4) 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.
Q1) a) in one year from now, expected wealth
EW = .9*100,000 + .1*50,000
= 90,000+5000
= 95,000
b) in full insurance case, in bad state, insurance company provides the entire loss suffered by insured person
When a firm breaks even, it's expected profit from selling insurance is zero
So, net expected profit = net expected loss
If M is premium, with p = good state Probability, no loss happens, so firm pays nothing .
expected profit = pM
In bad state, with Probability (1-P), company pays B
So profit = (M-B)
So, zero expected profit
When, pM = (1-P)(M-B)
pM = M-B - pM + pB
M = (1-p)B
premium = 50,000*.1
= $ 5000
c) the maximum willingness to pay to avoid risk in bad state
= Initial wealth - certainty equivalent of risky situation
= 100,000 - 85,000
= 15,000
4) A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his...
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. (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...
4) 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...
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...
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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4) 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...
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