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22 August, 23:09

lizabeth, the manager of the medical test firm Theranos, worries aboutthe firm being sued for botched results from blood tests. If it isn't sued, thefirm expects to earn profit of $120, but if it is successfully sued, its profit will beonly $10. Elizabeth believes that the probability of a successful lawsuit is 20%. If fair insurance is available and Elizabeth is risk averse, how much insurancewill she buy? (Hint: Assume that Elizabeth starts with a wealth ofwand shebuys insurance coveringx≤ (120-10) = 110 of her loss. Write down herexpected utility as a function ofxand then take a derivative with respect toxto find the optimal insurance. If you want more hints, have a look at the secondinsurance problem solved in the lecture notes.)

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  1. 23 August, 01:23
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    The value of variance is '0' at full insurance while expected profit therefore the individual will buy insurance $100

    Step-by-step explanation:

    Given that:

    Elizabeth, the manager of the medical test firm Theranos, worries about the firm being sued for botched results from blood tests.

    Earn Profit - $120

    Successfully sued Profit - $10

    Probability - 20% - 0.80

    so that above data we shown in below table

    Profit Probability

    120 0.08

    10 0.08

    so that expected profit & variance under this situation are

    expected profit = (120) (0.08) + (10) (0.80)

    = 96+8

    =104

    expected profit = 104

    Variance = (120-104) 2 (0.08) + (10-104) 2 (0.08)

    = (256) (0.08) + (8836) (0.08)

    = 9116.8

    Variance = 9116.8

    Further it is given that the individual is risk averse and is offered fair insurance since the probability loss is 20% so the fair insurance simples a premium of 0.08 for each dollar insurance coverage

    so it is required to be determine how much insurance individual will buy

    A fair insurance implies that the amount of insurance (coverage) bought has no impact on the expected values of individuals expected profit, but a higher insurance implies a lower variance

    A lower variance is desired by a risk average individuals

    Therefore in this a risk average individual will purchase full insurance because a full insurance would mean that the variance expected profiles will be minimized without any reduction in expected profit.

    The individual faces a potential loss of 100 hence a full insurance would be an insurance of 100

    since the probability loss is 20% the fair insurance implies a premium of 0.20 for each dollar of insurance

    premium of 22 = (0.02*100) for full insurance

    so individual buys full insurance, than she faces the following below table

    Profit probability

    104 (120-22) 0.98

    104 (10-22+100 0.20

    The expected profit variance

    expected profit (104) (0.98) + (104) (0.20)

    = 101. 92 + 20.8

    =104

    Variance (104-104) 2 (0.98) + (104) 4 (0.20)

    = (0) 2 (0.98) + (104-104) 2 (0.20)

    (0) 2 (0.98) + (0) 2 (0.20)

    = 0+0

    = 0

    As shown above the value of variance is '0' at full insurance while expected profit therefore the individual will buy insurance $100
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