# Suppose that an individual has a utility function U(c) = c 1=2 : They have 400 dollars….

Suppose that an individual has a utility function U(c) = c
1=2
: They have 400
dollars. With probability 0.1 they get sick, which results in complete loss of their wealth
(their wealth becomes 0.
a. What is their expected wealth? What is their expected utility? How much would
they being willing to pay for insurance which would fully cover the cost of being sick if they
become ill?
b. Now suppose there is a second individual who has the same wealth, and gets sick to
a similar degree (loses all of their money if they get sick), but who gets sick with probability
.5. What is their expected wealth? What is their expected utility? How much would
they being willing to pay for insurance which would fully cover the cost of being sick if they
become ill?

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Health Economics HWAssignment # 2 1. Suppose that an individual has a utility function U(c) = c1=2: They have 400 dollars. With probability 0.1 they get sick, which results in complete loss of their wealth (their wealth becomes 0. a. What is their expected wealth? What is their expected utility? How much would they being willing to pay for insurance which would fully cover the cost of being sick if they become ill? b. Now suppose there is a second individual who has the same wealth, and gets sick to a similar degree (loses all of their money if they get sick), but who gets sick with probability .5. What is their expected wealth? What is their expected utility? How much would they being willing to pay for insurance which would fully cover the cost of being sick if they become ill? c. Suppose an insurance company cant tell the di¤erence between individuals 1 and individual 2. What is the expected cost of insuring individual 1 (hint how much wealt does the insurance company expect to lose)? The expected cost of insuring individual 2? If the insurance company believes that individual 1 and individual 2 are equally likely to appl for insurance, what is the expected cost of insurance (hint: just use the law of expected value one more time)? d. If the insurance company o¤ers the averaged plan at cost (which you just calculated), are both individuals willing to purchase the plan? Is this an example of adverse selection, or moral hazard, or neither? Is the equilbrium a pooling equilbrium or seperating equilbrium. 2. Suppose you are interested in assessing the value of a statistical life for individuals. You nd a dataset on risk and wages. You consider running the following OLS regression. wagesi = 0 + 1fatal_riski + ui: Fatal_risk ranges from 0 to 100 in this example. a. Theoretically, do we expected 1 to be positive or negative? 1
b. Suppose 1 = 25; 000 (with a standard error of 5,000). What is the 95 %condence interval for 1? c. Calculate the VSL by using 1 and the…

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