Expected Income, Expected Utility, and Risk Aversion I

Expected income is calculated using expected value analysis by multiplying each possible income outcome by its probability, then summing the results. For example, if a job pays $81,000 with 0.5 probability or $49,000 with 0.5 probability, the expected income is (0.5 × $81,000) + (0.5 × $49,000) = $65,000. This provides the average income anticipated across all possible scenarios.

Expected utility differs from expected income because income alone does not capture how individuals value different income levels. Expected utility incorporates utility values—measures of satisfaction—corresponding to each income level. Since people experience diminishing marginal utility of income, additional dollars provide progressively smaller satisfaction increases, making expected utility a more accurate reflection of true preferences than expected income alone.

Diminishing marginal utility of income means that as income increases, each additional dollar generates progressively smaller increases in satisfaction or utility. For instance, the first $10,000 earned provides more utility gain than the next $10,000. This principle explains why individuals value income differently at various levels and is fundamental to understanding how people make decisions under uncertainty.

Mutually exclusive outcomes mean only one outcome can occur, and their probabilities must sum to 1. In a job scenario with two outcomes—earning $81,000 or $49,000—each with probability 0.5, these outcomes are mutually exclusive because the employee cannot simultaneously earn both amounts. This structure ensures that probability calculations accurately represent all possible scenarios without overlap.

To calculate expected utility, you need the probability of each possible outcome and the utility value corresponding to each income level. For example, if earning $81,000 yields utility of 10 and earning $49,000 yields utility of 8, with probabilities of 0.5 each, expected utility equals (0.5 × 10) + (0.5 × 8) = 9. Utility values reflect individual preferences and satisfaction levels at different income amounts.

The utility-income relationship reveals how satisfaction changes across different income levels, enabling better job evaluation. By mapping income amounts to their corresponding utility values and calculating expected utility, individuals can assess whether an uncertain job offer provides greater satisfaction than a certain alternative. This analysis accounts for personal risk preferences and the diminishing satisfaction from additional income, providing deeper insight than expected income alone.

Most people prefer certain income over uncertain income with the same expected value due to risk aversion combined with diminishing marginal utility of income. A guaranteed $65,000 provides more utility than a 50-50 chance of $81,000 or $49,000, also averaging $65,000, because the utility loss from earning $49,000 exceeds the utility gain from earning $81,000. This preference reflects how individuals value security and the diminishing satisfaction from additional income.