The question is as follows

Problem 2: Lexicographic preferences, G-continuity and preference representation In this problem we will look at a famous example of discontinuous preferences, called lemieogmphc preferences. Suppose that any two bundles ($1,:L'2) and (91, 92) are evaluated as follows: 1. The bundle that has more of good 1 is better, regardless of the amount of good 2. 2. If the amount of good 1 is the same, the bundle that has more of good 2 is better. For example, bundle x = (2,1) is better than bundle y = (1,100) because it contains more of good 1 and bundle z = (2, 200) is better than x because it contains the same amount of good 1, but more of good 2. (a) Suppose that any nonnegative quantities of good 1 and good 2 can be consumed. Prove that the preferences described above are not Gcontinuous. (b) Suppose that the only bundles that can be consumed are (1,1), (1,100) and (3,5). With this restriction, can lexicographic preferences be represented by a utility function