Home > Choice under uncertainty, Micro concepts > Risk premium and insurance

February 27, 2012

If somebody is risk averse then they are willing to pay a risk premium in order to avoid the risk – usually in order for someone else to bear the risk in the form of insurance.

Consider the case where a person has a utility function of $U=10W^{0.3}$ where U signifies utility and W signifies wealth in £. The more wealth they have, the more utility they have so the happier they are.

Say they start with wealth of £2000. They own a machine that has a 10% chance of breaking down in a particular time period. If it breaks down it will cost £800 to repair it.

There are two possible outcomes here, a good outcome where the machine doesn’t break down and the person has wealth of £2000, or a bad outcome where the machine breaks down and they have £1200. We can use the utility function to calculate the amount of utility in the respective states:
Good outcome: U = 97.793
Now if we went back into the original utility function to find what wealth corresponds to a utility level of 96.404, we get $96.404=10W^{0.3} \Rightarrow W = 1906.838$.