Choice

Question 1

What is a choice function with full domain?

Answer 1

A choice functrion with full domain is a function f: 2^X{∅} -> X that satisifies f(B) ∈ B for every B ∈ 2^X{∅}

Question 2

When a choice function with full domain is rationanlizable?

Answer 2

Whenever there is a rational preference ≽ such that, for every B ∈ 2^X{∅}, f(B) is the unique ≽ -best element of B

Question 3

What is the Weak Axiom of Revealed Preference?

Answer 3

A choice function with full domain satisfies the WARP if, for every B’ ∈ 2^X{∅}, {f(B), f(B’)} ⊆ B ∩ B’ implies f(B) = f(B’)

Question 4

A choice function with full domain satisfies the weak axiom of revealed function iff…

Answer 4

It is rationalizable. The rationalizing is unique

Question 5

What is a choice structure (B, c)?

Answer 5

B - is a collection of nonempty subsets of X

c - is a correspondence B⇉X such that ∅⊂ c(B) ⊆ B

Question 6

The revealed preference relatiopn for a choice structure (B, c) is defined as…

Answer 6

≽* = ∪ [c(B) X B]

Question 7

≽* must be transitive

Answer 7

False

Question 8

A choice structure satisfies the WARP if…

Answer 8

For every A, B ∈ scriptB and x,y ∈ A ∩ B, x ∈ c(A) and y ∈ c(B) imples x ∈ c(B)

Question 9

What is the Sen’s condition α?

Answer 9

If X∈ B ⊆ A and x ∈ c(A), then x ∈ c(B)

Question 10

What is the Sen’s condition β?

Answer 10

If x,y ∈ c(A), A ⊆ B, and y ∈ c(B) then x ∈ c(B)

Question 11

What is the Sen’s decomposition lemma ?

Answer 11

A choice structure (scriptB, c) satisifies WARP iff it satisfies Sen’s conditions α and β

Question 12

When a choice is rationalizable?

Answer 12

Whenever thre exists a rational preference ≽ such that for every B ∈ scriptB, c(B) is the set of ≽-best elemnts of B:
c(B) = {x ∈ B | ∀y ∈ B: x ≽ y}

Question 13

If the choice structure is rationalizable the it satisfies WARP

Answer 13

True

Question 14

If the choice satisfies WARP, then it is rationalizable

Answer 14

False

Question 15

What is a cycle in (scriptB, c)?

Answer 15

If it can be written as Y={x1, x2,…, xn} for some N ∈ doubleN so that
x1 ≽* x2 ≽* … ≽* xN ≽* x1

Question 16

When a choice satisfies the Generalized Axiom of Revealed Preference (GARP)?

Answer 16

If for every Y in (scriptB, c), A ∈ scriptB, x,y ∈ Y ∩ A and y ∈ c(A), we have that x ∈ c(A)

Question 17

What is the GARP Theorem?

Answer 17

A choice (scriptB, c) is rationalizable iff it satisfies GARP

Question 18

What is the weak rationalization?

Answer 18

A choice structure (scriptB, c) is weakly rationalizble whenever there exists a rational preference ≽ such that, for every B ∈ scriptB, every alternative in c(B) is a ≽-best elements of B:
c(B) ⊆ {x ∈ B | ∀y ∈ B: x ≽ y}

Question 19

When a collection of preferences is identified?

Answer 19

if for every choice structure is weakly rationalized by at most one preference in P

Question 20

When a collection of preferences is separated?

Answer 20

If for every distinct ≽1, ≽2, there is x,y in X such that x≻1 y ≻2 x

Question 21

If P is a collection of rational preferences then P is identifcated on scriptB iff P is separated

Answer 21

True