PERFORMANCE OF OPTIMALLY CONTROLLED ECONOMIC GROWTH MODELS WITH
GENERALIZED PRODUCTION FUNCTION: THE ROLE OF POPULATION GROWTH DYNAMICS
Abstract
As a sequel to previous papers, we assess, in a more general form, the
performance of real income per head / capita using generalized aggregate
production function under optimal control conditions. The role of the
population growth dynamics in all of this is carefully tracked,
especially as it varies from primarily exponential to sturdily logistic.
Analytical, qualitative and numerical simulation procedures are used to
decode 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 here used as the state vector,
whereas the output variable is income per effective labour, whilst
consumption and investments relative to the above production factors,
per effective labour apiece, become the control vector. The quadratic
cost functional consisting of the control and state vectors,
time-discounted, turns the objective functional. Largely, real income
per head rises much quicker and generates higher time-values provided
the population growth mechanism is chiefly exponential in contrast to
being largely logistic, given the technological process of research and
development (R & D). Contrarily, under any other technology, real
income per head rather rises much quicker and generates higher
time-values so long as the underlying population growth mechanism is
chiefly logistic, and remotely utterly exponential. Such outcomes exert
consequences across board with regard to economic management in
underdeveloped (where population growth is exponential) and developed
(where population growth is firmly logistic) economies alike, as well as
those in-between these two extremes.