What Is Expected Utility?
Let me explain expected utility to you directly: it's an economic term that sums up the utility, or satisfaction, that you or an entire economy might reach in various situations. You calculate it by taking the weighted average of all possible outcomes, with the weights based on the probability that each event will happen.
Key Takeaways
- Expected utility refers to the utility of an entity or aggregate economy over a future period of time, given unknowable circumstances.
- Expected utility theory is used as a tool for analyzing situations in which individuals must make a decision without knowing the outcomes that may result from that decision.
- The expected utility theory was first posited by Daniel Bernoulli who used it to solve the St. Petersburg Paradox.
- Expected utility is also used to evaluate situations without immediate payback, such as purchasing insurance.
Understanding Expected Utility
You derive the expected utility of an entity from the expected utility hypothesis, which states that under uncertainty, the weighted average of all possible utility levels best represents the utility at any point. I want you to know that this theory serves as a tool for analyzing decisions where you don't know the outcomes— that's decision making under uncertainty. You'll choose the action with the highest expected utility, calculated as the sum of probabilities multiplied by utilities for all outcomes. Your decision also factors in your risk aversion and the utilities of others involved.
This theory points out that the utility of money isn't the same as its total value. It explains why people buy insurance: the expected monetary value might mean a loss, but the risk of large losses could drastically reduce your utility due to diminishing marginal utility of wealth.
History of the Expected Utility Concept
Daniel Bernoulli first introduced the concept of expected utility to solve the St. Petersburg Paradox. Picture this paradox as a coin toss game: stakes start at $2 and double each time heads comes up, ending when tails appears, and you win the pot.
For example, you win $2 if tails on the first toss, $4 if heads then tails, $8 if two heads then tails, and so on. Mathematically, you win 2^k dollars where k is the number of tosses. If the game can go on forever with unlimited casino resources, the expected win is infinite.
Bernoulli resolved this by separating expected value from expected utility, using weighted utilities multiplied by probabilities instead of just weighted outcomes.
Expected Utility vs. Marginal Utility
Expected utility connects to marginal utility, where the expected utility of wealth decreases as you get richer. In those cases, you might pick the safer option over a riskier one.
Take a lottery ticket with $1 million expected winnings bought for $1 by someone with few resources. If a wealthy person offers $500,000 for it, the holder likely sells, preferring the sure gain due to diminishing marginal utility—gaining from $0 to $500,000 is more valuable than from $500,000 to $1 million. A millionaire, however, might keep it hoping for the full win.
Economist Matthew Rabin argued in a 1999 paper that expected utility theory doesn't hold for modest stakes, failing when marginal utility changes are small.
Example of Expected Utility
Decisions with expected utility involve uncertain outcomes. You calculate probabilities of outcomes and weigh them against expected utility before deciding.
Buying a lottery ticket offers two outcomes: lose the ticket price or win big. Assigning probabilities shows the expected utility of buying often exceeds not buying.
Expected utility also applies to no-immediate-payback situations like insurance. Weighing utility from payments (tax breaks, guaranteed income) against keeping the money for other uses, insurance usually comes out ahead.
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