Risk Neutral and Risk Loving

Consider two hypothetical jobs. 

Job A provides a guaranteed annual income of $40,000. 

Job B offers an uncertain income of $60,000 or $20,000, each with a 0.5 probability, resulting in an expected income of $40,000.

A risk-neutral person is indifferent between a guaranteed income and an uncertain income with the same expected value. They experience a constant marginal utility of income. 

For example, Nancy gets a utility of 28 units from Job A.

Her expected utility from Job B is 14, weighted by its probability of 0.5, added to 42, weighted by its probability of 0.5. She gets the same utility of 28 units from both jobs, reflecting her risk-neutrality.

In contrast, a risk-loving person prefers an uncertain income over a guaranteed income with the same expected value. They experience an increasing marginal utility of income. 

For example, Sarah gets a utility of 32 units from Job A and an expected utility of 42 from Job B. She chooses Job B, reflecting her risk-loving attitude.