please only do: if you can teach explain steps Prediction markets allow traders to bet on future events. One prediction market that isparticularly active this season involves betting on the winner of the U.S. presidential election.Thus, for example, if one trader buys one share of "Obama to win" from another trader,then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does notwin the seller pays nothing; either way, the seller keeps the money paid by the buyer for thepurchase of the share.(a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x) =In(x + 1) and initial wealth 4. Leila believes that Obama will win with probability 1/2.Find the highest price p, at which she is willing to buy at least one share.Solution: The price pu solveswhich implies thatand therefore,This equation has solutionsIn(5-ps)+ln(6-ps) = In 5,((5 – Ps)(6 — Ps) = 5,P-11p+50.Pb=111012Since the price must clearly be less than 1 for Leila to buy, we obtainPb=11-1012(b) How does ps compare to the lowest price p, at which Leila is willing to sell at least oneshare? Are they same? Explain.Solution: Since Leila is risk averse, she will only agree to buy or sell if doing so yieldsa positive expected value. Therefore, we must have p, > 1/2> p (and in particular,Ps > Pb).) How does p, compare to the lowest price p, at which Leila is willing to sell at least oneshare? Are they same? Explain.Solution: Since Leila is risk averse, she will only agree to buy or sell if doing so yieldsa positive expected value. Therefore, we must have p, > 1/2 > Ps (and in particular,Ps > Pb).) Vadim is more risk averse than Leila. He also believes that Obama will win with prob-ability 1/2. How does the highest price at which he is willing to buy at least one sharecompare to po (i.e. to the corresponding price for Leila)? Prove your answer.Solution: Let p denote the highest price at which Vadim is willing to buy, and let L(p)denote the lottery associated with buying one share at price p. For Leila, the certaintyequivalent of the lottery L(pt) is 4. Since Vadim is more risk averse than Leila, thecertainty equivalent of L(ps) for him is less than 4. But the certainty equivalent of L(ps)for Vadim is 4, and therefore p < Pb-

Prediction markets allow traders to bet on future events. One prediction market that is particularly active this season involves betting on the winner of the U.S. presidential election. Thus, for example, if one trader buys one share of "Obama to win" from another trader, then if Obama wins the election the seller pays 1 dollar to the buyer, and if Obama does not win the seller pays nothing; either way, the seller keeps the money paid by the buyer for the purchase of the share. (a) Leila is an expected utility maximizer with von Neumann-Morgenstern utility u(x)= In(+1) and initial wealth 4. Leila believes that Obama will win with probability 1/2. Find the highest price p, at which she is willing to buy at least one share. Solution: The price p solves In(5-ps)+In(6-ps) = In 5,