We consider several one-period reinsurance models and derive a rule which minimizes the ruin probability of the cedent for a fixed reinsurance risk premium. The premium is calculated according to the economic principle, generalized zero-utility principle, Esscher principle or mean-variance principles. It turns out that a truncated stop loss is an optimal treaty in the class of all reinsurance contracts. The result is also valid for models not involving ruin probability. An example is the Arrow model with the Kahneman-Tversky value function.

Are firms and households constrained in the use of a productive input? Theoretical approaches to this question range from exogenously imposed credit allocation rules to endogenous market failures stemming from some sort of limited-commitment or moral-hazard problem. However, when testing for constraints, researchers often simply ask firms or households if they would wish to borrow more at the current interest rate and/or test for suboptimal use of inputs in production functions relative to a full-information, full-commitment benchmark. We demonstrate that if credit is part of a much larger information-constrained (or limited-commitment) incentive scheme, then input use may very well be distorted away from the first-best. Further, households and firms, in certain well-defined circumstances, may, at the true interest rate or opportunity cost of credit, desire to borrow more (or less) than the assigned level of credit. In other, more constrained, contractual regimes, firms and households would say that they do not want to borrow more (or less), but these regimes are decidedly suboptimal, although the magnitude of the loss does depend on parameter values. We conclude with empirical methods that, in principle, could allow researchers armed with enough data to estimate parameters and distinguish regimes. Researchers then could see if firms and households are truly constrained and, if so, what the welfare loss might be.