HW_10_Part_I

HW_10_Part_I - →∞ c γ(There are several ways to do...

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Economics 11, Winter 2010; HW Assignment #10 - Part I Not to be turned in Some of these problems will require a calculator. 1. Shirley is a trader for Bear Stearns (an investment bank). If next year is Good, her income will be W G = 1 , 000 , 000; if next year is Bad, her income will be W B = 200 , 000. She estimates that Good and Bad years have equal probability π G = π B = 1 / 2. Shirley’s utility function is U ( x, y ) = π G u ( x ) + π B u ( y ) where x = wealth in the Good state, y = wealth in the Bad state. Find Shirley’s certainty equivalent for her risky income: (a) if u ( w ) = w 1 / 2 (b) if u ( w ) = log w (c) if u ( w ) = - 1 /w 3 2. Many other traders work at Bear Stearns, have the same risky income and face the same probabilities as Shirley and have the same form for utility functions – but with different functions u . (a) Find the certainty equivalent c γ for a trader with u ( w ) = w 1 - γ 1 - γ where γ > 0 , γ 6 = 1. (Your answer will involve γ .) (b) Larger values of γ correspond to being more risk averse. Find lim γ
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Unformatted text preview: →∞ c γ (There are several ways to do this problem; depending on how you do it, you might find it useful to use L’hospital’s rule.) 3. Tammy owns a car worth $10,000; in addition to her car, she has wealth of $40,000. Because she lives in a bad neighborhood, the probability of her car being stolen is π B = . 1 (so the probability of her car not 1 being stolen is π G = . 9. Tammy’s insurance company offers to sell her as much car insurance as she wants at the (unfair) price of $0.11 per dollar of insurance. (Remember that this gives implicit/state prices p G = . 89 , p B = . 11.) Tammy’s utility function is U ( x, y ) = π G u ( x ) + π B u ( y ) where x = wealth if her car is not stolen, y = wealth if her car is stolen. How much insurance should Tammy buy (a) if u ( w ) = w 1 / 2 (b) if u ( w ) = log w (c) if u ( w ) =-1 /w 3 2...
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This note was uploaded on 04/01/2010 for the course ECON 180052110 taught by Professor Mcdevitt during the Winter '09 term at UCLA.

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HW_10_Part_I - →∞ c γ(There are several ways to do...

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