Lecture 3: Expected Value and Utility Theory Flashcards
the gamble paradigm
making rational decisions in simple gambles
expected value (EV)
the value of a future gain should be directly proportional to the chance of getting it
null-bet
when the expected value is 0
how to make rational decisions in simple gambles
- calculate the expected value of each option/alternative
- choose the one with the highest EV
the expected value choice principle
choose the alternative with the highest EV
the expected value evaluation principle
the value of an alternative is equal to its EV
challenge for EV
St. Petersburg Paradox
- flip a goin and play until you flip tails
- round1: tails pays out 1 euro and ends game, heads doubles and repeated until tails
- EV = infinite
utility of wealth
according to Daniel Bernoulli, the utility of wealth follows the logarithmic function
- “the utility resulting from any small increase in wealth will be inversely proportional to the quanitity of goods already possessed”
- Expected Value ≠ Expected Utility
utility
the amount of joy, pleasure, or satisfaction you get from consuming or acquiring something
2 things in simple economics which determine what people do
- the pleasure people get from doing or consuming something
- the price of doing or consuming that something
decision utility
anticipated pleasure you feel at the time of decision
experienced utility
pleasure you actually feel from the consequences of your choice
total utility
refers to the satisfaction one gets from one’s consumption of a product
marginal utility
the satisfaction you get from the consumption of one additional unit of a product above and beyond what you have consumed up to that point
diminishing marginal utility
after some point, the marginal utility received from each additional unit of a good decreases with each additional unit consumed
rational choice and marginal utility
it is a basic principle of rational choice that you should spend your money on those goods that give you the most marginal utility per dollar
Ward Edwards
founder of behavioral decision theory
behavioral decision theory
an interdisciplinary discipline that addresses the question of how people actually confront decisions, as opposed to the question of how they should make decisions
- descriptive theory of decision making whereas economic theory is normative
theory of riskless choice
how people make decisions when there is no uncertainty involved with their decision
- most important assumption: the decision maker is considered to be an economic man
economic man
completely informed
- knows what alternatives are out there and what consequences they have
infinitely sensitive
- can make distinctions between all sorts of products and see all their differences
rational
- can weakly order states and can choose to maximize something
economic man can weakly order states
A > B, or A < B, or A = B
transitivity of preferences
if A > B, and B > C, then A must be > C
- if not true, you are intransitive which can lead to becoming a victim of a money pump
money pump
pay to trade A for C, pay to trade C for B, pay to trade B for A, and repeat
economic man maximizes something
central principle in theory of rational choice
- typically assumed to maximize utility
early utility maximizing theory
goal of human actions is seeking pleasure and avoiding pain
competing goods utility
- the utility derived from one competing good reduces the utility derived from the other
- consumers aim to maximize their total utility by choosing the product that offers the highest satisfaction, given the prices and preferences
completing goods utility
- the utility derived from complementary goods increases when both are consumed together
- the combined utility of using both goods together is greater than the sum of their individual utilities, as they enhance each other’s value when used in conjunction
Francis Y. Edgeworth
- non-independent utilities -> indifference curves
indifference curves
curves that give you lines which have the same utility
ordinal and cardinal utility
- ordinal utility is measured on an ordinal scale
- cardinal utility is measured on an interval scale
ordinal vs cardinal utility
indifference curve analysis in its various forms could do everyting that cardinal utility could do, with fewer assumptions
reinstating cardinal utility
Robertson pleaded for the reinstatement of cardinal utility in the interests of welfare economics
the best economic policy
the economic policy is best which results in the maximum total utility, summed over all members of the economy
Pareto’s principle
a change should be considered desirable if it left everyone at least as well off as they were before, and made at least one person better off
compensation principle (Kaldor)
if it is possible for those who gain from an economic change to compensate the losers for their losses, and still have something left over from their gains, then the change is desirable
theory of risky choices
choices where you don’t know beforehand what the outcome will be
risk vs uncertainty
- risk refers to known probabilities
- uncertainty refers to unknown probabilities
expected utility maximizing
the expected value of a bet is found by multiplying the value of each possible outcome by its probability of occurrence and summing these products across all possible outcomes
- contradicted by observable behavior in many risky situations
theory of games and economic behavior (Von Neumann-Morgenstern)
- risky propositions can be ordered in desirability, just as riskless ones can
- choices among risky alternatives are made in such a way that they maximize expected utility
Markowitz
suggested that the origin of a person’s utility curve for money to be taken as his customary financial status
- if the person’s customary state of wealth changes, then the shape of his utility curve will thus remain generally the same with respect to where he is now
- his risk-taking behavior will remain pretty much the same instead of changing with every change of wealth
Mosteller and Noggee
carried out the first experiment to apply the Neumann-Morgenstern model
- the hypothesis that subjects maximized expected utility predicted choices better than the hypothesis that subjects maximized expected money value
- showed that people are sensitive to changes with respect to the current situation
2 factors Edwards found most important in determining choices
- general preferences or dislikes for risk-taking
- specific preferences
general preferences or dislikes for risk taking
strong preference for low probabilities of losing large amounts of money to high probabilities of losing small amounts of money
- just didn’t like to lose
subjective probability
an individual’s personal judgment or belief about how likely an event is to occur, rather than relying on objective or statistical probabilities
transitivity in decision making
transitivity can never be violated
- since choices will be made in sequence, it can always be argued that the person may have changed their tastes between the first and third choice
