Κοίλες και οιονεί κοίλες συναρτήσεις
Πεσλή, Στυλιανή Κ.
Concave functions play a role in economic theory similar to the role that homogeneous functions play. Both classes arise naturally in economic models –homogeneous functions as demand functions, concave functions as expenditure functions. Profit functions and cost functions are naturally both homogeneous and concave. Both classes have desirable properties for utility and production functions. Both classes have straightforward calculus-based characterizations- homogeneous functions via Euler's theorem, concave functions via a second derivative test. Finally, both classes are cardinal and need to be modified for full use in utility theory. The goal of this dissertation is to understand concave and convex functions more deeply by working three concrete goals: to develop simple calculus-based tests for concavity or convexity, to discover the desirable properties that concave and convex functions have and to see how concave and convex functions arise in economic models.