Sustained Growth with Heterogeneous Households

I examine a model where agents differ in their discount factors. It has long been known that in the long-run, the most patient household or individual ends up owning all the capital, provided there is a maximum sustainable stock. I show that this is no longer true when there is sustained growth. I examine a model where there is endogenous growth due to learning-by-doing, the “Arrow-Romer” model. It is still the case that one household ends up with all the capital, but that household is no longer necessarily the one who has the lowest discount rate. The appropriate measure of impatience depends not just on the discount rate, but also on the form of the felicity function, and the technology. Different technologies can lead to a re-ranking of the households. In some cases, different technologies can even completely reverse the patience ordering, and alter the long-run distribution of capital. There is even the possibility that the most patient household may change depending on the state of development of the economy, causing capital to shift from one household to another as the economy develops. SUSTAINED GROWTH WITH HETEROGENEOUS HOUSEHOLDS 1