Probabilistic Models of Economic Dynamics with Endogenous Changes of Technology

Arkin, V.I. (1989). Probabilistic Models of Economic Dynamics with Endogenous Changes of Technology. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-89-100

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Abstract

We study economic dynamics models in which technological changes (the emergence of new technological modes) are related to the expenditures of resources taken from the sphere of material production. The production sphere is described by the dynamic model "input-output," which in turn is defined in terms of technological sets or production functions. New technologies arise from the sphere of "technological progress" (TP), described by a similar model. The instants at which new technologies emerge are taken to be random variables, whose characteristics depend upon the functioning of the TP sphere. So, we have the optimization problem of allocating resources between the production and the TP spheres and choosing the corresponding technological modes in the respective spheres. This approach was proposed in Arkin et al. (1976), in which a general scheme for describing economic dynamics models with endogenous TP was formulated in terms of the controlled random processes theory.

Two models are considered in this paper. The first is a generalization of the classical Gale model where the probability of technological change at instant t is determined by "funds" accumulated up to that time in the TP sphere. The second model is the stochastic analog of the multisectoral macroeconomic model that was discussed in Zelikina (1977) for the case of continuous time. As in the first model, the production function change is random and is determined by TP funds.

The main results discussed in this paper are a description of dual variables (stimulating prices) and the establishment of the related indicators of economic efficiency. In the system of obtained stimulating prices, the estimates of new technologies related to the stochastic nature of the models should be singled out. They have no deterministic analogs.

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