what is expected utility 
 expected utility is an economic term summarizing the utility that an entity or aggregate economy is expected to reach under any number of circumstances the expected utility is calculated by taking the weighted average of all possible outcomes under certain circumstances with the weights being assigned by the likelihood or probability any particular event will occur understanding expected utilitythe expected utility of an entity is derived from the expected utility hypothesis this hypothesis states that under uncertainty the weighted average of all possible levels of utility will best represent the utility at any given point in time 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 i e decision making under uncertainty these individuals will choose the action that will result in the highest expected utility which is the sum of the products of probability and utility over all possible outcomes the decision made will also depend on the agent s risk aversion and the utility of other agents this theory also notes that the utility of money does not necessarily equate to the total value of money this theory helps explain why people may take out insurance policies to cover themselves for various risks the expected value from paying for insurance would be to lose out monetarily the possibility of large scale losses could lead to a serious decline in utility because of the diminishing marginal utility of wealth history of the expected utility conceptthe concept of expected utility was first posited by daniel bernoulli who used it to solve the st petersburg paradox the st petersburg paradox can be illustrated as a game of chance in which a coin is tossed at each game s play for instance if the stakes start at 2 and double every time heads appear once the first time tails appear the game ends and the player wins whatever is in the pot under such game rules the player wins 2 if tails appear on the first toss 4 if heads appear on the first toss and tails on the second 8 if heads appear on the first two tosses and tails on the third and so on mathematically the player wins 2k dollars where k equals the number of tosses k must be a whole number and greater than zero assuming the game can continue as long as the coin toss results in heads and in particular that the casino has unlimited resources in theory the sum is limitless thus the expected win for repeated play is an infinite amount of money bernoulli solved the st petersburg paradox by distinguishing between the expected value and expected utility as the latter uses weighted utility multiplied by probabilities instead of using weighted outcomes expected utility vs marginal utilityexpected utility is also related to the concept of marginal utility the expected utility of a reward or wealth decreases when a person is rich or has sufficient wealth in such cases a person may choose the safer option as opposed to a riskier one for example consider the case of a lottery ticket with expected winnings of 1 million suppose a person with comparatively fewer resources buys the ticket for 1 a wealthy person offers to buy the ticket off them for 500 000 logically the lottery holder has a 50 50 chance of profiting from the transaction it is likely that they will opt for the safer option of selling the ticket and pocketing the 500 000 this is due to the diminishing marginal utility of amounts over 500 000 for the ticket holder in other words it is much more profitable for them to get from 0 500 000 than from 500 000 1 million now consider the same offer made to a very wealthy person possibly a millionaire likely the millionaire will not sell the ticket because they hope to make another million from it a 1999 paper by economist matthew rabin argued that the expected utility theory is implausible over modest stakes 1 this means that the expected utility theory fails when the incremental marginal utility amounts are insignificant example of expected utilitydecisions involving expected utility are decisions involving uncertain outcomes an individual calculates the probability of expected outcomes in such events and weighs them against the expected utility before making a decision for example purchasing a lottery ticket represents two possible outcomes for the buyer they could end up losing the amount they invested in buying the ticket or they could end up making a smart profit by winning either a portion of the entire lottery assigning probability values to the costs involved in this case the nominal purchase price of a lottery ticket it is not difficult to see that the expected utility to be gained from purchasing a lottery ticket is greater than not buying it expected utility is also used to evaluate situations without immediate payback such as purchasing insurance when one weighs the expected utility to be gained from making payments in an insurance product possible tax breaks and guaranteed income at the end of a predetermined period versus the expected utility of retaining the investment amount and spending it on other opportunities and products insurance seems like a better option 