“Expected utility” is an economic concept summarizing the utility that an entity or aggregate economy is expected to reach under varying circumstances. It is calculated by taking the weighted average of all possible outcomes, with weights assigned based on the likelihood of each event occurring.
Key Takeaways
- Expected utility refers to the anticipated utility of an entity or entire economy over a future period, given uncertain circumstances.
- It is a tool for analyzing situations where decisions must be made without knowing the outcomes, i.e., decision-making under uncertainty.
- The expected utility theory, introduced by Daniel Bernoulli, helps solve paradoxes like the St. Petersburg Paradox.
- It is also used to assess scenarios without immediate payback, such as in insurance purchasing.
Understanding Expected Utility
The expected utility of an entity stems from the expected utility hypothesis, which states that under uncertainty, the weighted average of possible levels of utility best represents overall utility over time. Individuals use this theory to make decisions under uncertainty by choosing actions that yield the highest expected utility. This decision-making also factors in an individual’s risk aversion and the utility of other agents.
This theory posits that the utility of money does not necessarily equate to its total value. For instance, people might take out insurance to cover various risks despite monetary loss over time because the potential for large-scale losses could significantly reduce utility due to the diminishing marginal utility of wealth.
The Roots of the Expected Utility Concept
Daniel Bernoulli introduced the concept of expected utility to resolve the St. Petersburg Paradox. This paradox can be depicted through a game where a coin toss determines the stakes. The stakes start at $2 and double with each head that appears until tails appear, ending the game. Mathematically, the payout is determined as 2k dollars, with k being the number of tosses. Assuming unlimited plays and resources, the theoretical sum becomes limitless, leading to an infinite expected win. Bernoulli differentiated expected value from expected utility by considering weighted utility multiplied by probabilities, not outcomes.
Contrasting Expected and Marginal Utility
Expected utility is intertwined with the concept of marginal utility. For wealthy individuals, the expected utility of additional rewards diminishes. Hence, they might prefer safer options over riskier ones.
For example, imagine a person buying a lottery ticket with expected winnings of $1 million. If a wealthy individual offers $500,000 for the ticket, a holder with fewer resources might sell for the guaranteed $500,000 due to the higher relative value of the amount. Conversely, a millionaire might decline, hoping for the additional $1 million, illustrating the diminishing marginal utility.
Economist Matthew Rabin, in 1999, posited that expected utility theory is implausible over modest stakes, emphasizing that incremental marginal utility changes are often insignificant.
Real-World Example of Expected Utility
Decision-making involving expected utility entails evaluating uncertain outcomes. Individuals assess the probability of outcomes and their expected utility before deciding.
Consider purchasing a lottery ticket. There are two outcomes: losing the invested amount or making a profit by winning. Assigning probability values to these outcomes, the expected utility derived from buying the ticket might seem higher than not participating.
Similarly, expected utility aids in evaluating investments like insurance. Comparing the expected utility from insurance payments (like tax breaks and guaranteed return) against the utility of spending the amount elsewhere reveals that insurance could be a better option. This optimization helps make sound economic and financial decisions.
Related Terms: utility, expected value, risk aversion, marginal utility, probability.
