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Revealed Preference Theory (A Detailed Explanation- Varian) - YouTube
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today i am going to explain the revealed
[2]
preference theory
[5]
in indifference curves we used the
[7]
information about the consumer's
[9]
preferences
[10]
and the budget constraint to determine
[12]
his demand
[14]
in revealed preference theory we are
[16]
discovering information
[17]
about the preferences of the consumer by
[20]
the observation of his behavior
[22]
we try to develop some tools to do that
[25]
from this
[26]
theory here we are assuming that the
[29]
preferences of the consumer
[31]
will remain unchanged while we observe
[33]
the behavior
[35]
over very long time spans this
[37]
assumption may not be very reasonable
[40]
but here we adopt the assumption that
[42]
consumers preferences
[44]
are stable over the time period for
[47]
which
[47]
we observe his choice behavior we also
[51]
assume that the underlying preferences
[53]
of the consumer
[54]
is strictly convex as discussed in the
[57]
concept
[58]
of indifference curves given this
[61]
background
[62]
let's move on to the idea of revealed
[64]
preference
[65]
now consider this figure where we have
[68]
depicted a consumer's demanded bundle
[71]
x1 x2 and another bundle y1 by 2
[75]
that is beneath the consumer's budget
[77]
line
[78]
here the bundle x1 x2 is assumed
[82]
to be demanded by the consumer and it is
[85]
quite clear that
[86]
the bundle y 1 by 2 was also affordable
[89]
to the consumer
[90]
as it lies inside the budget line
[93]
here the bundle x1 x2 that the consumer
[97]
chooses
[98]
is said to be revealed prefer to the
[101]
bundle y one by two
[102]
that is because y one y two was a bundle
[106]
that the consumer could have chosen as
[109]
it was inside his budget line
[111]
but he didn't do so here x1 x2
[115]
is considered the optimal bundle because
[118]
the consumer has chosen it it must be
[121]
better than any other bundle
[123]
that the consumer can offer and
[127]
x1 x2 must be preferred to any other
[129]
bundle in the blue shaded area
[132]
or on the budget line now let's assume
[135]
that
[136]
x1 x2 is a consumption bundle which is
[139]
purchased at prices p1 p2
[142]
when the consumer has income m x1 is a
[145]
bundle which has price p1
[148]
and x2 is a bundle which has price p2
[152]
now let's again have a look at the
[154]
speaker
[155]
it can be seen that the optimal bundle
[158]
x1 x2
[159]
is on the budget line this means that
[162]
his total income
[163]
is exhausted when the consumer purchases
[166]
the bundle
[167]
x1 x2 at the same time when we look at
[170]
the bundle
[171]
y 1 y 2 it lies inside the budget line
[174]
and the total income of the consumer is
[177]
not being exhausted
[179]
so this means that even y 1 plus p 2 y 2
[182]
is less than or equal to m
[185]
in our particular example even y1 plus
[188]
p2 y2
[189]
is less than m as the bundle y1 y2
[193]
lies inside the budget line as explained
[196]
before
[197]
but the idea of revealed preference
[199]
holds even if the bundle y 1 y
[201]
2 is equal to m which means even if
[205]
y 1 y 2 was on the budget line the
[208]
reveal preference theory
[209]
will continue to hold as long as x1 x2
[213]
is preferred to y1 y2
[215]
at the same time for the bundle x1 x2
[218]
p1 x1 plus p2 x2 is equal to m
[223]
now let's put these two equations
[225]
together
[226]
and we get the result that p 1 x 1
[229]
plus p 2 x 2 greater than or equal to
[232]
p 1 y 1 plus p 2 y 2 that is
[236]
the total expenditure on the bundle x x1
[239]
x2
[240]
must be greater than or equal to the
[242]
total expenditure on the bundle
[245]
y1 y2 for the idea of revealed
[248]
preference
[248]
to hold then only we can say that x1 x2
[252]
is directly revealed preferred to y 1 y
[255]
2.
[256]
the revealed preference is a relation
[258]
that holds between
[260]
the bundle that is actually demanded at
[262]
some budget
[263]
and the bundles that could have been
[265]
demanded at that budget here
[268]
the bundle that has actually been
[271]
demanded is
[271]
x 1 x 2 and the bundle that could have
[274]
been demanded at the budget
[276]
is y 1 y 2 and when we say that
[279]
x is revealed refer to y all we are
[282]
claiming is that
[284]
x is chosen when y could have been
[286]
chosen
[288]
if x 1 x 2 is chosen over y 1 y 2
[291]
or if x 1 x 2 is directly revealed
[295]
preferred
[296]
over y 1 by 2 then it essentially means
[299]
that
[300]
x 1 x 2 is preferred to y 1 by 2.
[303]
the principle of revealed preference
[305]
states that
[307]
let x 1 x 2 be the chosen bundle when
[310]
prices are p1 p2
[312]
and let y1 y2 be some other bundle such
[316]
that
[316]
p1 x1 plus p2 x2 is greater than or
[320]
equal to p1 y1 plus p2 y2
[323]
then if the consumer is choosing the
[326]
most preferred bundle she can afford
[329]
x one x two is preferred y one by two it
[332]
has to be noted that
[333]
just because x is revealed refer to y
[336]
doesn't mean that x is preferred to y
[339]
revealed preferred just means that x was
[343]
chosen when y
[344]
was available reference means that the
[347]
consumer ranks
[348]
x ahead of y now suppose that
[352]
y 1 y 2 is the bundle demanded by the
[354]
consumer at prices q 1 q 2
[357]
and assume that y 1 y 2 is itself
[360]
revealed refer to some other bundle
[363]
is said 1 is at 2. have a look at the
[365]
speaker
[366]
where there is a shift in the budget
[368]
line and the consumer
[370]
now demands the bundle y one by two the
[373]
bundle
[374]
is z1 z2 lies inside the new budget line
[378]
when there is a shift in the budget line
[380]
the relative prices changes
[382]
and let's assume that the relative
[384]
prices are now
[386]
q1 and q2 since y1 y2
[389]
lies on the budget line it exhaust the
[392]
total income of the consumer
[394]
hence q 1 y 1 plus q 2 y 2
[397]
is equal to m as it exhausts the total
[400]
income
[401]
as per the new budget line and z 1 y 1
[405]
plus e set to y 2 is less than or equal
[407]
to
[408]
m as the theory of revealed preference
[411]
suggest
[412]
but here since the bundle is z1 is set
[414]
to
[415]
was inside the shifted budget line
[418]
is z1 y1 plus z2 y2 is less than m
[422]
so combining these two equations we get
[425]
that
[426]
q1y1 plus q2y2 must be greater than
[429]
or equal to q1 z1 plus q2z2
[434]
then only the theory of revealed
[436]
preference may hold
[437]
we learned that x1 x2 is preferred to y1
[441]
y2
[442]
and that y1 y2 is preferred to z1 z2
[446]
so due to the assumption of transitivity
[449]
we can conclude
[450]
that x1 x2 is preferred to z1 z2
[453]
in this case we say that x1 x2
[457]
is indirectly revealed preferred to z1
[459]
z2
[460]
we can conclude from the figure that x1
[463]
x2
[464]
is revealed preferred to all of the
[466]
bundles in the blue shaded area
[468]
this is because x1 x2 is directly
[471]
revealed referred to y 1 by 2.
[474]
as explained earlier and indirectly
[476]
revealed preferred to
[478]
z1 z2 so bundle x1 x2
[481]
is preferred to all the bundles in the
[483]
blue shaded area
[485]
now have a look at the speaker where the
[488]
upper shaded area consists of all those
[490]
bundles
[491]
that are preferred to x in fact the
[494]
upper shaded area
[496]
shows the better bundles when compared
[498]
to the bundle
[499]
x this is because of the monotonicity of
[502]
preferences
[503]
if we are willing to assume that
[505]
preferences are monotonic
[507]
then all the bundles that have more of
[510]
both goods
[511]
than x y and z or any of the weighted
[515]
averages
[516]
are also preferred to x that is why
[519]
the upper shaded portion is preferred to
[521]
x
[523]
the lower shaded area consists of
[525]
bundles
[526]
revealed worse than x the region labeled
[529]
verse bundles
[530]
consists of all the bundles to which x
[533]
is revealed preferred
[535]
as i have explained earlier excess
[537]
directly
[538]
or indirectly revealed preferred to all
[540]
the bundles in the lower shaded portion
[543]
we can conclude that all of the bundles
[546]
in the upper shaded area
[547]
are better than x and all of the bundles
[550]
in the lower shaded area
[552]
are worse than x this is in accordance
[556]
with the preferences of the consumer
[558]
who made the choices the true
[560]
indifference curve
[561]
through x must lie somewhere between the
[564]
two shaded sets
[565]
this is because indifference curve is
[568]
the locus of combination of
[569]
points which gives the same level of
[572]
satisfaction to the consumer
[574]
so the indifference curve shouldn't lie
[577]
in any of the shaded areas
[579]
and it is tightly trapped in the middle
[582]
of the shaded regions
[583]
in the next video we will move on to the
[586]
weak axiom of the revealed preference
[588]
theory
[588]
thank you
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