A set S is a convex cone if and only if 1. S S for every

A set S is a convex cone if and only if
1. αS ⊆ S for every α ≥ 0
2. S + S ⊆ S
Convex cones arise naturally in economics, where quantities are required to be nonnegative. The set of nonnegative prices vectors is a convex cone Rn and the production possibility set is often assumed to be a convex cone (example 1.102).