John is evaluating a job offer from a company where his income will be uncertain. If the company performs well, John will earn an annual income of  $81,000; otherwise, he will earn $49,000. It is assumed that either outcome has an equal chance, assigning a probability of 0.5 to each. This results in an expected income of $65,000. His decision-making is affected by the diminishing marginal utility of income. 

John evaluates his options based on their utility. Expected utility accounts for risk preferences, unlike expected income. The expected utility is calculated as the sum of the utility values of possible incomes, weighted by their respective probabilities. 

Expected utility = (P₁×U₁) + (P₂×U₂)

where P₁ and P₂ are the probabilities of the two outcomes, and U₁ and U₂ are their corresponding utility values.

For John,

• If the company performs well, his income will be $81,000 with a probability of 0.5, and a corresponding utility value of 9 units.
• If the company does not perform well, his income will be $49,000 with a probability of 0.5, and a corresponding utility value of 7 units.

Thus, John’s expected utility is (0.5×9) units +(0.5×7) units = 8 units

However, John can achieve the same utility of 8 units with a guaranteed income of $64,000. This reflects his preference for certainty over risk, even though the expected income in the uncertain scenario is higher. 

The difference between the expected income of $65,000 and the guaranteed income of $64,000 represents John’s risk premium—$1,000. This is the amount he is willing to forgo to eliminate uncertainty and secure a guaranteed outcome. John’s preference for the guaranteed income highlights his risk-averse nature and demonstrates how diminishing marginal utility influences his decision.