Let W represents an individual’s annual earned income and U(W) = (W/10) 0.5 is t
ID: 1202649 • Letter: L
Question
Let W represents an individual’s annual earned income and U(W) = (W/10)0.5 is this individual’s von Neumann-Morgenstern utility index (or utility function) . This individual earned income is $49,000. This individual faces the prospect of a 20% chance of needing health care, with a price tag of $13,000. Assume this person is risk averse. Also assume that the insurance company has only claim costs and that administrative costs are $0. The maximum health insurance premium this individual is willing to pay is what number? (Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands). Show all steps.
Explanation / Answer
von Neumann-Morgenstern utility index (or utility function) shows that when a consumer is faced with a choice of items or outcomes subject to various levels of chance, the optimal decision will be the one that maximizes the expected value of the utility (i.e., satisfaction) derived from the choice made. Expected value is the sum of the products of the various utilities and their associated probabilities. The consumer is expected to be able to rank the items or outcomes in terms of preference, but the expected value will be conditioned by their probability of occurrence.
Since individual earned income is $49,000.
Utility function is U(W) = (W/10)0.5 = (49000/10) * 0.5 = $2450
Individual faces the prospect of a 20% chance of needing health care, with a price tag of $13,000.
Hence maximum health insurance premium this individual is willing to pay is = U(W) + (13000 * 0.2)
= 2450 + 2600 = $5050
Answer is $5050
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