Winter 2008 - Newhouse's Class - Problem Set 5

Winter 2008 - Newhouse's Class - Problem Set 5 - Econ 171...

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Econ 171 Winter 2008 Problem Set 5 1. Lottery A is ($101, 0.71; $100, 0.03; $0, 0.26). Lottery B is ($100, 0.74; $0, 0.26). a. Show that A first order stochastically dominates B . A ’s cdf is always below or equal to B ’s. b. Illustrate how K&T’s editing process could lead an individual to choose B over A . First remove the common component ($0, 0.26) which leaves us with: A = ($101, 0.71; $100, 0.03) and B = ($100, 0.74) Now round the ($100, 0.03) probability to 0 in lottery A . A = ($101, 0.71) and B = ($100, 0.74) Finally round the ($101, 0.71) outcome to $100 in lottery A . A = ($100, 0.71) and B = ($100, 0.74) Based on this final edited lottery B will be preferred to A . (Note: You could find other possible ways to get the same result.)
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2. Consider Anne’s decision whether or not to buy insurance. Specifically she can purchase a policy that costs $100 per month and provides full coverage in the event of an accident. The probability of an accident in a given month is 0.01. If there is an accident and Anne is uninsured it will cost her $5000. a. Suppose Anne simply maximizes her expected payout. Will she choose to buy insurance? E(payout|purchase insurance) = – 100 E(payout|no insurance) = 0.01(– 5000) = – 50 She won’t buy the insurance because her expected payout is higher if she doesn’t. b. Suppose Anne maximizes expected utility. Describe the condition under which she’ll purchase insurance. She’ll purchase insurance if her risk premium for the uninsured situation is at least $50. (Alternatively she’ll purchase it if her certainty equivalent for the uninsured situation is less than or equal to – $100.) c.
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This note was uploaded on 04/23/2008 for the course ECON 171 taught by Professor Newhouse during the Winter '07 term at UCSD.

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Winter 2008 - Newhouse's Class - Problem Set 5 - Econ 171...

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