A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year.
a. (5) What is the consumer’s expected wealth one year from now?
b. (5) An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? Explain.
c. (5) Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy? Explain.
a) wG = 100,000 , wB = 50,000
PG = .9, PB = .1
Expected wealth = .9*100,000 + .1*50,000
= 90,000+5,000
= $ 95,000
b) Actuarially Fair insurance premium, M = Loss in bad state*(probability of bad state)
L = wG-wB = 50,000
Probability of loss = .1
M = .1*50,000
= $ 5000
C) so Maximum possible premium = initial wealth- CE
CE : income at which individual is Indifferent between gamble & not playing
= 85,000
So = 100,000-85,000
= $ 15000
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth...
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. (5) What is the consumer’s expected wealth one year from now? b. (5) An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? Explain. c. (5) Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the...
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer’s expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? Explain. c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain...
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A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. (5) What is the consumer's expected wealth one year from now? b. (5) An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? Explain. c. (5) Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the...
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