A "folk theorem" originating, among others, in the work of Stiglitz maintains that competitive equilibria area always or "generically" inefficient (unless contracts directly specify consumption levels as in Prescott and Townsend, thus bypassing trading in anonymous markets). This paper critically reevaluates these claims in the context of a general equilibrium economy with moral hazard. We first formalize this folk theorem. Firms offer contracts to workers who choose an effort level that is private information and that affects worker productivity. The clarify the importance of trading in anonymous markets, we introduce a monitoring partition such that employment contracts can specify expenditures over subsets in the partition, but cannot regulate how this expenditure is subdivided among the commodities within a subset. We say that preferences are nonseparable (or more accurately, not weakly separate) when the marginal rate of substitution across commodities within a subset in the partition depends on the effort level, and that preferences are weakly separate when there exists no such subset. We prove that the equilibrium is always inefficient when a competitive equilibrium allocation involves less than full insurance and preferences are nonseparable. This result appears to support the conclusion of the above-mentioned folk theorem. Nevertheless, our main result highlights its limitations. Most common-used preference structures do not satisfy the nonseparability condition. We show that when preferences are weakly separable, competitive equilibria with moral hazard are constrained optimal, in the sense that a social planner who can monitor all consumption levels cannot improve over competitive allocations. Moreover, we establish epsilon-optimality when there are only small deviations from weak separability. These results suggest that considerable care is necessary in invoking the folk theorem about the inefficiency of competitive equilibria with private information. Keywords: competitive equilibrium, double deviations, efficiency, general equilibrium theory, monitoring partition, moral hazard. JEL Classifications: D52, D61, D62, D82.