Question

A risk averse consumer has a car valued at $10,000. There is a 10% probability that...

A risk averse consumer has a car valued at $10,000. There is a 10% probability that the car will be stolen this year, in which case the value of the car for the consumer is zero. For a premium $y, the consumer can buy an insurance plan that would replace the car if stolen.
The consumer has utility ? ? = ?
a) What is the maximum insurance premium $y the consumer would be
willing to pay?
b) What is the risk premium the consumer is willing to pay?
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Homework Answers

Answer #1

a) utility function=x,Probable value of loss=10%*10000=1000

Probable Utility=0.9*10000+0.1*0=9000 which corresponds to value of 9000

Now, Insurance premium+ value corresponding to probable utility without insurance= Value when insured

Hence,Maximum insurance premium=Value when insured- value corresponding to probable utility without insurance=10000-9000=1000

b) Probable utility without insurance =utility of (Probable value without insurance-Risk Premium)

Probable value without insurance=10000-0.1*10000=9000

Probable utility without insurance as calculated in a=9000 so, 9000=utility(9000-RP), 9000=9000-RP

Hence, RP(Risk Premium)=0

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