Expected Income, Expected Utility, and Risk Aversion I

• Understand Expected Income, Utility, and Risk Aversion in Decision-Making: Part I as the foundation for analyzing choices under uncertainty
• Identify how to calculate expected income using probability-weighted outcomes in various scenarios
• Analyze the relationship between expected utility and diminishing marginal utility of income
• Compare expected income calculations with expected utility assessments for the same decision
• Evaluate why individuals with identical expected incomes may make different choices based on risk preferences
• Apply expected value formulas to real-world career and investment decisions
• Recognize how utility curves demonstrate diminishing marginal returns from additional income
• Explore the mathematical framework underlying behavioral economics and decision theory

Understanding Expected Income, Utility, and Risk Aversion in Decision-Making

Expected income represents the probability-weighted average of all possible income outcomes in an uncertain situation. This fundamental concept bridges mathematics and economics, helping us understand why rational decision-makers sometimes choose options that appear suboptimal at first glance.

Calculating Expected Income: The Mathematical Foundation

The expected income formula follows basic probability theory: multiply each possible outcome by its probability, then sum the results. For Neil's job scenario, the calculation becomes:

Expected Income = (0.5 × $81,000) + (0.5 × $49,000) = $65,000

This same principle applies across numerous real-world contexts. A recent UCLA economics graduate considering a sales position might face base salary of $50,000 with 30% probability of earning a $20,000 bonus. The expected income equals $50,000 + (0.3 × $20,000) = $56,000.

Expected Utility vs. Expected Income: Why They Differ

While expected income provides the mathematical average, expected utility incorporates individual preferences about risk. Most people experience diminishing marginal utility-each additional dollar provides less satisfaction than the previous dollar. A person earning $40,000 values an extra $1,000 more highly than someone earning $100,000 values the same increase.

This concept frequently appears on AP Economics exams and college microeconomics midterms. Students must distinguish between expected monetary value and expected utility, recognizing that identical expected incomes can yield different utility levels based on risk distribution.

Real-World Applications in Career and Investment Decisions

Consider a Harvard Medical School graduate choosing between emergency medicine ($320,000 guaranteed) versus plastic surgery ($180,000 to $550,000 range). Even if both specialties offer identical expected incomes, risk-averse individuals prefer the certainty of emergency medicine, while risk-seeking personalities gravitate toward plastic surgery's potential upside.

Similarly, investment advisors use expected utility theory when recommending portfolios. A client nearing retirement typically prefers bonds over stocks, even when stocks show higher expected returns, because the utility loss from potential losses exceeds the utility gain from equivalent gains.