Poverty Traps, Indeterminacy, and the Wealth Distribution

We consider a one-sector growth model in continuous time with a production externality and endogenous labor supply. There is a continuum of households who have identical preferences but differ with respect to their initial wealth. We show that there exist economies such that an indeterminate steady state exists for some wealth distribution but not for others. A second result is that a redistribution of wealth may drive the economy from a steady state with strictly positive output to a poverty trap in which output converges asymptotically to zero. These results indicate that differences in the wealth distribution may be responsible for drastic differences in the long-run standard of living.