EconS 301 – Intermediate Microeconomics Review Session #13 ...

With this utility function both lotteries have the same expected value and same expectedutility. In general, when two lotteries have the same expected value and differentvariances, a risk-neutral decision maker will be indifferent between the two lotteries, i.e.,will have the same expected utility for both lotteries. Thus, this utility functioncorresponds with a risk-neutral decision maker.d)Expected Utility 0.90(0 500) 0.10(400 500)Expected Utility 306,000AA2 2Expected UtilityB0.50(30 500) 0.50(50 500)Expected Utility 291,700B2 2With this utility function the decision maker has a higher expected utility for Lottery Athan for Lottery B. In general, when two lotteries have the same expected value butdifferent variances, a risk-loving decision maker will prefer the lottery with the highervariance, Lottery A in this case.Exercise 15.12 Suppose you are a risk averse decision maker with a utility function given by 110 , where I denotes your monetary payoff from an investment in thousands. You are considering aninvestment that will give you a payoff of $10,000 (thus, I=10) with probability 0.6 and a payoff of $5,000(I=5) with probability 0.4. It will cost you $8,000 to make the investment. Should you make theinvestment? Why or why not?Answer:Let’s simply compare the payoff of not making the investment versus the payoff of making theinvestment…If you do not make the investment, your utility is: 1 – 10(8) -2 = 0.84375If you make the investment, your utility is:(0.6)(1 – 10(10) -2 ) + (0.4)(1-10(5) -2 )= (0.6)(0.9) + (0.4)(0.6) = 0.78Since the expected utility from the investment is less than the utility from not making the investment, youshould not make the investment.Exercise 15.18 Consider a market of risk-averse decision makers, each with a utility function √.Each decision maker has an income of $90,000, but faces the possibility of a catastrophic loss of$50,000 in income. Each decision maker can purchase an insurance policy that fully compensateshere for her loss. This insurance policy has a cost of $5,900. Suppose each decision makerpotentially has a different probability q of experiencing the loss.a) What is the smallest value of q so that a decision maker purchases insurance?4