This is a question of Preferences and Utility.

Tom has preferences that can be described by the utility function U = U(x, y) = ax + By, a > 0, B > 0, x > 0, y > 0, (x + y) = 0 Tom Junior's preferences can be described by a transformation of Tom's utility function G(U), where G(U) = (U - 36) 3 . Tom Ill's (i.e. Tom's grandson's) preferences can be described by a transformation of Tom's utility function H(U), where H(U) = (U - 18) 4 - 4a. Is G(U) a positive monotonic transformation? Show your work. What does that imply for Tom and Tom Jr's preferences? Explain why. 4b. Is H(U) a positive monotonic transformation? Show your work. What does that imply for Tom and Tom III's preferences? Explain why