def. Monotonic Transformation. A transformation of a Utility Function is one that preserves the order of preferences of the original function. i.e., is a monotomic transformation of utility function iff:

Simple monotonic transformations:

  • Adding or subtracting a constant
  • Multiplying or dividing by a positive constant
  • For always positive functions, exponentiation to a constant
  • For always positive functions, logarithm to a constant base

thm. monotonic transformation equivalence. If one utility function is a monotonic transformation of another, you may treat it for all practical purposes as the same utility function.