Question 1 True, False. or Uncertain? Justify your answers. (a) (4 marks) If the budget set is nite. completeness is necessary and suicient for the existence of the mostrpreferred bundle(s). (b) (4 marks) Suppose that the consumption set is {24.3.0}. Assume that A t B. B i: A. C i B, and A fl 0. This information is sufcient to establish that 'r; is transitive. (c) {4 marks) Assume that a consumption set is nite. If a preference is strongly monor tone and strictly convex5 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 mostpreferred bundle. (d) (4 marks) Angela's preferences over 9: and y can be represented by a differentiable function U(a:,y). Consider the function V(:r.. y) = f(U(m, 34)), where f : IR } R is a strictly increasing fulnction. Then the marginal utility of a: computed from U(:r. y) must be equivalent to the marginal utility of a: computed from V(I,y), that is= MU, : MVI. Similarly, MUy : ny. As a result, g: : % : MRSIQ. (e) {.4 marks) John's utility function is U(:c) = a:, Where :r; 2 0. The perunit price of a; is p: > 0 and the consumer's budget is [M > 0. John will buy 1"\" : E to maximise Pr his utility