i) The preferences are nondecreasing but not locally nonsatiated. (5 marks) (ii) The preferences are convex but not strictly.

Question 2 (30 marks). (1) Consider a consumer with consumption space X 2 R1 with ratio nal weak preferences : represented by a utility function 'u, : X > R. For each of the following cases give an example either by drawing a neat and well labelled diagram with indifference curves and an in dication of the direction in which preferences are increasing or by explicitly giving a utility function that represents the preferences. That is, you should either draw indifference curves or give a utility function; you don't have to do both. (i) The preferences are nondecreasing but not locally nonsatiated. (5 marks) (ii) The preferences are convex but not strictly. (5 marks) (2) Consider a consumer with consumption space X : REL with a util ity function u : X > R. In each of the following cases give an example of (i) a utility function that is strictly quasiconcave but not con cave. (10 marks) (ii) a utility function that is concave but not strictly quasiconcave. (10 marks)