Question

Harry Potter faces a probability of 0.5 that his boss, Severus Snape, will fire him. If he is fired, Harry will remain unemployed for a year, earning nothing. His yearly salary is $36,000.

(a) If Harry prefers earning $18,000 with a guarantee of employment to his current situation of receiving $36,000, then what can we say about Harry’s preferences toward risk – risk-neutral, averse, or loving?

(b) Now suppose that he would be just willing to take a pay cut of $20,000 per year (from his current income of $36,000) in exchange for a guarantee of not being fired; what is his risk premium?

(c) What might be a reason why employers, like Severus Snape, would choose not to offer an employment guarantee like this?

Answer 1

Harry Potter faces a probability of 0.5 that his boss, Severus Snape, will fire him. If he is fired, Harry will remain unemployed for a year, earning nothing. His yearly salary is $36,000.

(a) If Harry prefers earning $18,000 with a guarantee of employment to his current situation of receiving $36,000, then what can we say about Harry’s preferences toward risk – risk-neutral, averse, or loving?

Yearly Earning = $36,000

Probability 50% or 0.5

The expected value of Harry's earnings is 36,000 * 0.5 = $18,000.

Because Harry prefers getting the expected value for sure to taking the risk, he must be risk-averse.

A risk averse is an investor who prefers lower returns with known risks rather than higher returns with unknown risks.

(b) Now suppose that he would be just willing to take a pay cut of $20,000 per year (from his current income of $36,000) in exchange for a guarantee of not being fired; what is his risk premium?

Risk Premium = Expected Value – Certainty Equivalent.

The Certainty Equivalent is the amount of money Harry would be willing to take for sure that would give him the same expected utility as the risky gamble. Since Harry is willing to take a $20,000 pay cut, his Certainty Equivalent is $16,000. Therefore:

Risk Premium = Expected Value – Certainty Equivalent

$18,000 - $16,000 = $2,000

(c) What might be a reason why employers, like Severus Snape, would choose not to offer an employment guarantee like this?

The reason that the boss would not decide to offer the definite employment is that once Snape guarantees Harry $16,000 no matter what, Harry might not feel to work hard. The panic of being fired is a strong incentive. Once Snape gives up that inducement, Harry may be likely to avoid his tasks. We call the change of Harry's effort, or his actions, in reaction to the offer of insurance (or reduction of risk) - moral hazard.