I study the effect of the market arrangement on competitive allocations in a model in which the distribution of idiosyncratic uncertainty is determined endogenously. The particular application I consider is a search model of the labor market embedded in a general equilibrium model with production and asset accumulation. It is shown that costly search with incomplete markets introduces a wealth effect at low levels of wealth such that poor agents do not search much or even find optimal not to look for a job. The combination of this effect with the usual one at higher wealth levels delivers equilibrium allocations that are remarkably different from the one that obtains under complete markets. I also use numerical methods to obtain quantitative predictions in a calibrated version of the model. The effect of the market arrangement remains dramatically large due to search externalities.