Suppose the utility function U : R 2 ++ R+, given by U(x, y) = xy, represents Matt's preferences.1 Hence, for any a > 0, the utility functions (i) V (x, y) = 1 2 ln(xy) + a; (ii) V (x, y) = xy a ; and (iii) a xy also represent the same preferences.

True, False, or Uncertain? Justify your answers.

(d) (6 marks) Suppose the utility function U : R, R, given by U(z,y) = /T, ! Hence, for any a > 0, the utility functions (i) represents Matt's preferences. V(z,y) = 3ln(zy) + a; (i) V(z,y) = Z; and (iii) e" also represent the same preferences