This paper extends Kurz's (1968) growth model to a stochastic growth framework with social-status concern and unbounded production shocks. Using the stochastic monotonicity of a stochastic dynamic system and the methods adopted in Zhang (2007), the existence, uniqueness, and stability of invariant distribution are investigated. Different from the existence of multiple steady states under certainty, it is shown here that there exists a unique stable invariant distribution under uncertainty.

This paper studies capital accumulation and consumption in the traditional Ramsey model under an exogenous growth framework. The model has three important features: (1) treating health as a simple function of consumption, which enable the study of health and growth in an aggregate macroeconomic model; (2) the existence of multiple equilibria of capital stock, health, and consumption, which is more consistent with the real world situation-rich countries may end up with high capital, better health, and higher consumption than poor countries; (3) the fundamental proposition of a consumption tax instead of capital taxation from the traditional growth model does not hold anymore in our model. As long as consumption goods contribute to health formation, the issue of a consumption tax versus an income (or capital) tax should be re-examined.