Suppose an individual has a utility function over lotteries given by Tl U() I U((fL'1, ' ' ' 7 $77,)7 (p17 ' ' ' 71971)) : Zpii i=1 a. Show that this utility function represents preferences that are (1) complete, (ii) transitive, (iii) continuous and (iv) satisfy the axiom of independence. b. Determine Whether these preferences are riskloving, riskneutral or riskaverse. c. Derive the Risk premium, certainty equivalent and the ArrowPrat measure of risk aversion. d. Propose a utility function that satises completeness and transitivity, but not continuity or the alxiom of independence