Economics Assignment: Reduction in Wealth

Added on - 28 May 2020

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a)Reduction in wealth if Mary has bad heath,Loss of wealth If Mary does not have full and fair health insurance, then the reduction in Healthis $80000b)Expected Wealth = (Probability of Mary having Good Health X Wealth when Mary isHealthy) + (Probability of Mary having Bad Health X Wealth when Mary is Unealthy)We have U (W) = W0.5Therefore ,E (W) = 0.95 (90000) + 0.05 (10000)Expected Wealth (Without Insurance) = 86000c)Expected Utility = (Probability that Mary is healthy x Utility of Wealth if Healthy)= 0.95 X 900000.5= 0.95 X 300= 285.0d)Expected Utility = (Probability that Mary is unhealthy x Utility of Wealth if Unhealthy)= 0.95 X 100000.5= 0.05 X 100=5.0e)Expected Utility = (Probability that Mary is healthy x Utility of Wealth if Healthy) +(Probability that Mary is Unhealthy X Utility of Wealth if Mary is UnhealthyExpected Utility = 0.95 X 900000.5+ 0.05 X 100000.5Expected Utility =290
f)The Utility of wealth with certainty is the utility of wealth that is expected when there isinsurance i.e Mary is certain of an income when she has insurance. This Utility wascalculated as 290.Certainty Equivalent Utility = U (W)0.5290 = U (W)0.5Solving the Utility Function, squaring both sides we get,W= $ 84100g)Actuarially Fair Insurance Policy would pay Mary the size of her loss, in case she fallssick. The size of Mary’s loss of wealth is $90,000 - $10,000 if she falls sick.Therefore, the size of loss for Mary is $80,000 i.e Full insurance coverage is 80000. This is themaximum payout. However, Mary may not seek maximum pay outIf Mary has bad health, then probability of pay out is pX Full Insurance Coverage i.e 0.05 X80000.Expected Pay Out or the amount that insurance Company would pay Mary per year is $ 4000.h)Willingness of Mary to Pay is the Utility of the Wealth that Mary is certain to have if shehas Insurance. Let it be denoted as XU (90000- X) = U (90000- X)0.5U (290) = U (90000- X)0.5Squaring Both SidesU 84100= U (90000 –X)Therefore,X = 90,000 – 84100X = 5900.
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