Public health spending, old-age productivity and economic growth: chaotic cycles under perfect foresight

This paper analyses the dynamics of a double Cobb–Douglas economy with overlapping generations and public health investments that affect the supply of efficient labour of the old-aged. It is shown that the positive steady state of the economy is unique. Moreover, we provide necessary and sufficient conditions for the emergence of endogenous deterministic complex cycles when individuals are perfectly foresighted. Interestingly, (i) the equilibrium dynamics shows rather complicated phenomena such as a multiplicity of bubblings depending on the size of the public health system, and (ii) the higher the degree of thriftiness, the likelier an economy is exposed to endogenous fluctuations because the need to save when young to support consumption when old is reduced.