On Poverty Traps and Equilibria in Growth Models

We show that, contrary to a widely spread error, when the savings and the population growth rates are constant, an unstable equilibrium cannot exist in a neoclassical model, because it would imply an increasing average productivity of capital and therefore a negative marginal productivity of labor. As a consequence, a poverty trap, a dire reality, cannot be explained by such an unstable equilibrium, nor cannot it be eliminated by a capital "big-push". We finally give necessary conditions for an economy to escape a poverty trap