G E G U G P N B G O E https://moodle.co._. G G 3. (15 points) In class , and in the lecture notes you have seen the definition of homothetic preferences. Suppose the rational preference relation ~ is continuous, monotonic (may be weakly monotonic) and homothetic. Show that ~ is represented by a utility function that satifies, the following: for any a > 0, and any x E X, uax) = au(I)