L02

Preferences

Rationality in Economics

Behavioral Postulate:A decisionmaker chooses its most preferred alternative from the set of affordable alternatives.

Budget set = affordable alternatives To model choice we must have

decisionmaker’s preferences.

Last Week

apples

oranges

x=(2,3)p1=2p2=1M=6

Today: Preferences Rational agents: can rank any two

consumption bundles We call such ranking preferences–weak preference: x is at least as good as is

y. (x y)–strict preference: x is strictly better than is

y. (x y)– indifference: x is exactly as preferred as is

y. (x y)

~

~

Rational Decisionmaker

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I) Completeness:either or or both

~ ~x y y x

II) Transitivity:x y and y z x z.~ ~ ~yy

~x~

zz~ ~

~

Rationality Axioms (Assumptions)

Indifference Curves

Convenient representation of Indifference Curve Map

The set of all bundles equally preferred to x is the indifference curve containing x;

The collection of all bundles y x.

~

Representation: Indifference Curves

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x”x”

x”’x”’

x’ x’ x” x” x”’ x”’x’

Indifference curve = a collection of all indifferent bundles.

Indifference Curve Map

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zz xx yy

x

y

z

Can Two Indifference Curves Intersect?

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xxyy

zz

Two goods always consumed in the same proportion

Example: Right and Left Shoes

We like to have more of them but always in pairs

Example: Perfect Complements

Example 1: Perfect complementsLeft

Right

1:1

Example: Perfect complementsCoffee

Sugar (teaspoons)

1:2

Two goods that are substituted at the constant rate

Example: French and Dutch Cheese

(I like cheese but I cannot distinguish between the two kinds)

Example: Perfect substitutes

Example: Perfect substitutesDutch

French

Slopes of Indifference Curves (MRS)

The slope of an indifference curve is its marginal rate-of-substitution (MRS).

Why rate-of-substitution? Why marginal?

Slope: Marginal Rate of Substitution

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MRS(x) is a slope of the RS(x) is a slope of the indifference indifference

curve at xcurve at xxx

Slope of Indifference Curves

When more of a commodity is always preferred, the commodity is a good.

Two goods. Sign of MRS?

Good 2Good 2

Good 1Good 1

Slope of Indifference Curves

If less of a commodity is prefered the commodity is a bad. (Spinach)

Two goods. Sign of MRS?

Bad 2Bad 2

Good 1Good 1

Preferences Exhibiting Satiation

Many commodities become bads after some threshold of consumption (salt and pepper)

Bundle consisting of threshold quantities is called a satiation point or a bliss point.

A satiation point is strictly preferred to any other bundle.

Preferences Exhibiting Satiation

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xx1 1 (salt)(salt)

SatiationSatiation point point

x*x*11

x*x*22

(pepper)(pepper)

Well-Behaved Preferences

We will typically assume that preferences are well-behaved:

1) monotonic (all goods)

2) weakly convex

Convexity.

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x=(1,3)

y=(3,1)

z =(2,2)

Preferences are convex if mixtures “z”Preferences are convex if mixtures “z”are (weakly) preferred to extremes x and y.are (weakly) preferred to extremes x and y.

Convex preferences?

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