A consumer's preferences over the bundles of two goods (x1, x2) are represented by the utility function v(x1, *2) = xx7 . 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(x1, x2) = =Inx, + -In x2? Explain. If your answer is affirmative, use u(x1, x2) for the rest of the 3 question; if not, use v(x1, *2). (5 marks)Consider a price change in x1 from p, = $50 to p'1 = $10, with pz = $30 and m = 1900 being fixed. Calculate the substitution and income effects on x, for the given price change. At this range of price change: Are these goods normal or inferior? Are they ordinary or Giffen? Explain using the income and substitution effects that you calculated. (35 marks)For any p1,P2, and m, calculate the Marshallian demand functions of x, and x2 including the corner solutions if they exist. State the assumptions satisfied by the preferences of this consumer in order to calculate the demand functions