Problem 2 [2/pt] A household H consists of n members, each with complete, transitive, monotonic and G-continuous preferences, where G-continuity is defined below. For any two bundles x and y, define #{x >; y} as the number of household members who strictly prefer bundle x to bundle y. Define H's preferences as follows (as in a homework assignment): x> Hy if # {x>;y} > #ly >: x} and . X ~Hy if#{x >; y) = #{y >; x}. Definition: Preferences > satisfy G-continuity if for any two bundles x > > 0 and y, there exists a non-negative real number a such that a . X ~ y. (a) [15pt] Suppose that H consists of two members, A and B. Do preferences ># satisfy G-continuity? If you answer yes, provide a proof. If you answer no, give a counter-example. (b) [12pt] Suppose that H consists of four members, A, B, C and D. Do prefer- ences ># satisfy G-continuity? If you answer yes, provide a proof. If you answer no, give a counter-example