Question

In the upcoming year, the income from your current job will be $90,000. There is a .8 chance that you will keep your job and earn this income. However, there is a .2 chance that you will be layed off, forcing you to accept a lower paying job. In this case you income is $10,000. The expected value of your income is thus $74,000. if your utility function has the formula 100I - .0001I^2 determine the risk premium associated with this lottery.

Answer 1

Risk premium is the difference in the amount that the individual is willing to pay for full insurance and the expected loss. Here expected loss is 0.2*(90000 - 10000) = 16000

The most that one can pay for the insurance is the difference between the initial wealth and certainty equivalent. Find the expected utility and the certainty equivalent

Utility is U = 100I - .0001I^2

EU = 0.8*(100*90000 - 0.0001*(90000^2)) + 0.2*(100*10000 - 0.0001*(10000^2)) = 6,750,000

CE is given by

100I - .0001I^2 = 6,750,000

This becomes a quadratic quation

0.0001I^2 - 100I +  6,750,000 = 0

This gives I = 72800.

the maximum individual is willing to pay for full insurance is 90000 - 72800 = 17200

Hence the risk premium is 17200 - 16000 = 1200.