A consumer's preferences over the bundles of two goods (x1, x2) are represented by the utility function v(x1,*2) = x x2 . The income he allocates to consume these two goods is m. The prices of the two goods are p, and p2, respectively. a) Can these preferences be represented by the utility function u(x], x2) = =Inx, + -In x,? Explain. If your answer is affirmative, use u(x], x2) for the rest of the question; if not, use v(x1, x2). (5 marks) b) Determine the monotonicity and convexity of these preferences and briefly define what they mean. (10 marks) c) Determine and interpret the marginal rate of substitution (MRS(x], x2)) between the two goods for this consumer at the bundle (x1, X2) = (4,2). (10 marks)