The problem of identifying the model of substitution of production factors

The generalized Houthakker–Johansen model that makes it possible to identify the substitution of production factors on the basis of the available Russian statistical data is studied. Combinatorial structures related to the problem of elasticity of production factor substitution at the microlevel are investigated. A necessary and a sufficient conditions for the solvability of the moment problem arising in the estimation of the elasticity of production factor substitution at the microlevel are formulated and proved in the language of combinatorial structures called rhombus tilings. The generalized Houthakker–Johansen model is identified on the basis of the Russian statistical data. The estimates of the production factor import obtained on the basis of Leontief's hypothesis that the cost per unit is constant and the estimates calculated on the basis of the generalized Houthakker–Johansen model are compared.