Cobb-Douglas function, economic explanation?

Cobb-Douglas function, that is, Cobb-Douglas production function, is an economic mathematical model and an improvement of the general form of production function. It introduces the factor of technical resources to predict the production of industrial systems or large enterprises in countries and regions, and analyzes the ways to develop production.

The basic form of Cobb-Douglas production function is:

Where Y is the total industrial output value, At is the comprehensive technical level, L is the number of labor input (unit is 10,000 people or people), and K is the invested capital, which generally refers to the net value of fixed assets (unit is 100 million yuan or 10,000 yuan, but it must correspond to the unit of labor, such as the labor force is 10,000 people and the net value of fixed assets is 100 million yuan), α is the elastic coefficient of labor output, β is the elastic coefficient of capital output, and μ stands for.

It can be seen from this model that the main factors that determine the development level of industrial system are the number of labor force, fixed assets and comprehensive technical level (including management level, labor quality, advanced technology introduction, etc.). ). According to the combination of α and β, it has three types:

①α+β& gt； 1, which is called incremental reward type, shows that expanding the production scale according to the existing technology is beneficial to improve the output.

②α+β& lt； 1, called diminishing returns, shows that it is not worth the loss to increase the output by expanding the production scale according to the existing technology.

③ α+β = 1, which is called constant return type, indicating that the production efficiency will not increase with the expansion of production scale, and only by improving the technical level will the economic benefits be improved.