Reexamination of the Serendipity Theorem from the stability viewpoint

This paper reexamines the Serendipity Theorem of Samuelson (1975) from the stability viewpoint, and shows that, for the Cobb–Douglas preference and CES technology, the most-golden golden-rule lifetime state being stable depends on parameter values. In some situations, the Serendipity Theorem fails to hold despite the fact that steady-state welfare is maximized at the population growth rate, since the steady state is unstable. Through numerical simulations, a more general case of CES preference and CES technology is also examined, and we discuss the realistic relevance of our results. We present the policy implication of our result, that is, in some cases, the steady state with the highest utility is unstable, and thus a policy that aims to achieve the social optima by manipulating the population growth rate may lead to worse outcomes.