20.6: Risk Neutral and Risk Loving

Individuals make decisions based on their preferences toward risk. A risk-neutral person has constant marginal utility of income. This means that each additional unit of income provides the same increase in satisfaction. Suppose two jobs have the same expected income. However, one job provides a fixed salary which is certain, while the other offers an uncertain salary. A risk-neutral person values both options equally because their total expected utility from each is the same. Therefore, they remain indifferent between the two.

In contrast, a risk-loving person has increasing marginal utility of income. This means that each additional unit of income provides a greater increase in satisfaction than the previous one. Suppose two jobs have the same expected income. However, one job provides a fixed salary, which is certain, while the other offers an uncertain salary. A risk-loving person prefers an uncertain job because the potential for higher earnings gives them more satisfaction. This means that they choose the riskier option.

The degree of risk preference influences financial and career choices, shaping how people respond to uncertain but potentially rewarding outcomes.

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.