Stochastic demand as an addition to the Solow Growth Model

Abstract

The subject of this research is the Solow Growth Model. The relevance is substantiated by the fact that the Solow Growth Model is conceptually simple, and simultaneously it can be complicated with clarifications and additions. The authors believe that one of such clarification is consideration of the demand as a stochastic variable. The goal of this research is to propose a model that takes into account the random nature of consumer demand based on the Solow Growth Model. The article aims to examine the Solow Growth model; conduct a literature overview of the most common modifications of the model; analyze the well-known modifications and complications of the model; outline the methods of such modifications and complications; offer Solow Growth Model supplemented with microeconomic substantiation with consideration of the stochastic demand. The article employs the methods of analysis, synthesis, comparison, and differential calculus. The novelty lies in the statement  that consumption depends on demand; it is intuitively obvious that demand can be considered as stochastic variable. This is explained by the individual traits of the consumers. Therefore, the demand can be described via stochastic differential equation based on the standard Wiener process (analogy with Brownian motion). The article offers a stochastic differential equation of demand. The Solow Growth Model is supplemented with the stochastic differential equation of demand. In conclusion, the authors determine the key modification and complication trends of the Solow Growth Model; developed the model based on the Solow Growth Model with the stochastic differential equation of demand as its addition. Further research should be aimed at solution of the obtained mathematical model supplemented with the stochastic differential equation of demand.