Reminder: Assessed Test on this
coming Monday
• Test based on Problem Sheet 1 for Monday night
exercise classes
• All you really need
• … but should know what Adding-up and Cournot
conditions are
• ..and be able to identify an income and
substitution effect.
• Examples on J:\Files\Econ|Tests and Sols
• Note TFU Class Questions for Final Exam in
last week
• WORK Towards End of Term
• Econ 201 Week 9 Mon Test on Problem Sheet 2
Week 11 Mon Test on Problem Sheet 3
Week 11 Thur TFU Exam on Course
• Econ 203 Week 11 Exam on my last part of
course and Prof. Backhouse’s section
• Econ 204 Multiple Choice in January
• Econ 206 Computer Assessment Week 9 & 10
• Econ 212 Week 11 Last week for Essay
• Econ 211 Essay deferred to January
Revealed Preference Approach
• Chapter 7 Varian
• Previous process asked what properties
must utility functions have to yield the
demand functions we usually fit to observed
data
• Some people worry about this.
‘The Austrians’
• The Austrians were a group of economists
who rejected the use of utility and marginal
utility as they saw it as relying on
something unmeasurable
– Utility
• They pioneered a process called Revealed
preference where they tried to use the
‘known’ – the demands we actually observe
- to discover something about the nature of
peoples preferences
• What we will show is that the ‘reveled
preference approach’ yields essentially the
same outcomes.
• However, the approach is useful in its own
right as it allows to develop a variety of
welfare measures commonly used by
governments and other policy makers.
Revealed Preference
y
(x1, y1)

x2 , y2 
x
All affordable bundles must
satisfy the budget constraints
Px x  Py y  M
Optimal bundle will exactly
satisfy budget constrains
Px x1  Py y1  M
Revealed Preference
If we observe that (x1, y1) is chosen then
it is directly revealed preferred to
(x2,y2) , for all (x2,y2) that satisfy
y
(x1, y1)
Px x1  Py y1  Px x2  Py y2
x2 , y2 
x
All affordable bundles must Px x  Py y  M
satisfy the budget constraints
Optimal bundle will exactly
satisfy budget constrains
Px x1  Py y1  M
Revealed Preference
If we observe that (x1, y1) is chosen then
it is directly revealed preferred to
(x2,y2) , for all (x2,y2) that satisfy
y
(x1, y1)
Px x1  Py y1  Px x2  Py y2
x2 , y2 
x
Thus, we know that
x1, y1   x2 , y2 
*
*
P
,
P
If at another set of prices x y
we observe that the bundle (x2,y2) is chosen,
then for all (x3,y3) that satisfies
y
Px* x2  Py* y2  Px* x3  Py* y3 ,
x1, y1 
x2 , y2 
x2 , y2   x3 , y3 
x3 , y3 
Since
x
.
x1, y1   x2 , y2 
It follows that
x1 , y1   x3 , y3 
So (x1,y1) is indirectly revealed preferred to (x3,y3)
We can now extend this idea, suppose that (x3,y3) is
chosen at another set of prices. Then that bundle is
preferred to everything we could have bought and didn’t
y
Px** x3  Py** y3  Px** x4  Py** y4 ,
x1, y1 
x2 , y2 
So now know
x1, y1   x4 , y4 
x3 , y3 
x
So (x1,y1) is indirectly revealed preferred to (x4,y4)
But what have we got now?
Look at the edge of this revealed preference set.
It is forming an indifference curve
y
x1, y1 
x2 , y2 
So revealed preference theory is
essentially the same as indifference
theory
x3 , y3 
x
If (x1, y1) is directly revealed preferred to (x2,y2),
and the two bundles are not the same, then it cannot
happen that (x2,y2) is directly revealed preferred to
(x1, y1).
This is the weak axiom of revealed preference
(WARP)
If this occurs then
WARP is violated
2 , y2 
1, y1 
That is:
If (x1,y1) is revealed preferred when
(x2,y2) was affordable then (x1,y1) is
preferred always (or at all prices).
Formally:
If we observed two bundles of purchases, (x1,,y1) at
px1,py1 and (x2,,y2) at px2,py2
Then if we observe (x1,,y1) is purchased when
p1x x1  p1y y1  p1x x 2  p1y y2
then we cannot observe
p2x x 2  p2y y2  p2x x1  p2y y1
Optimising consumers must satisfy WARP
If (x1,y1) is revealed preferred to (x3,y3) either
directly or indirectly) then (x3,y3) cannot be
directly or indirectly revealed preferred to (x1,y1)
Strong Axiom of Revealed Preference (SARP)
SARP is a necessary and sufficient condition for
observed behaviour to be consistent with the
underlying model of consumer choice
Revealed Preference and the
(Slutsky) Substitution effect:
(xs,ys)
2 , y2 
1, y1 
• Given revealed preference it MUST be the
case that xs  x1 and ys  y1