Behavioral Economics Midterm

theorems and definitions for exam

Complete Relation

x is preferred to y or y is preferred to x for all x which does not equal y

Transitive Relation

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

Asymmetric Relation

x is preferred to y, then y is not preferred to x

Rational Decision Maker

The DM is rational if there is a total order preference relation such that she picks the preference maximal element from each choice problem

Utility Function represents a Preference

A utility function represents a preference relation if for all options x and y, x is preferred to y if and only if the utility of x is preferred to the utility of y

Increasing Transformations

a utility function, v, is an increasing transformation of utility function u if there exists an increasing function such that v(x)=f(u(x)) for all x ∈ X

Theorem I

The utility function v represents the same preference as the utility u if and only iff v is an increasing transformation of u

Rational Choice Function

A choice function, c is rational if there is a preference relation such that c is preference maximal in each problem S

Theorem II

c is rational if and only if it satisfies the following property of Independence Irrelevant Alternatives (IIA) for all choice problems R⊆S if c(S)∈R, then c(S)=c(R)

Observed Choice Function

An observed choice function, Cobs, singles out an element Cobs(S) from each problem S in a collection P

Observed Choice Function Consistent with Rationality

Cobs is consistent with rationality if there exists a rational choice function c that coincides with Cobs on P

Revealed Preference for Rationality

Option x is revealed preferred to y if the DM picks x in the presence of y that is , Cobs(S)=x for some choice problem S containing y

Theorem IV

A simple algorithm allows to check whether revealed preference is acyclic (number of operations is cubic in the number of operations)

Unambiguous preference for Rationality

Option x is unambiguously preferred to y if x is preferred to y for all total orders preference such that Cobs picks the preference maximal element in each choice problem P

Theorem V

x is unambiguously preferred to y if and only if x is the transitive closure of revealed preference to y

Valid Forecasts for Rationality

Option x in unobserved problem S is a valid forecast for S if there exists a total order preference such that:

i. x is preference maximal in S

ii. Cobs picks the preference maximal element from each choice problem in P

Theorem III

Data is consistent with rationality if and only if revealed preference is acyclic

Theorem VI

Option x in an unobserved problem S is a valid forecast for S if and only if there is no y ∈ S such that y is unambiguously preferrred to x

Choice Correspondence

A choice correspondence associates a subset c(S) of chosen options to each choice problem S

Generalized IIA

For all choice problems R⊆S, c(S)∩R ⊆ c(R)

Expansionary Consistency

Consider any choice problem R, S, and suppose R⊆S, if c(R)∩c(S)=/=0 then c(R)⊆c(S)

Theorem VII

C is rational if and only of it satisfies generalized IIA and Expansionary Consistency

Demand Data

Demand data is a collection D={(p^k, x^k) I k=1,…,K} of price vectors and consumption bundles with the interpretation that the consumer picked x^k when facing the price vector p^k

Rationalized Demand

Demand data D is rationalizable if there exists an increasing utility function u such that, for all (p,x) ∈ D , the bundle x utility is maximal over the set of affordable bundles y∈R² + (meaning that p1y1 + p2y2 greater than or qual to p1×1 +p2×2)

Revealed Preference in Consumer Thoery

Given D bundle x is revealed preferred to y if there exists a price vector P such that (p,x)∈D and p1y1 +p2y2 is greater than or equal to p1×1 +p2×2 if the inequality is strict, then x is said to be revealed strictly preferred to y

Theorem VIII

D is rationalizable if and only of it satisfies the Generalized Axiom of Revealed Preference  (GARP): it is impossible to sequence (x^j)^J j=1 of chosen bundles such that x^j is strictly preferred to x^j+1, for all j<J and x^J is strictly preferred to x1

Critical Cost Efficiency Index CCEI

CCEI measures nu how much income would have to be scaled down to rationalize the data

Satisficing

Rationality requires the DM to:

i. identify all the options available to her

ii. determine how to rank any 2 options

iii. correctly maximize her preference

these tasks are presumably difficult and costly to preform thus the DM may simply search through all feasible options until she find an acceptable one

Observed choice Function is consistent with theory of choice overload

Cobs is consistent with choice overload if there exists a total ordered preference and A satisfying the overload property such that, for each choice problem S, Cobs(S) is preference maximal within A(S)

Theorem IX

Cobs is consistent with the choice overload if and only if the above revealed preference is acyclic

Attraction Effect

aka asymmetric dominance effect/ decoy effect is the phenomenon whereby the market share of an option increases by introducing an option that is clearly inferior to it, but hard to compare to others

Narrow Bracketing

looking at each decision problem instead of a whole

Loss Aversion

assessing options in comparison to a reference point with the added feature that losses typically loom larger than gains

Status Quo Bias

set of available options is sometimes accompanied with a preselected option(e.g. default subscription plan highlighted on a magazines webpage which provides a natural reference point for which moving away from can be hard)

Willingness to Pay WTP

Maximal price you are willing to acquire the item

Willingness to Accept WTA

Minimal price you need to be willing to sell an item

Reservation Price

the amount that leaves the DM indifferent between getting that item or amount