ECON

Abstract

well defined so long as 0 < β <1. Since the above function is a pointwise limit of linear combinations of concave functions with positive weights, the above is also concave. Finally, since the expectation operator is linear, it keeps the concavity, too. This proves that the objective function is concave over positive sequences of consumption. ii) Conditions (2) through (4) define subsets of the space of sequences. The intersection of all these subsets is the feasible set. Intersections of convex sets are convex. Conditions (3) and (4) define sets by linear equality or inequality constraints, which are automatically convex. We are going to show the convexity of the set which satisfies (2) for a given t.