The Interaction between Technical Change and Capital Investment Growth and Stability of R&D Model

Faced with an ever-changing economic environment, we have focused our attention on the study of the evolutionary relationship between the main factors of production. The originality of this work comes from a qualitative and quantitative analysis of the R&D model and considers the dynamic between labor, capital investment and technological progress. To understand the dynamics of the relationship between these variables in detail and to understand their long-term behavior, we have used the classical properties of Lotka Volterra’s differential equations. The results of the Lyapunov function which we introduced have proved that the growth rate of technological progress and capital accumulation reach a stable long-term equilibrium. A numerical application was carried out on Canon industry and proved an evolution in the nature of the link between capital and R&D investment. We have attributed this behavioral change to the process of learning through interaction.