Optimally Controlled Economic Growth Models with Generalised Production Function: Performance and the Role of Population Growth Dynamics

As a follow-up to previous studies, this article assesses, in a more general form, the performance of real income per head using generalised aggregate production function under optimal control settings. The study carefully examines the role of population growth dynamics in all of this, especially as it varies from chiefly exponential to sturdily logistic. Additionally, this study uses analytical, qualitative and numerical simulation procedures to interpret the population associated parameters that engender qualitative variations in the evolution of real income per head. Non-labour factors of production per effective labour are treated as the state vector, whereas the output variable is real income per effective labour. Consumption and investments relative to the above production factors, per effective labour apiece, constitute the control vector. The quadratic cost functional, which incorporates the control and state vectors, time-discounted, serves as the objective functional. The constructed system is found to be controllable, stable and detectable, and hence, obtained results are valid and reliable, and there exists unique solution to the associated Riccati equation. Overall, real income per head rises much quicker and generates higher time-values provided the population growth mechanism is predominantly exponential, and in contrast to being largely logistic, given the technological process of research and development (R & D). Conversely, under other technologies, real income per head rises much quicker and attains higher time-values when the population growth mechanism is mainly logistic, rather than purely exponential. These outcomes exert consequences across board with regard to economic management in underdeveloped economies in which population growth is exponential, and in developed economies alike, where population growth is firmly logistic, as well as in economies that fall between these two extremes. Consequently, the results adduced can serve as guide in economic policy formulations, especially in population management, education and skill-training, innovation, research and development, the creation and use of new technology.