Midterm 2005 - Answers

# Alex is evaluating his various investment options and

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Alex is evaluating his various investment options and has a utility over wealth given by  ) ln( ) ( w w U = A. Calculate the expected net  payoff from investing in umbrellas. Net payoff = 0.6(15-25) +0.4(35-25) = -2. B. Would Alex invest in umbrella only? No:  the expected value is negative and her utility function indicates that she is risk  averse  -- or compare expected utilty with utility from not investing. EU(investment in umbrellas) = 0.6ln(15-25+16) + 0.4 ln(35-25+16) = 2.375. EU(No investment) = ln(16) = 2.77. So don’t invest. C. Would Alex invest in ice-cream only? EU(ice-cream only) = 0.6ln(100-40+16) + 0.4ln(25-40+16) = 2.598 EU(No investment) = 2.77 So don’t invest. D. Which is Alex’s optimal investment plan:   EU(invest both) = 0.6ln(100-40+15-25+16)+0.4ln(25-40+35-25+16) = 3.47 Since it is higher than EU(ice cream), EU(umbrella) and EU(no investment), invest in both is  the best investment plan. E.  Explain why umbrellas are or are not part of Alex’s investment plan, taking into account  your answer to part (A). The gains from diversification make the investment in umbrellas worthwhile, even though the expected profit from the investment in umbrellas is negative (as calculated in part a). The profit from umbrellas is negatively correlated with the profit from ice-cream. ["diversification"or "acts like insurance" ] 17

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F.  Suppose now that umbrellas are not available, and that the government is considering a  subsidy to the investment in ice-cream.  Provide an equation that gives the minimum subsidy  necessary to induce Alex to invest in ice-cream. Lets say subsidy =s, then invest in ice-cream only if:  EU(investment in ice-cream with subsidy)   EU(no investment) 0.6 ln( w - 40 + s + 100) + .4 ln (w - 40 + s + 25)   ln(w) = 2.773. 18
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• Spring '09
• Brian
• Marginal product, The Profit, perfect price discrimination, Ratna Shrestha Ratna Shrestha Stephen Meyer Ralph Winter Ratna Shrestha Timothy Beatty, two­part tariff

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