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