4.6* In this exercise, we will explore some logical relationships between families of tastes that satisfy different assumptions.

A. Suppose we define a strong and a weak version of convexity as follows: Tastes are said to be strongly convex if whenever a person with those tastes is indifferent between A and B, the person strictly prefers the average of A and B to A and B. Tastes are said to be weakly convex if whenever a person with those tastes is indifferent between A and B, the average of A and B is at least as good as A and B for that person.

a. Let the set of all tastes that satisfy strong convexity be denoted as SC and the set of all tastes that satisfy weak convexity as WC. Which set is contained in the other? We would, for instance, say that WC is contained in SC if any taste that satisfies weak convexity also automatically satisfies strong convexity.

b. Consider the set of tastes that are contained in one and only one of the two sets defined previously.

What must be true about some indifference curves on any indifference map from this newly defined set of tastes?

c. Suppose you are told the following about three people: Person 1 strictly prefers bundle A to bundle B whenever A contains more of each and every good than bundle B. If only some goods ar