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1. Prove that if the consumer is risk averse, her acceptance set, as illustrated
in Figure 11.2, must be a convex set.



4. A consumer has an expected utility function of the form u(w) = √w.
He initially has wealth of $25. He has a lottery ticket that will be worth $75 with
probability 0.2 and will be worth $0 with probably 0.8. What is his expected utility?
What is the lowest price that he is willing to accept in order for him to sell his ticket?

5. There are two lotteries, X and Y .
X =2/3 ◦ ($10) ⊕1/3 ◦ ($20)
Y =1/3 ◦ ($5) ⊕5/9 ◦ ($15) ⊕1/9 ◦ ($30).
Show that a risk-averse consumer prefers X to Y.