The Cobb-Douglas production function is a two-factor model
In addition to multifactorial complex modelseconomic growth, often, simplified, two-factor models are used. The Cobb-Douglas production function is a model that shows the dependence of the volume of production (Q) on the factors that create it: labor costs - (L) and capital investments - (K).
Economists proposed two feasible options for constructing two-factor models: taking into account NTP and without taking it into account.
The Cobb-Douglas production function, taking into account the NTP
The model of the economy in which realachievements of scientific and technical progress, labor and capital are more effective. In such circumstances, it is possible to obtain higher profits at the same cost of labor and funds. In this model, some types of investments contribute to increased cash costs and provide labor saving, while others - lead to a reduction in investment. The first type of investment leads to the saving of labor, and the second - to the saving of capital.
The approach that does not take into account NTP
In the conditions of the model in the economy, when notNTP is taken into account, capital accumulation occurs at constant costs. Studies by economists show that the use of this approach leads to a reduction in the final product.
On the one hand, this situation may seemunnatural. But in practice this phenomenon is quite possible, when on the one hand the NTP is imposed, and on the other hand it is denied by enterprises, since there are no effective incentives for introducing innovations into production. As a result, the enterprise suffers excess costs for the purchase of new equipment that is not used in the production process, but only hangs on the balance sheet of the enterprise, worsening its performance.
It is easy to see that intermediate versions are possible, combining the two described approaches.
The Cobb-Douglas model for determining economic growth
This model was first proposed by KnuthWicksail. But only in 1928 it was tested in practice by economists Cobb and Douglas. The Cobb-Douglas production function allows you to determine the level of the total output Q by the amount of labor and capital invested (L and K).
The function looks like this:
Q = A × Lα × Kβ
Where: Q - Volume of production;
L - Labor input;
K - Capital investments;
A - Technological coefficient;
α - the value of elasticity by labor;
β - the value of elasticity on investment.
For example, we can consider the equality Q = L0.78 K0.22. In this equation, it can be seen that in the aggregate product the share of labor is 78%, and the share of capital is 22%.
Limitations of the Cobb-Douglas model
The Cobb-Douglas production function assumes certain limitations, which must be taken into account when using the model.
The volume of production increases if one of thefactors remains unchanged, and the second increases. This is the essence of the first and second limitations. Moreover, if one of the factors is fixed, and the other grows, then each limiting unit of the growing factor is not as effective as the previous value.
If the value of one of the factors is unchangedthe gradual growth of another factor will cause a decrease in the increase in the value of the volume of production (Q). This is the third and fourth limitation of the Cobb-Douglas model.
The fifth and sixth limitations assume that each of the factors of production matters. That is, if one of the factors is 0, then, respectively, and Q will also be zero.
