Identification of a production function with age limit for production capacities

The micro-level dynamics of the age-limited vintage production capacity sets a macrolevel production function. The micro-description is based on the hypothesis of a capacity falling at a constant rate and a constant number of workplaces from the moment the production unit is created to its liquidation when the age limit is exceeded. An analytical expression for the endogenous production function with a given maximum age of capacity was obtained in characteristic exponential growth modes with a constant share of new capacity. It is conceded a transitional growth mode with a changing incremental capital intensity of the new capacities. The parameters of the production function can be determined even with significant changes in the share of new capacities in the total capacity that occurred in the Russian economy. For this, the initial microeconomic model of production capacity dynamics was used in numerical calculations of the production function. The parameters are estimated indirectly on the basis of a comparison of the results of calculations by the model with statistical data 1970–2017. The obtained value of the average age limit of capacities A = 25 for the Russian economy explains the vanishing of cost inflation in 2017. Identification of the parameters of the endogenous production function also showed that the value of the average incremental capital intensity for the entire Russian economy decreased significantly from 1970 to 2017. The decrease is explained by the increase in the share of primary industries in output.