We revisit the first-order approach to the moral hazard problem. Our fundamental claim is that in well-behaved problems, a condition we term No Upward Crossing (NUC) holds. We show how NUC facilitates analysis by both simplifying the relevant conditions for the validity of the first-order approach and giving them an economic interpretation. We provide extensive analysis of sufficient conditions...

The rate of upward creeping in negatively geotropic rats aged 13 to 14 days is a function of the gravitational stimulus. The rate of upward movement on the creeping plane, like the angle of orientation, is directly proportional to the logarithm of the gravity component. The variability in the speed of creeping decreases in proportion to the logarithm of the gravitational effect. When weights ar...

in this paper, given a poset $(x,leq)$, we introduce some  drifts on a groupoid $(x,*)$ with respect to $(x,leq)$, and we obtain several properties of these drifts related to the notion of $bin(x)$. we discuss some connections between fuzzy subalgebras and upward drifts.