The production function is its algebraic and graphical description. Production function

Answer

Entrepreneurs purchase factors of production on markets, organize production and produce products. Production function is a technological relationship between the number of factors of production used and the maximum possible output produced during a certain period of time. Such a technological connection exists for each specific level of technological development. The production function expresses the maximum output for each combination of factors of production. A function can be presented as a table, a graph, or analytically as an equation.

If the entire set of resources necessary for production is represented as the costs of labor, capital and materials, then the production function will take the following form:

Q = F (T, K, M),

where Q is the maximum volume of products produced using a given technology in a given ratio: labor - T, capital - K, materials - M.

The production function shows the relationship between factors and makes it possible to determine the share of each in the creation of goods and services.

Graphically, the relationship between factors of production can be depicted as an isoquant. An isoquant is a curve reflecting various combinations of resources that can be used to produce a certain volume of output. The set of isoquants forms an isoquant map that shows the alternatives to the production function. Isoquants have the following properties:

Isoquants cannot intersect, because are the geometric locus of equal outputs;

Isoquants are strictly convex to the origin and have a negative slope;

The higher and to the right the isoquant, the greater the volume of output it characterizes.

The production function can only be determined empirically (experimentally), i.e. through measurements based on actual performance.

Question 7. Production capabilities of the economy

Answer

A common property of economic resources is their limited quantity, so the economy is constantly faced with the question of alternative choice: increasing the production of one product (commodity set) means refusing to produce part of another. Society strives to ensure full employment and full production in order to satisfy its needs as much as possible. Concept full employment characterizes the economically feasible use of all resources. Under full volume production implies the efficient allocation of resources, ensuring the highest output.

Alternative choice in economics can be characterized using production possibilities curve, each point of which reflects the maximum possible volume of production of two products with given resources. Society determines which combination of these products it chooses. The functioning of an economy on the production possibilities frontier indicates its efficiency and the correctness of the choice of the method of producing a good. Points located outside the production possibilities curve contradict the accepted condition.

The number of other products that must be sacrificed in order to obtain any quantity of a given product is called alternative ( opportunity) production costs of this product. It is necessary to distinguish between the opportunity costs of an additional unit of goods and the total (or total) opportunity costs. The absence of perfect elasticity or interchangeability of resources has been established. It follows from this that when switching resources from the production of one product to another, each additional unit of product will require the involvement of an increasing number of additional products. This phenomenon is called law of increasing opportunity costs. Thus, law of opportunity costs reflects the process of constant increase in opportunity costs.

The theory of opportunity costs and the production possibilities curve are used to justify investment programs and projects, as well as to formulate the optimal structure of products, study consumer behavior and solve other issues requiring the redistribution of resources.

Question 8. Stages of social production

Answer

Factors of production (funds or capital) go through three stages: purchase of factors of production; the production process, where the means of production and labor are combined; selling goods and making a profit.

A continuously repeating production process is called reproduction. Distinguish prime(descending) And expanded reproduction. Simple reproduction ensures the recreation of the previously achieved state of the economy - this is production on an unchanged scale. Decreasing production is typical for crisis states of the economy. With it, the scale of production is reduced. Expanded manufacturing is characterized by a constant increase in the scale of production. There are intensive and extensive types of expanded reproduction. At intensive type, expansion of the scale of production is achieved through qualitative improvement and better use of production factors, the use of more efficient technologies, and increased labor productivity. Extensive type is characterized by a quantitative increase in factors of production.

The sequential passage of production assets (capital) through three stages forms circulation of production assets. The circulation of production assets, considered as a continuously repeating process, is called turnover of funds (capital). The turnover time of funds consists of production time And time of appeal. The turnover of funds (capital) ends when, in the process of selling goods, the owner of the funds fully reimburses the capital advanced into factors of production.

Depending on the specifics of turnover, production assets are divided into basic, serving for a long time, and negotiable, which are consumed during one production cycle.

Distinguish physical And obsolescence fixed production assets. The process of compensating for the depreciation of fixed production assets by gradually including their value in the production costs of the created goods is called depreciation. The ratio of the amount of annually transferred depreciation deductions to the cost of labor instruments as a percentage is called depreciation rate.

Circulation funds enterprises include finished products and enterprise cash. Together with working production assets they form working capital enterprises. Working capital turnover is an important indicator of the efficiency of their use.

Production efficiency in In general, it is determined by the relationship between the effect (result) and the cause that causes it. The most important indicators of production efficiency are: labor productivity, labor intensity, capital-labor ratio, capital productivity, capital intensity, material intensity.

Question 9. Product as a result of production

Answer

Product represents the result of the purposeful activity of people - labor (thing or service) and at the same time acts as a condition for the flow of the labor process. The product ensures the reproduction of personal and material factors of production.

There are material and social aspects of the product. Natural - real the side of a product is the totality of its properties (mechanical, chemical, physical, etc.) that make this product a useful thing that can satisfy human needs. This property of the product is called consumer value. Public side product is that each product, being the result of human labor, accumulates a certain amount of this labor.

A product manufactured by a separate manufacturer acts as single or individual product. The result of all social production is public a product that represents the entire mass of use values ​​created in society and serves as the basis of its material and spiritual life.

According to its natural-material form, the social product is divided into means of production and items of personal consumption. Means of production returned during production. They serve to replace worn-out production assets and to increase (expand) them. Personal items finally leave the sphere of production and enter the sphere of consumption. The division of the social product into means of production and personal consumption items allows us to divide all material production into two large divisions: production of means of production(1 division) and production of personal consumption goods(2nd division).

In a commodity economy, the social product has a value, the external manifestation of which is price. The cost of a product is determined by the total (total) costs of its production, i.e., the costs of past (materialized) labor and the costs of living labor. In Western literature, instead of the term “product,” the term “good” is often used.

Manufacturing is actually the process of transforming one product into another. In the process of which, from a combination of simple things, something more complex in essence is obtained. The Cobb-Douglas production function, like any other, reflects the existing relationship between the result obtained and the combination of factors that were used to achieve it. The differences between different models lie in the depth of their coverage of the real state of affairs. The simplest is linear, which reflects the relationship between the number of workers and real output. The Cobb-Douglas production model no longer considers only labor as a resource for obtaining results, but also capital. The most complex are modern multifactor models. They include land, entrepreneurial skills, and even information.

Production as a process

Production at its core is the transformation of various material and intangible investments (plans, know-how) to create items intended for consumption. It is the process of creating a product or service that is useful to individuals. Increased production means improved economic well-being. This is because all products are directly or indirectly used to satisfy human needs. And the latter, as you know, are limitless. Therefore, the economic well-being of a state is often assessed by the degree to which the needs of its citizens are satisfied. Its increase is associated with two factors: an improvement in the quality-price ratio of available products and an increase in the purchasing power of people due to more efficient market production.

Source of economic wealth

There are mainly only two processes in the economy: production and consumption. And there are just as many types of actors. Manufacturers produce products to satisfy consumer needs. Economic well-being thus consists of two components. The first is efficient production, the second is the interaction between factors. The well-being of consumers depends on the products they can afford, and producers - on the income they receive as compensation for their labor and the tangible and intangible assets invested in the production process.

Product creation process

Every enterprise deals with many separate activities in the course of its work. However, to make it easier to understand production, it is customary to distinguish five main processes, each of which has its own logic, goals, theory and key figures. And it is important to study them not only as a whole, but also separately. Thus, during production the following processes are distinguished:

Economic definition

The production function is the relationship between output and the combination of factors used to produce it. The main one is labor. A simple linear model considers only this. The Cobb-Douglas production function, an example of which will be discussed below, takes into account not only labor, but also capital as a factor in the production process. Other models additionally take into account land (P) and entrepreneurial ability (H). Thus, production is a function of the combination of these indicators or Q = f (K, L, P, H). Each sector of the economy or even a separate enterprise has its own characteristics. Therefore, an infinite number of production functions can be invented.

Simple linear model

The Cobb-Douglas production function takes into account two factors, as is common in neoclassical theories. However, it is much easier to consider only one. Adam Smith's theory of absolute advantage, with which virtually all modern economics began, was based only on labor as a factor of production. David Ricardo did not escape this assumption either. And only in the 60s of the last century, Swedish economists Eli Heckscher and Bertil Ohlin took it upon themselves to begin to consider another factor - capital. The simplest production model is linear. It describes the relationship between the quantity of labor and output. Her equation includes only one independent variable. Thus, the linear production function has the following form: Q = a * L, where Q is the volume of output, a is the parameter, L is the number of workers employed in production. Let's look at a separate example. One worker can make 10 chairs per day. In this case, the equation will look like this: Q = 10 * L.

Law of Diminishing Returns

Let's continue with the example given above. A linear function implies that an increase in the number of workers always leads to an increase in output. One master can make 10 chairs a day, five - 50, one hundred - 1000. However, in reality everything is a little more complicated. In such models, fixed capital funds and diminishing returns must be taken into account. Therefore, an additional parameter appears in the equation - b. It lies between zero and one, which follows from its economic essence. Now the relationship between the volume of output and the number of workers can be described as follows: Q = a * L b. The equation from the previous example in reality will look like this: Q = 10 * L 0.5. And this means that one worker produces 10 chairs, and five do not produce 50, but only 22. A hundred craftsmen can actually make not a thousand products, but only a hundred. And this is the law of diminishing returns in action.

Multifactor models

The Cobb-Douglas production function is: Q = a * L b * K c . As can be seen from the formula, we are already dealing with three parameters (a, b, c) and two factors (L, K). It takes into account not only labor resources (number of workers), but also capital resources (number of saws at disposal). The parameters of the Cobb-Douglas production function depend not only on the industry sector, but also on the technology used in an individual enterprise. We must not forget about the effect of the law of diminishing returns from any factor used. Our equation from the example above can be expanded as follows: Q = 10 * L 0.5 * K. The Cobb-Douglas production function is used most often in modern neoclassical theories because of its relative simplicity and closeness to reality. More complex models are just beginning to become widespread.

Fixed proportions

Suppose the only way to produce a chair is to give each worker a saw. In this case, extra tools are simply useless. This means that the release of a product requires a certain ratio of capital and labor resources. In this case, the production volume is determined by the “weak link”. For this case, economists came up with a special function. It has the following form: min (L, K). If to create a chair you need two workers and one saw, then min (2L, K).

Ideal substitutes

If one factor can be replaced by another, this will have an effect on the shape of the production function. For example, suppose robots could be used instead of carpenters. The formula from the example will then look like this: Q = 10 * L + 10 * R. Or more generally: Q = a * L + d * R, where a, d are parameters, and L and R are the number of carpenters and robots. If machines are 10 times faster than workers, then the formula will look like this: Q = 10 * L + 100 * R.

Cobb-Douglas production function: properties

Let's start looking at the most popular neoclassical model with its main features:

1. Cobb-Douglas production functions take into account two factors: labor and capital.

2. Positively decreasing marginal product.

3. Constant elasticity of output equal to b for L and c for K.

4. The Cobb-Douglas production function has the form: Q = a * L b * K c.

5. Constant economies of scale equal to the sum of b and c.

Historical information

The basis of any economic theory is the factors of production. The Cobb-Douglas production function considers two of the four basic ones: labor and capital. Today, for each enterprise, you can come up with separate examples of it. The solution to the Cobb-Douglas production functions did not occur without the work of Knut Wicksell (1851-1926). It was he who first designed this model. Charles Cobb and Paul Douglas, after whom it was later named, only tested it in practice. In 1928, their book was published, which described the economic growth of the United States in 1899-1922. Scientists explained it using two factors: labor resources used and capital invested. Of course, economic growth is influenced by many other parameters, but statistics have proven that the decisive ones are the two that Knath Wicksell identified.

According to Paul Douglas, the first formulation of the function appeared in 1927. At this time, he tried to derive a mathematical expression for the relationship between workers and capital. He turned to his colleague Charles Cobb. The latter managed to derive a modern equation, which, as it turned out, was previously used in his works by Knath Wicksell. Using the least squares method, scientists were able to derive the exponent of labor (0.75). Its importance has been confirmed by data from the National Bureau of Economic Research. In the 1940s, scientists moved away from constants and declared that exponents could change over time.

Model assumptions

If output is a derivative of two factors (labor and capital), then the elasticity of the entire function will depend on the marginal productivity of each of them. Thus, Cobb and Douglas based their model on the following assumptions:

• Production cannot continue in the absence of one of the factors. Labor and capital are not substitutes that can replace each other in the output process. Additional saws cannot create chairs without the participation of carpenters.
• The marginal productivity of each factor is proportional to the volume of output per unit.

Release elasticity

Obviously, reducing the volume of materials used leads to a reduction in the volume of products. The Cobb-Douglas production function deals with marginal output. Elasticity in economics is the percentage change in the value of one indicator in response to a decrease or increase in another associated with it. The Cobb-Douglas production function assumes that b and c are constants. If b is equal to 0.2 and the number of workers increases by 10%, then output will increase by 2%.

Economies of scale

To actually increase output, the volume of factors of production used must increase proportionally. If this happens, then we say that we are using economies of scale. The Cobb-Douglas production function, the properties of which we have already examined, takes it into account. If b + c = 1, then this means that we are dealing with a constant effect of scale, >1 - increasing,<1 - уменьшающимся.

Time factor

The Cobb-Douglas production function model is often used to describe the medium- and long-term outlook. Obviously, it is often much easier to hire new people than to increase capital resources. Therefore, some economists argue that a simple linear model is best suited to describe short time periods of enterprise operation. The company owns a certain size of premises, a limited number of machines, which can only be changed with the help of long-term planning. The time period it takes may vary from one plant to another, as can the elasticity of the Cobb-Douglas production function.

Application problems

Although the two-factor production function has gained widespread acceptance and has been statistically tested by Cobb and Douglas, some economists still doubt its accuracy across industries and time periods. The main assumption of this model is the constancy of the elasticity of labor and capital in developed countries. However, is this really so? Neither Cobb nor Douglas provided a theoretical basis for its existence. The constancy of the coefficients b and c greatly simplifies the calculations, and that's all. At the same time, scientists knew nothing about engineering, technology and production process management. In addition, the possibility of its application at the micro level does not indicate its correctness in macroeconomic conditions, and vice versa.

Criticism has dogged the Cobb-Douglas production function since its introduction in 1928. At first, it upset scientists so much that they wanted to quit working on it. But then they decided to continue. In 1947, Douglas came forward with further confirmation of its correctness as president of the American Economic Association. The scientist was unable to continue working on it due to health problems. The production function was later refined by Paul Samuelson and Robert Solow, forever changing the way we study macroeconomics.

The Cobb-Douglas production function is one of the most important concepts today. It describes the relationship between the input factors and the resulting result. Unlike simple linear models, which are only suitable for describing a short period of the life of an enterprise, it can be used for long-term planning. However, we must not forget about a number of assumptions and problems associated with its application.

Production refers to any human activity to transform limited resources - material, labor, natural - into finished products. Production function characterizes the relationship between the amount of resources used (factors of production) and the maximum possible volume of output that can be achieved provided that all available resources are used in the most rational way.

The production function has the following properties:

1. There is a limit to the increase in production that can be achieved by increasing one resource and keeping other resources constant. If, for example, in agriculture we increase the amount of labor with constant amounts of capital and land, then sooner or later a moment comes when output stops growing.

2. Resources complement each other, but within certain limits their interchangeability is possible without reducing output. Manual labor, for example, can be replaced by the use of more machines, and vice versa.

3. The longer the time period, the more resources can be revised. In this regard, instantaneous, short and long periods are distinguished. Instantaneous period - a period when all resources are fixed. Short period- a period when at least one resource is fixed. Long period - a period when all resources are variable.

Typically, the production function in question looks like this:

A, α, β - specified parameters. Parameter A is the coefficient of total productivity of production factors. It reflects the impact of technological progress on production: if a manufacturer introduces advanced technologies, the value A increases, i.e. output increases with the same quantities of labor and capital. Options α And β are the elasticity coefficients of output for capital and labor, respectively. In other words, they show by how many percent output changes when capital (labor) changes by one percent. These coefficients are positive, but less than one. The latter means that when labor with constant capital (or capital with constant labor) increases by one percent, production increases to a lesser extent.

Isoquant(equal product line) reflects all combinations of two factors of production (labor and capital) for which output remains unchanged. In Fig. 8.1 next to the isoquant the corresponding release is indicated. Thus, output is achievable using labor and capital or using labor and capital.

Rice. 8.1. Isoquant

If we plot the number of units of labor along the horizontal axis, and the number of units of capital along the vertical axis, then designate the points at which the firm produces the same volume, we get the curve shown in Figure 14.1 and called an isoquant.

Each isoquant point corresponds to a combination of resources at which the firm produces a given volume of output.

The set of isoquants characterizing a given production function is called isoquant map.

Properties of isoquants

The properties of standard isoquants are similar to those of indifference curves:

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).

Market concept. In its most general form, a market is a system of economic relations that develop in the process of production, circulation and distribution of goods, as well as the movement of funds. The market develops along with the development of commodity production, involving in exchange not only manufactured products, but also products that are not the result of labor (land, wild forest). Under the conditions of the dominance of market relations, all relations of people in society are covered by purchase and sale.

More specifically, the market represents the sphere of exchange (circulation), in which

communication is carried out between agents of social production in the form

purchase and sale, i.e. the connection between producers and consumers, production and

consumption.

Market subjects are sellers and buyers. As sellers

and buyers are households (consisting of one or more

persons), firms (enterprises), state. Most market participants

act simultaneously as both buyers and sellers. All household

subjects interact closely in the market, forming an interconnected “flow”

purchase and sale.

Firm is an independent economic entity engaged in commercial and production activities and possessing separate property.

The company has the following characteristics:

1. is an economically separate, independent economic unit;
2. legally registered and in this regard relatively independent: it has its own budget, charter and business plan
3. is a kind of intermediary in production
4. any company independently makes all decisions related to its functioning, so we can talk about its production and commercial independence
5. The company's goals are to make a profit and minimize costs.

The company, as an independent economic entity, performs a number of important functions.

1. Production function implies the ability of a firm to organize production of goods and services.

2. Commercial function provides logistics, sales of finished products, as well as marketing and advertising.

3. Financial function: attracting investments and obtaining loans, settlements within the company and with partners, issuing securities, paying taxes.

4. Counting function: drawing up a business plan, balance sheets and estimates, conducting inventories and reports to state statistics and tax authorities.

5. Administrative function– a management function, including organization, planning and control over activities as a whole.

6. Legal function carried out through compliance with laws, norms and standards, as well as through the implementation of measures to protect production factors.

Elasticity and the slope of the demand curve cannot be equated, because these are different concepts. The differences between them can be illustrated by the elasticity of the straight line of demand (Figure 13.1).

In Fig. 13.1 we see that the straight demand line at each point has the same slope. However, above the middle, demand is elastic, below the middle, demand is inelastic. At the point in the middle, the elasticity of demand is equal to one.

The elasticity of demand can be judged by the slope of only the vertical or horizontal line.

Rice. 13.1. Elasticity and slope are different concepts

The slope of the demand curve—its flatness or steepness—depends on absolute changes in price and quantity, while elasticity theory deals with relative, or percentage, changes in price and quantity. The difference between the slope of a demand curve and its elasticity can also be clearly understood by calculating the elasticity for various combinations of price and quantity located on a straight-line demand curve. You will find that although the slope apparently remains constant throughout the curve, demand is elastic in the high-price segment and inelastic in the low-price segment.

INCOME ELASTICITY OF DEMAND - a measure of the sensitivity of demand to changes in income; reflects the relative change in demand for a good due to a change in consumer income.

Income elasticity of demand appears in the following main forms:

· positive, suggesting that an increase in income (other things being equal) is accompanied by an increase in demand. The positive form of income elasticity of demand applies to normal goods, in particular luxury goods;

· negative, suggesting a reduction in the volume of demand with an increase in income, i.e., the existence of an inverse relationship between income and the volume of purchases. This form of elasticity extends to inferior goods;

· zero, meaning that the volume of demand is insensitive to changes in income. These are goods whose consumption is insensitive to income. These include, in particular, essential goods.

Income elasticity of demand depends on the following factors:

· on the importance of a particular benefit for the family budget. The more a family needs a good, the less elastic it is;

· whether this good is a luxury item or a necessity. For the former good the elasticity is higher than for the latter;

· from conservatism of demand. As income increases, the consumer does not immediately switch to consuming more expensive goods.

It should be noted that for consumers with different income levels, the same goods can be classified as either luxury goods or basic necessities. A similar assessment of benefits can also take place for the same individual when his level of income changes.

In Fig. Figure 15.1 shows graphs of QD versus I for various values ​​of income elasticity of demand.

Rice. 15.1. Income elasticity of demand: a) high-quality inelastic goods; b) high-quality elastic goods; c) low-quality goods

Let us make a brief comment on Fig. 15.1.

Demand for inelastic goods increases with income only when household incomes are low. Then, starting from a certain level I1, the demand for these goods begins to decline.

The demand for elastic goods (for example, luxury goods) is absent up to a certain level I2, since households do not have the opportunity to purchase them, and then increases with increasing income.

The demand for low-quality goods initially increases, but starting from the value of I3 it decreases.

Related information.