10 - revealed preferences Flashcards
what are the assumptions necessary for revealed preferences?
we assume that the preferences remain unchanged while we observe their behaviour
we assume that the underlying preferences are known to be strictly convex#
what is a directly revealed preference?
If for given prices (π_1,π_2 ) bundle π=(π₯_1,π₯_2) is chosen, and bundle π satisfies the following inequality:
π_1 π₯_1+π_2 π₯_2β₯π_1 π¦_1+π_2 π¦_2,
then we will say that π is directly revealed preferred to π.
what do we observe when looking at revealed preferences?
we just observe what she has bought, and what she could have bought but did not
what is the principle of revealed preferecnes?
if people are choosing the best thing they can afford then if X is directly revealed preferred to Y then X is in fact preferred to Y. suppose at some prices bundle X is seen to be chosen. if bundle Y is also affordable at the same prices then X>= Y as utility of X os greater or equal to utility of Y. under the assumption of strict convexity of preferences there is a unique demanded bundle for each budget therefore if X is seen to be chosen while X is also affordable then X> Y as U(x) >U (Y)
what can we infer from the infer from a statement which says price of both goods and the chosen bundle arrangement?
we can infer that the bundle will lie on the budget line
we know that in the set given by the price vector, the bundle X gives the highest utility. bundle X is preferred to any bundle inside the set. we do not know anything about the bundles outside the set
what is indirecly revealed preferences?
Now suppose that we know that
At prices (π_1,π_2) bundle π=(π₯_1,π₯_2) is revealed preferred to bundle π=(π¦_1,π¦_2)
At prices (π_1,π_2) bundle Y=(π¦_1,π¦_2) is revealed preferred to bundle Z=(π§_1,π§_2)
That means two following inequalities are satisfied:
π_1 π₯_1+π_2 π₯_2β₯π_1 π¦_1+π_2 π¦_2
π_1 π¦_1+π_2 π¦_2β₯π_1 π§_1+π_2 π§_2
In this case, we will say that π is indirectly revealed preferred to π.
The transitivity tells us that π must be better than π.
what is weak axiom of revealed preferences or WARP?
the key consistency requirement is that in the altered price situation Y mustnt be chosen, the consumer may either stick with X or chose a new bundle that wasnβt previously affordable
the formal definition is
If π=(π₯_1,π₯_2) is directly revealed preferred to π=(π¦_1,π¦_2), and the two bundles are not the same, then it cannot happen that Y is directly revealed preferred to X.
In other words, if a bundle π is purchased at prices (π_1,π_2) and a bundle π is purchased at prices (π_1,π_2) then if
π_1 π₯_1+π_2 π₯_2β₯π_1 π¦_1+π_2 π¦_2,
it must not be the case that
π_1 π¦_1+π_2 π¦_2β₯π_1 π₯_1+π_2 π₯_2.
what is one trouble with the requiment of the weak axiom of revealed preferences?
One trouble with the requirement of WARP is that if the consumer was indifferent between π and π, and if initially she had chosen π (perhaps randomly over π), then she must continue to reject π in all future situations whenever both π and π are affordable.
what is the solution to the one trouble of the weak axiom of revealed preferences?
strict convexity of underlying preferences β it helps us to avoid situations when the consumer is indifferent between two affordable bundles.
what does the strong axiom of revealed preferences mean?
If π=(π₯_1,π₯_2) is revealed preferred to π=(π¦_1,π¦_2) (either directly or indirectly), and the two bundles are not the same, then it cannot happen that Y is either directly or indirectly revealed preferred to X . roughly speaking, SARP tells us that the revealed preference should be transitive
what is the relationship between the number of price changes and the amount of information which is revealed?
More information is generated by more price changes, and we are able to say quite a lot about preferences
what type of demand does the revealed preference unconditionally prove?
The Revealed Preferences theory (unconditionally) proves only the inverse relationship of a βcompensated demandβ, rather than a Marshallian demand.
