Definitions
The twin notions of concavity and convexity are used widely in economic theory and are also central to optimization theory. A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point. These concepts are illustrated in the following figures.
Here is a precise definition.
definition f be a function of a single variable defined on an interval. Then f is
- concave if every line segment joining two points on its graph is never above the graph
- convex if every line segment joining two points on its graph is never below the graph.
