Question: 3. (15 points) In class , and in the lecture notes you have seen the definition of homothetic preferences. Suppose the rational preference relation _

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 o > 0, and any r E X, u(ox) = au(x)

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