8 revealed preferences

Question 1

State and explain WARP

Answer 1

A list of observations (pt,xt)
satisfies WARP provided that for every t,s ∈ {1,…,n}, pt· xt ≥ pt· xs implies ps· xt > ps· xs

Suppose for prices pt the bundle xt is chosen and xs costs less or the same. For prices ps, if the bundle xs
is chosen, then xt costs more.

Question 2

for two bundles when is x revealed weakly preferred

Answer 2

x is revealed weakly preferred to y provided x is
chosen and y costs less than or the same as x (p · y ≤ p · x)

Question 3

what is the completeness axiom

Answer 3

all pairs of bundles can be compared

Question 4

what is the transitivity axiom

Answer 4

indirect comparisons carry over to direct comparisons

Question 5

what is the monotonicity axiom

Answer 5

more is better

Question 6

what is the strong convexity axiom

Answer 6

combinations of equally bundles is better

Question 7

what does monotonicity imply

Answer 7

the whole income is used at solutions to the consumer problem

Question 8

what does strong convexity imply

Answer 8

there is at most one solution to the consumer problem

Question 9

what axioms do we assumer consumers preferences fit

Answer 9

compete and monotonic

Question 10

when is u(x) ≥ u(y) for bundles x and y

Answer 10

when bundle x is weakly preferred to y (x ≿ y)

Question 11

if u(x) ≥ u(y), for x ≿ y, what axioms does this preference show

Answer 11

complete and transitive

Question 12

why does WARP not imply transitivity

Answer 12

• WARP does ensure revealed preferences are transitive for ℓ = 2
• WARP does not ensure revealed preferences are transitive for ℓ ≥ 3