We study the impact of a minimum consumption requirement on the rate of economic growth and the evolution of wealth distribution. The requirement introduces a positive dependence between the intertemporal elasticity of substitution and household wealth. This dependence implies a transition phase during which the growth rate of per-capita quantities rise toward their steady-state values and the distributions of wealth, consumption, and permanent income become more unequal. We calibrate the minimum consumption requirement to match estimates available for a sample of Indian villagers and find that these transitional effects are quantitatively significant and depend importantly on the economy's steady-state growth rate.