Pre-print, Working paper: That paper formalizes the idea that when the magnitude of the moral hazard phenomenon is not important, the distortions like equilibria multiplicity or equilibrium discontinuity relative to the economic fundamentals disappear. We study a two state of nature insurance model, with a risk neutral principal, a risk averse agent and separable costs. Typically, in such economies, non convexities imply that the set of Pareto optimal allocations is not connected. Surprisingly, we prove that it is never the case under weak and realistic assumptions. That result is in particular valid under simple regularity assumptions on the cost function when the productivity of effort is always positive. We show that such regularity of the moral hazard economy is compatible with remaining strong non convexities.