Term 2 - Week 1 - Introduction and Choice under Uncertainty

What is the focus of microeconomics?

The behavior of individuals and firms, interactions, and decision making.

What is the rationality assumption in consumer choice theory?

It assumes agents exhibit rational behavior with internally consistent preferences.

What does the term 'bounded rationality' refer to?

Models that acknowledge individuals cannot perfectly calculate every action's consequences.

What is a preference relation in utility theory?

A binary relation that compares pairs of alternatives, indicating which is preferred.

What does completeness in preference relations imply?

Consumers can compare and rank all alternatives without indecision.

What is transitivity in preference relations?

If x is preferred to y and y to z, then x is preferred to z.

What does it mean for preferences to be rational?

Preferences are complete and transitive, allowing for consistent comparisons.

What is monotonicity in consumer preferences?

More of a good is always preferred to less, indicating that scarcity is a concern.

What does convexity in preferences imply?

Individuals prefer averages over extremes, leading to convex indifference curves.

What is continuity in utility?

Utility changes gradually with small changes in consumption bundles.

What is a utility function?

A mapping that represents a preference relation, indicating how alternatives are ranked.

How can non-selfish preferences be represented?

Utility depends on both an individual's consumption and the consumption of others.

What is a lottery in the context of choice under uncertainty?

A situation with multiple outcomes, each associated with a probability.

How is a compound lottery defined?

A lottery that consists of other lotteries, each with its own probabilities.

What is the significance of risk aversion in consumer choice?

It reflects a preference for certain outcomes over uncertain ones, even if the expected value is higher.

What is a certainty equivalent?

The guaranteed amount an individual would accept instead of taking a risky lottery.

What is the relationship between studying hours and exam marks?

There is a positive correlation, but outcomes are uncertain based on study effectiveness.

What does the notation L = [x1, x2; ρ1, ρ2] represent?

A lottery where outcomes x1 and x2 occur with probabilities ρ1 and ρ2, respectively.

What is the utility function for altruistic preferences?

It incorporates both the individual's consumption and the consumption of others in its ranking.

What does the exercise involving a Warwick student illustrate?

It demonstrates how preferences can be represented using a utility function.

What is the graphical representation of a lottery?

A visual depiction showing outcomes and their associated probabilities.

What does the term 'exercise' refer to in the lecture context?

Practical applications or problems posed to illustrate theoretical concepts.

What is the importance of the rationality assumption in economics?

It provides a foundation for analyzing economic problems and decision-making.

What are the criticisms of the rationality assumption?

Critics argue it may not hold in real-world applications and can be overly simplistic.

What is the role of indifference curves in consumer choice?

They represent combinations of goods that provide the same level of utility to the consumer.

How does the concept of 'self-destructive behavior' relate to rationality?

Such behavior may appear irrational but can still involve rational comparisons of options.

What is the significance of the 'bliss point' in utility theory?

It represents the optimal consumption level where utility is maximized.

What is a compound lottery?

A probability distribution over possible outcomes.

What does the preference relation ≿ signify in lotteries?

It indicates a consumer's ability to compare and rank lotteries.

What is the completeness axiom in the context of lotteries?

A preference relation is complete if for all lotteries L and L′, either L ≿ L′ or L′ ≿ L (or both).

What does the transitivity axiom imply for lotteries?

If L ≿ L′ and L′ ≿ L′′, then L ≿ L′′, ensuring consistency in ranking.

What does the Expected Utility Theorem state?

A utility function over any lottery can be expressed as the expected utility of its outcomes.

How is expected utility calculated for a lottery?

U(x1, x2, x3) = ρ1u(x1) + ρ2u(x2) + ρ3u(x3), where ρ represents probabilities.

What is an expected utility function?

A utility function that can be transformed into a positive affine transformation while preserving expected utility properties.

What is the significance of the St. Petersburg Paradox in expected utility?

It highlights inconsistencies in defining utility as the expectation of a random variable.

What is the certainty equivalent?

The sure amount of money an individual is willing to accept instead of a lottery.

What does it mean for an individual to be risk averse?

Eu(L) < u(E(L)), indicating they prefer certain outcomes over risky ones.

What is the Arrow-Pratt measure of absolute risk aversion?

Ra(w) ≡ −u′′(w) / u′(w), indicating risk aversion levels.

What is relative risk aversion?

Rr = −u′′(w)w / u′(w), measuring changes in marginal utility with wealth increases.

What is the utility function form for Matthew's betting scenario?

u(x) = −e−rx, representing a constant relative risk aversion (CARA) utility function.

What does the independence axiom state?

The preference ordering over two lotteries does not depend on a third lottery mixed with them.

What is the expected utility for a lottery with outcomes £5 and £15 at 50% probability?

Expected utility is calculated as 0.5 × u(£15) + 0.5 × u(£5).

What is the relationship between risk aversion and the shape of the utility function?

A more concave utility function indicates greater risk aversion.

What is the risk premium?

The difference between the expected amount from a gamble and the certainty equivalent.

What does a risk loving individual demonstrate in terms of expected utility?

Eu(L) > u(E(L)), indicating a preference for riskier options.

What is the expected utility of lottery A = [0, 100; 0.5, 0.5] with utility function u(x) = x?

U(A) = 50.

What is the expected utility of lottery B = [50; 1] with the same utility function?

U(B) = 50.

What does continuity in lotteries imply?

Small changes in probabilities do not affect the ordering between lotteries.

What is the significance of the in-class experiment by Maurice Allais?

It demonstrates violations of consumer behavior axioms in lottery selections.

What are the outcomes of lottery selection 1 in the Allais experiment?

L1 = [£55, £48, £0; 0.33, 0.66, 0.01] and L2 = [£48; 1].

What are the outcomes of lottery selection 2 in the Allais experiment?

L3 = [£55, £0; 0.33, 0.67] and L4 = [£48, £0; 0.34, 0.66].