Harrod–Okishio investment function, business cycle, and decreasing population

Sir Roy F. Harrod argued that the warranted rate of growth is unstable. Professor Nobuo Okishio insisted that capitalism has the property of cumulative disequilibrium. Therefore, an aggressive reversal of the disequilibrium process should be forced to continue its reproduction. Cyclical fluctuations with alternation of economic crises and turnovers are the characteristics of a capitalist society. This study introduces a simple Keynesian saving function into a growth model with the Harrod–Okishio investment function. We show that there is a business cycle constrained by full emolument at the ceiling and zero investment at floor if the population growth rare is positive. Furthermore, if the rate of population growth is negative, there is no cycle, and the economy finally moves to zero growth of capital. Then the output decreases at the same rate of the decreasing rate of the population with under capital utilization and unemployment. If the rate of population growth is zero, then the economy finally reaches the stationary state with unemployment. In contrast, according to the neoclassical theory of growth, in the case of a negative rate of population growth, the per capita capital and the per capita output increase forever as time passes. This proposition is dependent on the postulates of full employment and no investment function.