Suppose an individual has the following utility function defined over wealth: U

Question

Suppose an individual has the following utility function defined over wealth: U = U(wealth). The individual has an initial wealth level of $20,000.

A new drug has been developed that is effective in preventing heart attacks. Taking the drug reduces the chance of a heart attack to 10%, but the loss associated with the attack increases to $10,000.

a) What is the expected loss?

b) What is the maximum amount this individual is willing to pay for insurance against a heart attack?

c) What is the risk premium?

Explanation / Answer

U = W^1/2

NO Heart Attack: W = 20,000 ,So U = 141.421
HeartAttack : W = 1000, So U = 100

Probability of no Heart Attacks = 0.90 and of heart Attack is ).10

So calculating Expected utility = 0.90* 141.421 + 0.10*100

= 137.2789

Putting this expected utility in Utility fn to find W

W = (137.27)^2

= 18,845.49

So 20000 - 18,845.49 =1154.50 is the maximum amount individual is willing to pay as utility is same for this level.

Hence the risk premium will be 1154.50 .

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