Question 1 True, False, or Uncertain? Justify your answers. (a) (4 marks) If the budget set is finite, completeness is necessary and sufficient for the existence of the mostpreferred bundle(s). (b) (4 marks) Suppose that the consumption set is {A,B,C}. Assume that A f, B, B i A, C i B, and A f, C. This information is sufficient to establish that i is transitive. (c) (4 marks) Assume that a consumption set is finite. If a preference is strongly mono tone and strictly convex, there exists only one most preferred bundle. However, if a preference is strongly monotone and weakly convex, it is possible to have more than one mostipreferred bundle. (d) (4 marks) Angela's preferences over ."L' and y can be represented by a differentiable function U(.'L', y). Consider the function V(.'L',y) : f(U(.L',y)), Where f : R > R is a strictly increasing function. Then the marginal utility of :L' computed from U (I, 3;) must be equivalent to the marginal utility of .'L' computed from V(;'L',y), that is, fly/[Um : MIL/x. Similarly, M'Uy : M'Vy. As a result, :23: : g: : M'RSW. (e) (4 marks) John's utility function is U (L) : ;L', where .L' 2 0. The persunit price of :L' is pm > 0 and the consumer's budget is M' > 0. John will buy 3;\" : to maximise Pr his utility. Question 2 Suppose there are only two goods: Beer and Milk. Jose's preferences over bundles of beer (b) and milk (m) can be represented by the following utility function: 1 if b g m u(b,m) = 0 if m