggregate demand for the industry's products equals the aggregate industry supply. Such equality is achieved at a certain price level, which then tends to maintain this level over the short term.
The solution of the problem
Let's determine the equilibrium price of the product on the first day; to do this, we equate the demand function to the supply function Q D =Q S ;
P=140 - equilibrium price
Let's find the volume of supply and demand on the first day
Q D =200-140=60 units.
Q S =0.5*140-10=60 units.
Finding the volume of demand on the second day
Q S =60+30=90 units.
This means that the equilibrium price after an increase in demand becomes
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 different combinations of factors of production when producing the same amount of output. The isoquant curve has a negative slope and resembles By kind of an indifference curve. But utility, as a characteristic of an indifference curve, cannot actually be measured, whereas it is isoquant measurable (in the number of units, weight measure, etc.). Each of the combinations of production factors (5 in total) represents a separate technological method (Table 11.4). Total output increases as labor intensity increases, with fixed capital input. Output also increases when capital costs increase while labor costs are fixed.
Table 11.4
Results of product output for various combinations of production factors
The set of combinations of factors can increase or decrease in total. An isoquant map is a set of isoquants, each of which shows the maximum output achieved when using certain combinations of factors (Fig. 11.5). The isoquant curve located to the right and higher according to the graph shows a higher level of output (Q 3), and the one located to the left and lower shows 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 is expressed by MRTS - maximum rate of technological substitution:
MRTS LK = - (MR 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 constructed. This line is expressed as isocost, each point of which determines the ratio of units of two types of production factors that require the firm the same amount of costs for their use. In its appearance, the isocost resembles a budget line; changes in the angles of inclination of the line and its parallel shifts to the right or left can also occur, but from the position of the budgetary capabilities of the manufacturer (Fig. 11.6).
Parallel isocost shifts Rice. 11.6
Producer equilibrium position
Rice. 11.7
Producer Equilibrium occurs when he selects resources for production, and graphically - at the point of tangency between 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 company involves choosing the required scale of production and size of the company. If, when factors of production change by L times (L>0), the volume of output increases by more than L times, then such a process expresses positive effect of scale of production. Graphically, the distances between equilibrium points shifting to the right
isoquants and isocosts decrease. If, when factors of production change by L times (L>0), the volume of output increases by L times, then such a process expresses a constant effect of scale of production. Graphically, the distances between the isoquant and isocost equilibrium points shifting to the right are the same. If, when factors of production change by L times (L>0), the volume of output increases less than s L times, then the taxi process expresses negative effect of production scale. Graphically, the distances between the isoquant and isocost equilibrium points shifting to the right increase.
A positive effect can be the result of increasing the productivity of production factors through the introduction of advanced technologies, finding a market segment for goods and services in high demand, and developing new, more competitive product models. Constant economies of scale usually preclude significant innovation in production. Negative economies of scale are the result of a company's inefficient operation and its poor adaptation to dynamically developing market conditions.
Production costs and the rule of least
Costs
Based ultimate goal of its activities, any company must know what profit it will receive; for this it must study demand, determine the selling price of its products, and compare its planned income with the costs to be incurred. Costs or expenses express everything that a manufacturer needs to produce a given, planned product in order to generate income and profit. In microeconomics, a firm's costs of resources and factors of production are of particular importance. In this regard, there is a classification of production costs.
Economists' understanding of costs is based on taking into account the limited resources and the possibility of their alternative use. Economic costs take on a double meaning. Firstly, economic costs aimed at minimizing them in order to obtain maximum profits. Second, the economic or opportunity costs of producing a particular economic good are mentally equated to the cost of the best option for other possible costs. For example, the financial cost of producing or purchasing an additional 100 computers is the same as the opportunity cost of 20 home theater systems not being produced or purchased.
Economic costs can be internal and external. External or explicit costs- these are cash expenses in favor of outside suppliers, aimed at paying for the factors of production used. All the firm's explicit costs ultimately add up To reimbursement of basic revolving funds, remuneration of production and sales organizers. External costs are considered and how accounting costs. Internal or ridiculous costs- all kinds of opportunity costs aimed at using the company's own resources. They are equal to cash payments that could be spent to use these resources. “Taking into account explicit and implicit costs allows a firm to more accurately estimate benefits, revenues and profits.
In the short run, all costs can be either fixed or variable. Fixed costs (FC)- these are costs, the value of which does not depend on changes in production volume. They must be paid even if there is zero production. Fixed costs may include: payment of loan obligations, rent payments, insurance premiums, administration salaries, maintenance of security, payment for the most necessary minimum services of energy, communications, communications, etc. Variable costs (VC) - These are costs, the value of which depends on changes in production volume. These include expenses for renewable wages of employees, maintenance and reproduction of the company's fixed and working capital. Total costs (TC) - This is the sum of fixed and variable costs for each 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=TS/Q,
The tabular and graphical form of 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 appearance, since their value is unchanged, and VC and TC are parallel to each other by the value of FC and have an upward appearance with a positive slope.
Table iris. 11.8
| TR | F.C. | V.C. | TC | M.C. | A.C. |
| 353,333 | |||||
| 288,75 | |||||
25(38). Isocosta. Equation and slope of isocost. Shifting the isocost and changing the slope of the isocost.
The same output volume can be obtained using different technologies. The company solves the problem of choosing a technology at which costs are minimal. TC = P L *L+P K *K (total costs=labor costs+capital costs). All combinations of resources that have the same cost are combined into one line. Isocost is an equal cost curve. The isocost equation is: K=TC\P K -(P L *L\P K) so it has an ISOCOST SLOPE.
Properties: 1) the isocost has a negative slope, because resources are interchangeable and complementary, an increase in one leads to a decrease in the other; 2) the points of intersection of the isocost with the coordinate axes show the max. Quantity of one of the resources; 3) if costs increase at constant prices for resources, then the isocost shifts or shifts (costs increase - up, costs decrease - down); 4) if the price of one of the resources changes. While maintaining a constant value of TC, the TO isocost rotates (price decreases - to the right, increases - to the left)
26(39). Optimal combination of production factors. The company's growth line.
Producer equilibrium is achieved when the isoquant and zocost have one thing in common, i.e. touch each other.Rl/Rk = MRl/MRk; МРл/Рл = МРк/Рк. - all used resources have the same value of the marginal product per unit of cash costs. - to optimize its costs, for a given volume of production, it is advisable for a company to replace one factor with another until the ratio of the marginal product of each factor to the price of a unit of each factor will not be equal for all factors involved. A firm minimizes its costs when the costs of producing an additional unit are the same, regardless of which additional factor is involved in the production process. For each volume of production there are optimal costs and if we take the tangent points isoquants and isocosts and draw a curve through them, then we get the company’s development trajectory line. The growth line is characterized technically possible ways expansion of production, that is, a transition from a lower to a higher isoquant. Among possible growth lines, isoclines are of interest, along which the marginal rate of technical substitution of resources for any volume of output is constant.
27(40). Production costs and their structure. Accounting and economic costs. Accounting, economic and normal profit.
Costs – the totality of costs in in cash in production and sales of products. They reflect all the positive and negative sides companies. The concept of a company's costs is based on two premises: 1) resources are limited, so there are alternatives to using the same resource (the best one must be selected from among them); 2) resources are assessed taking into account their current value and taking into account lost profits. There are 2 approaches to determining the structure and classification of costs. 1 approach – accounting. Accounting costs are the actual costs of purchasing resources at market prices. Approach 2 - determines economic costs - opportunity costs - the value of other goods that could be obtained if the best option resource use. Economic costs = explicit costs + implicit costs + normal profit. Explicit costs are direct cash payments to resource owners. These are accounting costs. Implicit costs - the cost of resources that are owned by the owners of the company; these are unpaid costs of the company. These include: implicit lease, implicit rent, etc. Economic costs include normal profit - the profit that an entrepreneur receives for working in a given industry. This profit is included in costs. Dividing costs into accounting and economic costs involves dividing profits into accounting and economic costs. Profit=TR-TC(total income - costs). EKp = TR-EI (economic costs). Bp = TR-BI (maintenance accountant). If the accountant's profit is greater than normal, then resources are being used inefficiently. In the best case scenario, accountant profit = profit economy
In the long run, the firm can change the quantity of all factors used, so the manufacturer needs to determine the optimal combination of inputs used to ensure maximum output. To solve this problem, consider two new economic categories: isoquant (equal output or equal product curve) and isocost (equal cost line).
Isoquant is a curve whose points reflect various combinations of input factors that ensure the same output.
Rice. 2.24. Isoquant map
Let us assume that the firm uses only two factors – labor and capital. Then the isoquant ( Q 1 ) will have the following form (Fig. 2.24):
If we place several isoquants on one graph, 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 the decrease in the amount of capital must be compensated by an increase in labor input to maintain the same volume of production;
2) isoquants do not intersect;
Q 2 > Q 1 .
The replacement of one factor of production by another while maintaining a constant volume of output reflects the angular coefficient of 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:
The marginal rate of technological substitution of capital by labor represents the amount by which capital must be reduced by using one additional unit of labor at a fixed level of output (always treated as a positive quantity and 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 use of capital decreases.
more effective. Conversely, the more labor is replaced by capital, the less productive capital becomes, and labor more productive.
The entrepreneur buys the factors used on the market and when choosing a combination of them, he must take into account their market prices, as well as the size of his budget.
Isocosta is a straight line, each point of which shows different combinations of two variable factors involved in production at the same costs for their acquisition (Fig. 2.25, line C 1 ).
2.25. Isocost map
The isocost equation has the form:
(2.21)
Where C– manufacturer’s budget or costs of purchasing factors of production; r– price of capital; w– price of labor,
where is the angle of inclination of the isocost to the abscissa axis.
The properties of isocosts are similar to the properties of the budget line (see subsection 2.2): negative slope, points of intersection with the axes, line slope angles, changes in the producer budget and prices of production factors.
If there are many combinations of using production factors to achieve a certain volume of output, then the question inevitably arises: which combination of their many will be the most optimal, i.e. allowing to achieve a given output volume with minimal costs?
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 concerns the isoquant. This means that the entrepreneur’s acquisition costs production factors will be minimal. Other combinations of factors (for example, points A And B) are not optimal, since with the same costs for their acquisition (points A, B, E belong to the same isocost) provide a smaller volume of output (points A And B lie on an isoquant Q 1 , and point E– on an isoquant Q 2 ). Combination of factors corresponding to a point F(which belongs to the same isoquant as the point E, and, therefore, provides the same volume of output Q 2 ) is not available to the manufacturer, since it does not lie on the isocost.
Therefore, the point E – This is the producer's equilibrium point, which corresponds to a combination of production factors that ensures maximum output at minimum costs for the acquisition of production resources.
It should also be noted that at the point E the condition called cost minimization rules when using production factors. This condition has the following form:
Thus, to minimize costs (for a given volume of production), it is advisable for a company to replace one factor with another until the ratio of the marginal product of each factor to the price of a given factor is equal to the value for all factors involved. In other words, equation (2.23) shows that at minimum total costs, each additional monetary unit of input costs adds the same amount of output.
The production function can be graphically represented in the form of a special curve - an isoquant.
Product isoquant is a curve showing all combinations of factors within the same volume of production. For this reason, it is often called the equal output line.
Isoquants in production perform the same function as indifference curves in consumption, therefore they are similar: on the graph they also have a negative slope, have a certain proportion of factor substitution, do not intersect with each other, and the further they are located from the origin, the greater the result of production they reflect:
A,b,c,d – various combinations; y, y 1, y 2, y 3 are product isoquants.
Isoquants can have different kind:
- linear – when it is assumed that one factor is completely replaceable 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 substituting resources;
- smooth curve - the most general case of interaction between production factors
An isoquant shift is possible under the influence of an increase in attracted resources, technical progress and is often accompanied by a change in its inclination. This slope always determines the marginal rate of technical substitution of one factor for another (MRTS).
where MRTS is the maximum rate of technical substitution of one factor by another.
Properties of an isoquant:
1. An isoquant, like an indifference curve, is a continuous function, and 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 manufacturer with the same volume of production (isoquants describing a given production function never intersect).
3. Isoquants do not have increasing areas (If an increasing area existed, then when moving along it, the amount of both the first and second resource would increase).
Isocosta.
Isocosta- a line that limits the combination of resources to the monetary costs of production, therefore it is often called the line of equal costs. WITH it helps determine the budgetary capabilities of the manufacturer.
The manufacturer's budget constraints can be calculated:
C = r + K + w + L,
where C is the manufacturer’s budget constraint; r – price of capital services (hourly rent); K – capital; w – price of labor services (hourly wage); L – labor.
Even if an entrepreneur uses his own funds rather than borrowed funds, these are still resource costs and 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 capabilities shifts the isocost to the right, and a decrease - to the left. The same effect is achieved under conditions of constant costs when market prices for resources decrease or increase.
The combination of resources that ensures the minimum level of total costs for the company is called optimal and lies at the point of tangency between the isocost and isoquant lines:
34. The concept of the optimum of a manufacturing company.
The production function reflects different ways of combining factors to produce a certain volume of output. The information carried by a production function can be represented graphically using isoquants.
Isoquant represents a curve on which all combinations of production factors are located, the use of which ensures the same volume of output (Fig. 11.1).
Rice. 11.1. Isoquant chart
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 factors of production (MRTS)
,
where DK and DL are changes in capital and labor for a separate isoquant, i.e. for constant Q.
The company is faced with the problem of how to achieve a certain volume of production with minimal costs. Let us assume that the price of labor is equal to the rate wages(w), and the price of capital is equal to the rental price for equipment (r). Production costs can be represented as isocosts. Isocosta includes all possible combinations of labor and capital with equal total costs
Rice. 11.2. Isocost chart
Let's rewrite the equation of total 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 gives up a unit of labor and saves w (cu) to purchase a unit of capital at a price r (cu) per unit, then the gross cost of production remains unchanged.
The firm's equilibrium occurs when it maximizes profit on a certain volume of production with an optimal combination of production factors that minimize costs (Fig. 11.3).
On the graph, the firm's equilibrium is reflected by the tangency point 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 at point T the isoquant and isocost have the same slope and that the slope of the isoquant is measured by MRTS, the equilibrium condition can be represented as
.
The right side of the formula reflects the utility for the producer of each unit of factor of production. This utility is measured by the marginal product of 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 one ruble invested in capital.
35. The concept of returns to scale.
Economies of scale are associated with changes in the cost of a unit of output depending on the scale of its production by the firm. Considered in the long term. Reducing costs per unit of production during the consolidation of production is called economies of scale. The shape of the long-term cost curve is associated with economies of scale in production.
Companies of any size can benefit from economies of scale by increasing 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 over a larger range of products). Using any of these factors reduces long-term average costs. 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.
Formal definition
Let the parameter K- unit of capital, parameter L- unit of labor, parameter a- increase/decrease by a-times.
We can say that for the production function when:
positive returns to scale
constant returns to scale
diminishing returns to scale
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