Title: Microeconomics / Q1 / lecture1

Q: Two models of individual choice behavior
A: preference relations and choices

Q: preference relations
A: individuals rank different choices and starts
by modeling the objectives or goals of the decision-maker and can be assigned to pairs of alternatives (pairs of choices).

define rationality

Q: Completeness
A: for all alternatives available, the decision maker can compare them and decide which is preferred. In other words, the
decision maker is “decisive” and “always knows
what he or she wants”

Q: Transitivity
A: Ability to rank the choices that are present.

irreflexive

reflexive

Q: symmetric
A: If x is indifferent to y then y must be indifferent to x

Q: “just perceptible” differences
A: Small changes make no difference till you build them up. If I asked if you wanted lunch between 12pm and 2pm and you said you were indifferent but I asked if you cared that lunch was at 12:01, 12:02 all the way to 2pm you may say "no wait 2pm is too late to have lunch"

Q: characteristics of a utility function
A: - the function is not unique
- utility function u( ) is ordinal, not cardinal
- a preference relation [latex]$\succsim$[/latex] can be  by a utility function only if  [latex]$\succsim$[/latex] is rational.

Q: If X has infinite choices can it be used to represent a utility function?
A: No,  but if X is finite then any rational preference relation can be represented by a utility function.

Q: choice structure components
A: B and C( )
1. B is a “family” (a set) of nonempty subsets of X. You can think of each B as a “budget set”: what a consumer can afford given his or her budget. More generally, each B is a set of all possible options (all possible choices) available to the decision maker.
2. C( ) is a choice rule (mathematically, a correspondence) that assigns a nonempty set of chosen elements of B

Q: weak axiom of revealed preference (WARP)
A: if a consumer chooses one good over another, they should not reverse that preference in the future, given the same set of goods and budget constraints.
This axiom states the following: if x is ever chosen when y is available, then there can be no budget set containing both alternatives for which y is chosen but x is not chosen.
If a consumer chooses alternative x when alternative y is available, then it is revealed that the consumer prefers x to y (or is at least indifferent between x and y). Consequently, there should be no budget set containing both alternatives where the consumer would choose y but not x, as this would contradict the initial revealed preference.

Q: utility function
A: 1. They are not unique
2. They are ordinal not cardinal
3. Can represet a preference relation only if the preference relation is rational
4. X must be finite

Q: revealed preference relation
A: 1. Does not need to be either complete or transitive
“If x is revealed at least as good as y, then y cannot
be revealed preferred to x."

Q: Choice rule
A: a collection of alternatives or goods available to the consumer for selection. In the context of consumer choice theory, the choice set represents the feasible options that a consumer can consider when making a decision. The choice set can be finite or infinite, depending on the problem at hand. For example, a choice set could be a list of three different products: {A, B, C}, or it could represent a continuous range of quantities of two goods, such as {x, y} where x and y can take any non-negative real value.