In addition to multifactor complex models of economic growth, simplified, two-factorial models are often used. The Cobb-Douglas production function is a model that shows the dependence of production volume (Q) on the factors creating it: labor costs - (L) and capital investment - (K).
Economists have proposed two acceptable options for constructing two-factor models: taking into account the scientific and technical progress and without taking it into account.
Cobb-Douglas production function with NTP
An economy model that takes into account the real achievements of scientific and technical progress, labor and capital are more effective. In such conditions, it is possible to obtain higher profits at the same costs of labor and funds. In this model, some types of investments contribute to an increase in cash costs and provide labor savings, while others lead to a reduction in investment. The first type of investment leads to labor saving, and the second to capital saving.
NTP-free approach
Under the conditions of the model in the economy, when STP is not taken into account, capital accumulates at constant costs. Studies by economists show that using this approach reduces the final product.
On the one hand, such a situation may seem unnatural. But in reality, such a phenomenon is quite possible when on the one hand the achievements of scientific and technical progress are 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 extra 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 options are possible that combine the two approaches described.
Cobb-Douglas Model for Economic Growth
This model was first proposed by Knut Wicksell. But only in 1928 was it tested in practice by economists Cobb and Douglas. The Cobb-Douglas production function allows you to determine the level of total output Q by the amount of labor and invested capital (L and K).
The function looks like this:
Q = A × Lα × Kβ
Where: Q - volume of production;
L - labor costs;
K - capital investments;
A - Technological coefficient;
α is the value of labor elasticity;
β is the value of capital investment elasticity.
For example, we can consider the equality Q = L0.78 K0.22. In this equality it can be seen that in the total product, the labor share is 78%, and the capital share is 22%.
Limitations of the Cobb-Douglas Model
The Cobb-Douglas production function implies certain limitations that must be taken into account when using the model.
Production volumes increase if one of the factors remains unchanged, and the second increases. This is the essence of the first and second restrictions. 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 one of the factors remains unchanged, a gradual increase in the other factor will cause a decrease in the increase in the value of output (Q). This is the third and fourth limitation of the Cobb-Douglas model.
Fifth and sixth constraints suggest that each of the factors of production matters. That is, if one of the factors is 0, then, accordingly, Q will also be zero.
