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Preferences and Choice
• Two ways to think about preferences
– Everyone has them. And uses them.
– It’s a handy construct useful to economists.
New symbol
• You already know:
x>y
“the number x is larger than the number y”
• There is also:
xy
“Given the choice of x and y, I’d rather have x”
• x y Is called a “preference relation”
• Preferences are “rational” if:
– For any x and y, someone can say
• x is preferred to y, or
• y is preferred to x, or
• They are equally preferred (called indifference: x ~ y)
– For any x, y and z
• If x is preferred to y and y is preferred to z, then x is preferred
to z.
• The first property is called completeness
and the second is called transitivity.
• If preferences are rational, then we can’t
have the following:
– “Do you prefer Coke or Pepsi?”
– “I don’t know.”
• The first property is called completeness and the
second is called transitivity.
• If preferences are rational, then we can’t have
the following:
– “Would you prefer a Coke or Pepsi?”
– “Coke.”
– “Would you prefer a Pepsi or a Sprite?”
– “Pepsi.”
– “Well, we only have Coke and Sprite, so I guess you
want a Coke.”
– “No, I prefer Sprite to Coke.”
• Both assumptions are vital to economic
modeling, but transitivity is really the most
important one.
Fun (ok, dorky fun)
• Soritites (soros = heap) paradox
– Do we all agree that 100,000 grains of wheat
would be considered a heap of wheat?
Which of these two boxes do you
prefer, or are you indifferent?
And these?
And these?
• We could keep going…and we would
eventually reach this choice….
Ugly, I know.
• I bet you have an opinion about this…
• Framing
– The question matters
– Daniel Kahneman won the 2002 Nobel Prize
in Economics for his workon this problem:
"for having integrated insights from
psychological research into economic
science, especially concerning human
judgment and decision-making under
uncertainty."
• Kahneman and Tversky (1984)
• “Imagine that you are about to purchase
an Ipod for $125 and a calculator for $15.
The salesman tells you that the calculator
is on sale for $5 less at another branch of
the store located 20 minutes away. The
Ipod is the same price.”
• “Imagine that you are about to purchase a
Ipod for $125 and a calculator for $15. The
salesman tells you that the Ipod is on sale
for $5 less at another branch of the store
located 20 minutes away. The calculator is
the same price.”
Stupid Games
• This is a more serious example:
– The casual smoker: They prefer 1 cigarette to
zero cigarettes, but prefer zero cigarettes to a
pack of cigarettes.
– Problem: Once they have one cigarette, they
have many (change of tastes)
Odyssey XII, 6
• To the Sirens first shalt thou come, who bewitch all men,
whosoever shall come to them. Whoso draws nigh them unwittingly
and hears the sound of the Sirens’ voice, never doth he see wife or
babes stand by him on his return, nor have they joy at his coming;
but the Sirens enchant him with their clear song, sitting in the
meadow, and all about is a great heap of bones of men, corrupt in
death, and round the bones the skin is wasting. But do thou drive thy
ship past, and knead honey-sweet wax, and anoint therewith the
ears of thy company, lest any of the rest hear the song; but if thou
myself art minded to hear, let them bind thee in the swift ship hand
and foot, upright in the mast-stead, and from the mast let rope-ends
be tied, that with delight thou mayest hear the voice of the Sirens.
And if thou shalt beseech thy company and bid them to loose thee,
then let bind thee with yet more bonds.
John William Waterhouse, Odysseus and the Sirens
Stupid Games
• This is a more serious example:
– The casual smoker: They prefer 1 cigarette to
zero cigarettes, but prefer zero cigarettes to a
pack of cigarettes.
– Problem: Once they have one cigarette, they
have many (change of tastes)
– Solution: They don’t smoke at all
(commitment).
Edvard Munch, The Day After
Stupid Games
• This is a more serious example:
– The casual smoker: They prefer 1 cigarette to
zero cigarettes, but prefer zero cigarettes to a
pack of cigarettes.
– Problem: Once they have one cigarette, they
have many (change of tastes)
– Solution: They don’t smoke at all
(commitment).
– Problem: Commitment breaks down around
alcohol.
Stupid Games
• This is a more serious example:
– The tomorrow dieter: They prefer eating cake
to not eating cake, but prefer not eating cake
to getting fat.
– Problem: They will have the cake today and
start a diet tomorrow (time-inconsistency)
– Solution: They don’t buy snack foods at the
grocery store (commitment).
Indifference Curves
• Lets run with completeness and
transitivity.
• Let x be a bundle of goods. Find all the
other bundles that you would be equally
happy having (wouldn’t care if you traded).
• If you graphed these, it would be an
indifference curve.
Example
Indifference Curve
16 1, 16
14
12
Would trade 1 football
Football tickets
ticket and 16 hockey tickets
10
for 4 of each
8
6
4 4, 4
2
16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Example
Indifference Curve
16 1, 16
14
Do you think you’d prefer 5
12
Football tickets
of each to 4 of each?
10
8
6
5, 5
4 4, 4
2
16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Example
Indifference Curve
16 1, 16
14
12
Football tickets
10
8
6
5, 5
4 4, 4
2
16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Can’t Cross
Indifference Curve
16
14 A
A~ C
12
Football tickets
B~C
10
B
8 But, A and B are not on the
6 C same indifference curve.
5, 5
4
Violate transitivity!
2
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Rationality
• Completeness: every point in the graph is
on some indifference curve.
• Transitivity: Indifference curves can’t
cross.
Example
Indifference Curve
16 1, 16
14
Do you think you’d prefer 5
12
Football tickets
of each to 4 of each?
10
8
6
5, 5
4 4, 4
2
16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Example
Indifference Curve
16 1, 16
14
Do you think you’d prefer 5
12
Football tickets
of each to 4 of each?
10
8 If so (more is better) then
6 preference is increasing
5, 5 toward the northeast
4 4, 4
2
16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Look familiar?
Indifference Curve Isoquants
16 1, 16 16
14 14
12 12 Q = 16
Football tickets
10
Capital
10
8
8
6
6
5, 5 4
Q = 25
4 4, 4
2
2
0
16, 1 0 Q=9
0 2 4 6 8 10 12 14 16 0 2 4 6 Labor10 12 14 16
8
Hockey tickets
Look familiar?
Indifference Curve Isoquants
16 1, 16
16
14
14
12 Q = 16
Football tickets
12
10
10
Capital
8
8
6
6
4
5, 5
4, 4
4
Q = 25
2
16, 1 2
0
0 2 4 6 8 10 12 14 16
0 Q=9
Hockey tickets 0 2 4 8
6 Labor10 12 14 16
All that’s missing is a label for each indifference curve.
What if we labeled each with number?
And, the only numbering rule is a higher number means every bundle
on that curve is preferred to every bundle on a curve with a lower
number.
Look familiar?
Indifference Curve Isoquants
16 1, 16
16
14
14
12 Q = 16
Football tickets
12
10
10
Capital
8
8
6
6
4
5, 5
4, 4
4
Q = 25
2
16, 1 2
0
0 2 4 6 8 10 12 14 16
0 Q=9
Hockey tickets 0 2 4 8
6 Labor10 12 14 16
Utility: label on an indifference curve to tell you which curve is preferred
to which.
1) Completeness
2) Transitivity
3) Something technical, but not strange.
Look familiar?
Indifference Curve
16 1, 16
14
12
Football tickets
10
8
6
5, 5
4 4, 4
U=2
2 U=1 16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Utility: label on an indifference curve to tell you which curve is preferred
to which.
Look familiar?
Indifference Curve
16 1, 16
14
12
Football tickets
10
8
6
5, 5
4 4, 4
U=200
2 U=100 16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Utility: label on an indifference curve to tell you which curve is preferred
to which.
Look familiar?
Indifference Curve
16 1, 16
14
12
Football tickets
10
8
6
5, 5
4 4, 4
U=200,000,000
2 U=100,000,000 16, 1
0
0 2 4 6 8 10 12 14 16
Hockey tickets
Utility: label on an indifference curve to tell you which curve is preferred
to which.
• How you label:
– Find a utility function that is consistent with
the data (bottom up)
– Use a utility function that is convenient for the
math you want to do (top down)
Example of a bad
Indifference Curve
Homework is a bad, not a
16
good.
14
12 If you are going to increase
Football tickets
10 my homework, you have to
give me more football
8
tickets to be indifferent
6
4
2
0
0 2 4 6 8 10 12 14 16
Homework
