Bertrand and Walras equilibria under moral hazard

We consider a simple model of competition under moral hazard with constant return technologies. We consider preferences that are not separable in effort: marginal utility of income is assumed to increase with leisure, especially for high income levels. We show that, in this context, Bertrand competition may result in positive equilibrium profit. This result holds for purely idiosyncratic shocks when only deterministic contracts are considered and extends to unrestricted contract spaces in the presence of aggregate uncertainty. Finally, these findings have important consequences on the definition of an equilibrium. We show that, in this context, a Walrasian general equilibrium a la Prescott-Townsend may fail to exist: any "equilibrium" must involve rationing.