Chapter 3
Preferences
If this is coffee, please bring me some tea; but if this is tea, please bring me some coffee. –Abraham Lincoln
Consumer Preferences
Matter!
Jul. 2011
“It’s not just that the loyalty program cards or key chain fobs are a hassle. Savvy customers understand that loyalty programs gather and utilize customer data to make marketing decisions” .
“They give retailers loads of data on shoppers’ habits and preferences”. Consumer Preferences
Matter!
Cisco Costumer
Experience Report for
Automobile Industry,
May.2013 (1,511 consumers in 10 countries)
Rationality in Economics
Behavioral Postulate:
A decisionmaker always chooses its most preferred alternative from its set of available alternatives.
So to model we must model decisionmakers’ choice
.
Preference Relations
Comparing two different consumption bundles, x
= (x1, x2) and y = (y1, y2):
◦ Strict preference: x is more preferred than is y.
◦ x > y means bundle x is preferred strictly to bundle y.
◦ Weak preference: x is as at least as preferred as is y.
◦ x >= y means x is preferred at least as much as is y.
◦ Indifference: x is exactly as preferred as is y.
◦ x ~ y means x and y are equally preferred.
Preference Relations
Strict preference, weak preference and indifference are all preference relations.
Particularly, they are ordinal relations; i.e. they state only the order in which bundles are preferred.
Eg. We cannot say x is twice or fourth times as preferred as y.
Preference Relations
x
f f~ y and y ~
x
f f~ y and (not y ~
x imply
x~y
x) imply
x>y
Assumptions about Preference
Relations
Completeness: For any two bundles x and y it is always possible to make the statement that either x >= y, y >=
or both i.e., x ~ y
x
Assumptions about Preference
Relations
Reflexivity: Any bundle x is always at least as preferred as itself; i.e. x >= x
Assumptions about Preference
Relations
Transitivity: x is at least y is at least x is at least x >=
If as preferred as y, and as preferred as z, then as preferred as z; i.e.
y and y >=
z
x>=
z.
Indifference Curves
Take a reference bundle x’. The set of all bundles equally preferred to x’ is the indifference curve containing x
; the set of all bundles y~x
.
Since an indifference “curve” is not always a curve a better name might be an indifference “set”.
Indifference Curves x2 x’ x” Indifference curve
x”’ x1 Indifference Curves
I1
x2
x z I2 y I3
All bundles in I1 are strictly preferred to all in I2.
All bundles in I2 are strictly preferred to all in I3.
x1
Indifference Curves x2 x
I(x)
WP(x) the set of bundles weakly preferred to x
WP(x) includes
I(x).
x1
Indifference Curves x2 x
Sp(x), the set of bundles strictly preferred to x does not include I(x)
I(x) x1 Indifference Curves Cannot Intersect
x2
I1
I2
x
Proof: assume y>z
From I1, x~y
FromI2,x~z
Therefore,y~z which is a contradiction
Transitivity is violated y z x1 Classic Examples of Preferences
Perfect Substitutes
If a consumer is willing to substitute one commodity for the other at a constant rate, commodities 1 and 2 are perfect substitutes and only the total amount of the two commodities in bundles determines their preference rank-order.
E.g.
Perfect Substitutes x2 15 I2
8
I1
Slopes are constant at - 1.
Bundles in I2 all have a total of 15 units and are strictly preferred to all bundles in
I1, which have a total of only 8 units in them. x1 8
15
Perfect Complements
If a consumer always consumes commodities 1 and 2 in fixed proportion
(e.g. one-to-one), then the commodities are and only the number of pairs of units of the two commodities determines the preference rank-order of bundles.
E.g.
Perfect Complements (ex,left shoes, right shoes) x2 45o
9
5
Each of (5,5), (5,9) and (9,5) contains
5 pairs so each is equally preferred.
I1
5
9
x1
Perfect Complements x2 Since each of (5,5),
(5,9) and (9,5) contains 5 pairs, each is less
I2 preferred than the
