Preferences

Neoclassical microeconomics assumes that consumers make choices to maximize their utility. This is based on the theory of rational choice, which serves as the foundation of modern economics.

The theory of rational choice being "axiomatic" means that it is based on a set of fundamental axioms or propositions that are accepted as true without being proven within the theory itself. These axioms provide the foundational principles from which economic behaviors and decisions are analyzed and predicted.

A consumption bundle in microeconomic theory is a vector composed of various quantities of goods. It is typically represented as a point in a space where each dimension corresponds to the quantity of one good in the bundle. For example, bundle A with 4 units of bread and 3 units of apples would be represented as (4, 3).

The transitivity axiom ensures that a consumer's choice behavior is internally consistent, meaning if they prefer bundle A over bundle B, and bundle B over bundle C, then they must also prefer bundle A over bundle C, thus ruling out cyclical preferences.

Consumers prefer bundles with more of at least one good and no less of any other good compared to alternatives.

The imperceptible differences scenario implies a potential violation of the transitivity axiom, as it suggests that while a consumer may be indifferent between small changes in alternatives (like room temperatures), they may still have a strong preference when comparing the extremes of the range, thus challenging the consistency implied by transitivity.

In economic theory, risk refers to situations where the probabilities of various outcomes are known and can be calculated, while uncertainty refers to situations where the probabilities of outcomes are unknown and cannot be quantified with mathematical precision.

An actuarially fair game is a gamble where the expected monetary gain is zero, implying that over the long term, there is neither a financial gain nor loss expected. It is related to decisions under uncertainty as it assumes that the probabilities of outcomes are well-defined and known.

Subjective probabilities are based on an individual's personal judgment or experience about the likelihood of an event, rather than on formal calculations or objective data. They reflect personal beliefs and past experiences, differing from probabilities calculated from empirical data which rely on observed frequencies or statistical evidence.

The St. Petersburg paradox is a game of chance where a coin is flipped until it lands on heads. The player is paid $2ⁿ for each flip where n is the number of flips it takes to get heads. The expected value of this game is infinite, but no one would be willing to pay an infinite amount to play the game.

Risk aversion is the preference for a certain outcome over a risky outcome with the same expected value. Risk neutrality is the indifference between a certain outcome and a risky outcome with the same expected value.

The expected utility theory resolves the St. Petersburg paradox by considering the diminishing marginal utility of wealth. Instead of calculating the expected value of dollar prizes, it calculates the expected utility, which accounts for the fact that as wealth increases, the additional satisfaction gained from each additional dollar decreases.

Bounded rationality, introduced by Herbert Simon, suggests that people have limited information processing capabilities and cannot analyze every outcome in complex situations. This challenges the expected utility theory's assumption that individuals have the capacity to process all available information and make fully rational decisions under uncertainty.

The expected value of a game involving risk is calculated by summing the products of the probabilities of each outcome and its respective monetary value. For a risk-averse person with decreasing marginal utility for wealth, the utility of the expected value of the game is higher than the expected utility of the game itself, reflecting their preference for certain outcomes over uncertain ones.

Risk-averse individuals tend to refuse to engage in fair games, even when the expected value of the game equals the cost of playing. They prefer a certain outcome over a risky one with the same expected value, due to their preference for less risky situations

The certainty equivalent (CE) is the guaranteed amount that gives the same utility to an individual as a risky outcome, which is typically lower than the expected value of the risky option for a risk-averse person. The risk premium is the difference between the expected value of the risky option and the certainty equivalent. It represents the monetary amount a risk-averse individual is willing to pay to avoid risk.

The Allais Paradox presents scenarios where people's choices do not align with the Expected Utility Theory, specifically violating the independence axiom. It shows that individuals make choices under uncertainty that are inconsistent with expected utility maximization, as they may choose a certain outcome over a risky one even when the expected values are the same.

Prospect Theory differs from Expected Utility Theory by proposing that people value gains and losses differently and think in terms of utility relative to a reference point, such as current wealth, rather than absolute outcomes. It also introduces a value function defined over gains and losses, showing that people are risk-averse towards gains and risk-seeking towards losses.

"The fourfold pattern" refers to the observation that people's attitudes towards risk are not consistent across different scenarios. They may be risk-averse in some situations (e.g., high probability gains or low probability losses) and risk-seeking in others (e.g., low probability gains or high probability losses). This pattern illustrates the complex ways in which people value outcomes and adjust their decision-making process accordingly.

The framing effect refers to the phenomenon where people's choices change depending on how a problem or information is presented or 'framed' to them, even if the underlying facts remain the same.

The kink occurs at the reference point, separating gains and losses. It signifies that a loss of a given amount feels worse than a gain of the same amount.

The endowment effect is the phenomenon where individuals value an item they own more than a similar item they do not own. This is related to loss aversion because it shows that the disutility of giving up an owned item (loss) is greater than the utility of acquiring a new item (gain), leading to higher willingness to accept (WTA) compared to willingness to pay (WTP) for the same item.