The sustainability of the pay-as-you-go system with falling birth rates

A model is presented that explains the mix between funded and unfunded pension systems. It turns out that total pension and the relative shares of the two systems may be explained and are determined by the population growth rate, technological growth, the time-preference discount rate, the relative risk aversion, the production function, and the degree of altruism. A fall in the population growth rate, even to negative values, will imply a reduction of the interest rate and an increase in the capital-output ratio, while the pension system will shift to more funding. A fall in the population growth rate will result in a reduction of average welfare and an increase in the income inequality between workers and retired people/individuals.