Production function

production function - is expressed by means of economic and mathematical model of dependence of the amount of goods produced from the corresponding factors of production with which it is made.Consider this concept in more detail.

production function always has a particular form, since it is designed for a specific technology.The introduction of new technological developments entail a change or create a new kind of dependence.

This function is used to find the optimal (minimum) amount of the costs, which are necessary for the production of a certain amount of goods.For all production functions, no matter what type of production they represent, is characterized by such common properties:

• growth in the volume of goods produced by only one factor (resource) has a finite limit (in the same room can normally only work a certain number of workersbecause seats are limited area);

• factors of production can be used interchangeably (automation of the production process) and complementary (staff and to


In the most general form of the production function is as follows:

Q = f (K, L, M, T, N), in this formula

Q - the volume of goods produced;

K - equipment (capital);

M - costs of materials and raw materials;

T - the technology used;

N - entrepreneurial skills.

Types of production functions

There are many types of this dependence, which take into account the influence of both one and several of the most important factors.However, the best known are two main types of production function: two-factor model of the form Q = f (L; K) and the Cobb-Douglas function.

two-factor model of Q = f (L; K)

This model considers the dependence of the output (Q) of the cost of labor (L) and capital (L).Quite often, analysis of this model uses a group of isoquants.Isoquants - it is a curve that connects all the possible combinations in terms of factors of production, allowing to produce a specific amount of goods.The X-axis will be observed labor costs, and on the axis Y - capital.On the same graph draw isoquants several, each of which corresponds to a certain volume of production using a particular technology.The result is a map of isoquants with different amounts of manufactured goods.She will be the production function for the company.

For isoquants characterized by the following general properties:

• the further the curve is from the origin, the greater the volume of production;

• concave isoquant and downward view stems from the fact that the reduction in the use of capital with a steady volume of manufactured goods causes the growth of labor costs;

• concave shape of the isoquants depends on the maximum allowable rate of technical substitution (the amount of capital that can replace one additional unit of labor).

Cobb-Douglas function

This production function is named in honor of two American pioneers, where the total volume of output Y is in according to the in-process resources such as labor and capital K. L Its formula:

Y = AKαLβ,

where α and b - is the constant (α & gt; 0 and b & gt; 0);

K and L - respectively capital and labor.

If the sum of the constants α and b are equal to one, it is believed that such a function is present constant returns to scale production.If the parameters K and L are multiplied by a coefficient, then Y must also be multiplied by the same coefficient.

Model Cobb-Douglas is quite possible to use for any individual firm.In this case, α - is the proportion of total costs going to capital, and β - the share that goes to work.Cobb-Douglas models may also contain more than two variables.For example, if N - is the land, the production function takes the form Y = AKαLβNγ, where γ - the constant (γ & gt; 0) and α + β + γ = 1.