Production function

The production function is the dependence of the quantity of manufactured goods expressed on the basis of the economic-mathematical model on the corresponding factors of production with which it is manufactured. Consider this concept in more detail.

The production function always has a specific form, since it is intended for a specific technology. The introduction of new technological developments entails changing or creating a new type of dependence.

This function is used to find the optimal (minimum) number of costs that are required to produce a certain number of goods. For all production functions, no matter what type of production they express, such general properties are characteristic:

• the growth in the volume of goods produced due to only one factor (resource) has a final limit (only a certain number of workers can work normally in one room, since the number of places is limited by the area);

• Factors of production can be interchangeable (automation of the production process) and complementary (workers and tools).

In the most general form, the production function looks like this:

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

Q - the volume of goods produced;

K - equipment (capital);

M - the cost of materials and raw materials;

Т - used technologies;

N - entrepreneurial abilities.

Types of production functions

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

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

This model considers the dependence of the volume of production (Q) on labor input (L) and capital (L). Quite often an isoquantum group is used to analyze this model. Isoquanta is a curve that connects all possible points of combinations of production factors that allow you to produce a specific volume of goods. On the X axis, labor costs are usually noted, and on the Y-axis, capital. Several isoquants are drawn on the same chart, each of which corresponds to a certain volume of production using a specific technology. The result is a card isoquantum with different quantities of manufactured goods. It will be a production function for this enterprise.

The following general properties are typical for isoquantas:

• the further the curve is from the origin, the higher the output;

• concave and descending form of isoquant due to the fact that a decrease in the use of capital with a stable volume of manufactured goods causes an increase in labor costs;

• The concave shape of the isoquant curve depends on the maximum allowable rate of technological replacement (the amount of capital that can replace 1 additional unit of labor).

Cobb-Douglas function

This production function, named after two American pioneers, where the total output of Y depends on the resources used in the production process, for example, labor L and capital K. Its formula:

Y = AKαLβ,

Where α and b are constants (α> 0 and b> 0);

K and L are capital and labor, respectively.

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

The Cobb-Douglas model can be used for any particular company. In this case, α is the share of total costs going to capital, and β is the share going to labor. Cobb-Douglas models can also contain more than two variables. For example, if N is land resources, then the production function takes the form Y = AKαLβNγ, where γ is a constant (γ> 0), and α + β + γ = 1.