Probabilistic approach to determining production functions

The article considers a probabilistic method for determining production functions. The method consists in finding the expected value of the function that determines the economic and mathematical principle of production. It is assumed that the factors of production and/or their specific values included in this function are random variables. It is shown that depending on the principle of production such averaging gives different probabilistic classes of production functions. Functions that are elements of the same class differ from each other in the probability distribution of the relations of production factors to their specific values. Two probabilistic classes of production functions are constructed. The first class is generated by the Leontief production principle, the second – by generalization of this principle for the case of partially or completely fungible factors of production. There are established the laws of probability distribution and the conditions, under which the linear combination of the AK-model and the Cobb-Douglas production function, as well as the CES production function, are elements of the class of Leontief production functions. It is shown that the linear production function belongs to the class of generalized Leontief production functions. The probability density functions of the products number for these two classes of production functions are found.