Optimum Population -- A New Look: A Hamiltonian Approach Towards A Dynamic Analysis

The current optimum population models found in economic literature define static optimum population used in forming policy i.e. at a given instant what should be the optimum number of people in a (closed) economy. We believe that although this definition is useful, it is very limiting as far as policy implications are concerned. When making policies, we are hardly concerned with what should be the absolute number of people in the country at any given time, for the parameters are ever changing. Especially so, if the optimum population is defined via market conditions. As an effort to improve these models, we define dynamic optimum population, or the optimum population growth trajectory. Our model, therefore deals with population growth rather than the absolute level of population. This gives a dynamic goal (and a more realistic one) to the policy makers and discussions can be held in familiar language once again, 'we want to decrease/increase the population growth to .... .' This paper applies Hamilton's principle of least action to find optimum control trajectories of population and net consumption. This is done using a neoclassical economic growth model using capital stock, net national income and investment in the equations of motion to maximize social welfare. The major difference between our model and any previous work is that welfare is not maximized only at one period thus defining a static optimum, but rather over an entire range of periods thus defining optimum population and consumption control trajectories which maximize social welfare and are used for policy analysis. We analyze some of the more popular population policies in light of our model. These policies have been divided into two categories: long-run and short-run. More specifically, in the long-run, policies are ascribed to control the endogenous factor, population growth. In the short-run, the policy implications are to try and control other variables in the economy so that the natural growth of the population, now an exogenous factor, is the optimum growth.