Y6

Question B2 Consider a consumer whose consumption set is X = R4. a) Define a quasi-concave utility function u() on the consumption set X = R4. [5 marks] b) Show that a utility function () that represents a rational preference relation > on the consumption set X = R4 is quasi-concave if and only if the preference relation convex. is [5 marks] c) Show that the Walrasian budget set B (p, w) is convex. [5 marks] c) Suppose that a consumer optimally chooses a consumption bundle from her budget set B(p, w), given her wealth w and the price vector p > 0. Show that if the consumer's utility function is strictly quasi-concave, then this choice problem has at most one solution. [5 marks]