FSU ECP 4530 - Demand for Private Medical Insurance

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ECP 4530 Weekly Summary Feb 24 Feb 26 Demand for Private Medical Insurance textbook ch 4 Wealth w income y Actual outcome of an event in UNKNOWN uncertainty o Explains why there is a market for insurance Probability of an event is KNOWN Expected value of an outcome o probability of the outcome x value of the outcome o ex Coin Flip Tails I pay you 100 Heads You pay me 50 EV 0 5 100 0 5 50 25 your winnings Prince of Insurance Premium actuarially fair premium loading fee Actuarially fair premium the expected value of the insurance pay out Loading fee includes marketing claims processing fees and capital costs Expected value of loss o probability of loss x size of loss Why do People Buy Insurance Risk loving o Graph C o If risk loss is small you tend to exhibit risk loving behavior especially true for low income individuals o Positive and increasing marginal utility o Graph A o Positive and diminishing marginal utility Risk averse Risk neutral o Graph B o Positive and constant marginal utility Graph A risk averse graph B risk neutral graph C risk loving General illustration of a RISK AVERSE utility function Notations for RISK AVERSE ONLY utility function graph A if the individual is sick W wealth of the individual if he she is sick U Ws utility of the individual is he she is sick B if the individual is healthy Wh wealth of the individual if he she is healthy U Wh utility of the individual if he she is healthy C expected value of the individual Ww expected wealth of the individual U Ww expected utility of the individual D individual is insured for the actuarially fair price Ww wealth when insured for actuarially fair price U Ww utility when insured for actuarially fair price E insured for maximum willingness to pay W w wealth when insured for maximum willingness to pay U Ww utility when insured for maximum willingness to pay EL expected loss maximum loading fee Remember Points A B and C involve risk Points D and E involve no risk Any point on the chord involves risk and is a weighted average Utility gains for RISK AVERSE ONLY individuals from actuarially fair insurance Measured by o Distance between the expected value of utility and the utility if insured o Vertical distance between the chord and the utility function U Ww U Ww Willingness to pay for insurance by RISK AVERSE ONLY individuals Increases with degree of risk aversion Related to probability of loss o Highest with the probability of loss is midrange o Lowest when probability is known 0 0 or 1 0 Increases as size of loss increases Example for RISK AVERSE individual Need to know Utility function U W2 Wealth A Loss if injured B Probability of risk C Probability of being well 1 C a Wealth if healthy injury free A Utility if healthy U W2 U A2 b Wealth if injured sick W A B Utility if injured sick U A B 2 c Expected value of wealth probability of being well income if well probability of being sick income if sick E W 1 C A C A B d Expected value of utility probability of being well utility if well probability of being sick utility if sick E U 1 C A2 C A B 2 e Actuarially fair price of full coverage insurance expected value of loss probability of loss size of loss E L C B to check your math take wealth if healthy and subtract expected value of wealth f Wealth if risk adverse individual purchases full coverage insurance at actuarially fair price Sick income if healthy expected value of loss actuarially fair price of insurance loss if injured loss if injured expected value of wealth Well income if healthy expected value of loss actuarially fair price of insurance expected value of wealth g Utility if risk adverse individual purchases full coverage insurance at actuarially fair price U wealth if insured for actuarially fair price expected value of wealth 2 h Will this risk adverse individual buy insurance at the actuarially fair price Yes if the individual gains more utility Compare utility with risk and with no risk i What is the most this individual is willing to pay for full coverage insurance In other words what premium price of insurance leaves this individual with his her expected value of utility U W2 1 C A2 C A B 2 W2 find the square root of both sides W subtract this W from income if well A to find premium REMEMBER Whether or not a person is worse or better off is based on utility NOT income wealth


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FSU ECP 4530 - Demand for Private Medical Insurance

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