Activities of university in cluster structure based on Cobb–Douglas

Economic & mathematical methods and models

The degree of economic development of any country is determined by the level of development of production. The process of production of products (tangible and intangible) is associated with consumption of a variety of resources, which include everything that is necessary for production activities, i.e., raw materials, labor, energy, equipment, etc. The Cobb–Douglas production function reflects the dependence of the volume of production on the factors of production that create it, while being relatively simple, universal and adequate. We have constructed a two-factor Cobb–Douglas production function based on statistical data of one of St. Petersburg’s national research universities for 2008-2017. We have chosen the value of the total income of the university from all activities (education, research and other income-generating activities) as an indicator of the volume of production and the real cost of fixed assets (machinery and equipment) of the university and the average monthly salary of a fulltime employee as factors of production. The following coefficients of the production function have been obtained: the total index of technological productivity of factors, the coefficient of technological elasticity of capital, the coefficient of technological elasticity of labor. Analysis of these coefficients has revealed fund-saving (extensive) growth for the university in 2008–2017; extended reproduction of production factors was also observed in that period. We have established that the values of the given coefficients differ slightly. This indicates that technical re-equipment, as well as increase in the average monthly salary of an employee are equal factors in the production process of the university. A set of isoquants forming a map of the isoquants obtained at different values of the output volume (university income) has been constructed. In the future, it is planned to modify the two-factor Cobb–Douglas function for current conditions of socio-economic development due to the fact that in practice there is no direct relationship between the factors of production and production volumes and a quality product cannot always be obtained without a sufficient amount of necessary fixed assets but with a larger number of employees.