Strictly convex vs. convex and well-behaved preferences in economics

A utility-maximizing consumer has strictly convex, strictly monotonic preferences and consumes two goods, x1 and x2, cach of which has a price of 1. He cannot consume negative amounts of either good. The consumer has an income of m every year. His current level of consumption is (x1^*, x2^*) where x1^* > 0 and x2^* > 0 . Suppose that next year he will be given a grant of g1 ≤x1^* which must be spent entirely on good 1 . (If he wishes, he can refuse to accept the grant.) (a) True or False? If goo

Explain why convex preferences means that "averages are preferred to extremes." | Numerade