We define and explore no-upward-crossing (NUC), a condition satisfied by every parameterized family of distributions commonly used in economic applications. Under smoothness assumptions, NUC is equivalent to log-supermodularity of the negative of the derivative of the distribution with respect to the parameter. It is characterized by a natural monotone comparative static and is central in establishing quasi-concavity in a family of decision problems. As an application, we revisit the first-order approach to the moral-hazard problem. NUC simplifies the relevant conditions for the validity of the first-order approach and gives them an economic interpretation. We provide extensive analysis of sufficient conditions for the first-order approach for exponential families.
- first-order approach
- moral hazard
ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)