01 Preferences

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Consumers preferences

ECO61

Udayan RoyFall 2008


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Goods bundles

Origin


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Preferences

Consumers have preferences that they can use

to compare different goods bundles

The preferences may be over goods bundlesconsumed by oneself or over goods bundles

consumed by someone else

For example, a parent may have preferences over

various bundles of food and clothing bought by

the parent but consumed by a child


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Assumptions about Preference

Orderings

Completeness: the consumer is able to rank allpossible bundles of goods and services.

For any two bundles A and B, the consumer knows

whether A is better, or B is better, or they are equallygood

Transitivity: for any three bundles A, B, and C, ifAis at least as good as B and B is at least as good as

C, then A is at least as good as C. These two assumptions imply the ranking

principle


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The Ranking Principle

A consumer can rank, in order of preference,

all potentially available alternatives


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Assumption: More-Is-Better

Other things equal, more of a good is

preferred to less.

We ignore goods that are harmful or poisonous,for which more is notbetter than less. Such goods

are jokingly referred to as bads


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Indifference

Indeed, for any

consumption bundle, it

is possible to find other

bundles that are equally

good

Origin

Wis worse than A. Z is

better than A. So, on the

line joining Wand Z,

there must exist a goods

bundle such as B that the

consumer considers

equally good as A. By

using this logic

repeatedly, we can find

many other bundles

such as B, C, and Dthat

are equally good as A.

W2

Z2

D


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An Indifference Curve

An indifference curve is a

set of consumption

bundles that the

consumer prefers equally

Origin

Kis inferior and

Lis

superior to the bundles on

the indifference curve


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Part of an Indifference Map

Origin


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Properties of Indifference Maps

1. Bundles on indifference curves farther from

the origin are preferred to those on

indifference curves closer to the origin.

2. There is an indifference curve through every

possible bundle.

3. Indifference curves cannot cross.

4. Indifference curves slope downward.


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Impossible Indifference Curves

Lisa is indifferentbetween e and a, andalso between e and b

so by transitivity sheshould also be indifferent

between a and b

but this is impossible,

since b must be preferred

to a given it has more ofboth goods.

B,

Burritospersemester

Z, Pizzas per semester

I1

I0a

b

e


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Lisa is indifferentbetween b and asince both points arein the same

indifference curve But this contradicts

the more is betterassumption. Can youtell why?

Yes, b has more ofboth and hence itshould be preferredover a.

B,

Burritospersemester


I

a

b


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Substitution Between Goods

Economic decisions involve trade-offs

Indifference curves provide information on

the amount of one good that the consumer iswilling to give up to gain a unit of another

good

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Rates of Substitution

Consider moving along an indifference curve, from

one bundle to another

This is the same as taking away units of one good

and compensating the consumer for the loss byadding units of another good

Slope of the indifference curve shows how much of

the second good is needed to make up for a loss of

the first good

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Figure 4.8: Rates of Substitution

Look at the move frombundle A to C

Consumer loses 1 soup ((S= -1); gains 2 bread ((B =+2)

A and C are equallydesirable

Slope of indifference curve= (B/(S = -2

Consumer is willing tosubstitute for soup withbread at 2 ounces per pint

4-16


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Marginal Rate of Substitution

The marginalrate of substitution for X with Y, MRSXY, is therate at which a consumer must adjust Y to maintain the samelevel of well-being when X changes by a tiny amount, from agiven starting point

Tells us how much Y a consumer needs to compensate forlosing a little bit of X, per unit of X

Tells us the maximum amount ofY a consumer would bewilling to pay per additional unit of X

That is, MRSXY is the consumers willingness to pay Y for aunit of X

curveceindifferenofslope!

((!

XY

XY

MRS

XYMRS

4-17


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Figure 4.9: Marginal Rate of Substitution

Slope = (B/(S = 3/(-2) =-3/2

MRSSB= -(B/(S=-3/(-2) = 3/2

The slopeand its negative, theMRSat bundle A can beapproximated by the slope ofthe line AD, or the line AE, orthe line AF, etc.

But the precise value is obtained

from the slope of the line that istangent to the indifferencecurve at bundle A.

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What Determines Rates of Substitution?

Tastes

Preferences for one good over another affect the slope ofan indifference curve and MRS

Starting point on the indifference curve; the initial

goods bundle People like variety. So most indifference curves get flatter

as we move from top left to bottom right

Link between slope and MRS implies that MRS declines;

the amount ofY

required to compensate for a givenchange in X decreases as X increases

One gets bored with X as consumption of X increases. Therefore,one needs less Y to compensate for a unit loss of X

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Figure 4.10: Indifference Curves and

Consumer Tastes

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Preferences and time

To a non-economist, food is food is food. To an economist, food delivered this year and

food delivered next year are different goods


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Preferences and chance

To an economist, food delivered tomorrow ifit is sunny and food delivered tomorrow ifthere is a hurricane are different goods


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Figure 4.11: MRS along an Indifference

Curve

4-23


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Perfect Substitutes and Complements

Two products areperfect substitutes if theirfunctions are identical; in such a case, a consumer iswilling to swap one for the other at a fixed rate

Two products areperfect complements if they arevaluable only when used together in fixedproportions

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Figure 4.12: Perfect Substitutes

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MRSRE

=


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Figure 4.13: Perfect Complements

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Utility

Recall that under the completeness andtransitivity assumptions, the ranking principle istrue:

the consumer can rank all bundles according to herpreference

Therefore, the consumer can assign a number toeach bundle such that the numbers assigned to

the bundles represent the consumerspreferences

The number assigned to a bundle is called itsutility


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Utility functions

If the utility numbers assigned by a consumer tothe various consumption bundles can berepresented by a mathematical formula, thatformula is called a utility function

Example: Consider two goods, food and clothing and let the

quantities consumed be Fand C.

Then, the formula U(F,C) = Fv Ccan be used to assign

a number to any bundle. (For example, ifF= 11 and C= 3, then U = 33.)

And if the assigned numbers agree with theconsumers preference ranking, then the formula is autility function.


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CONSUMER PREFERENCES

A utility function can be

representedby aset of

indifference curves,each

with a numerical

indicator.

This figureshows threeindifference curves (with

utility levels of25,50,

and100, respectively)

associated with the utility

function:

Utility and Utility Functions

utility Numerical score representing thesatisfaction that aconsumer gets from a given market basket.

utility function Formula that assignsa level of utility to individualmarket baskets.

Utility Functions and Indifference Curves

u(F,C) = FC


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Indifference Curves for the Utility Function

U= Fv S


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Marginal Utility

Marginal utilityis the increase in a consumers

utility resulting from the addition of a very small

amount of some good, per unit of the good

XUMUX

((!

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MU and MRS

Consider changes inconsumption, (X and(Y, that leaveutilityunchanged

A small change in X, (X,

causes utility to changeby MUX(X

Small change in Y, (Y,causes utility to changeby MU

Y(Y

If we stay on sameindifference curve, thenMUX(X + MUY(Y = 0.Therefore,

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XY

Y

X

Y

X

YX

YX

MRSX

Y

MU

MU

YXMU

MU

YMUXMU

YMUXMU

!(

(!

(!(

(!(

!(( 0


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Utility and

Marginal Utility

As Lisa consumes morepizza, holding herconsumption of burritosconstant at 10, her totalutility, U, increases

and her marginalutility of pizza, MU

Z,

decreases (though itremains positive).

Marginal utility is theslope of the utilityfunction as we hold thequantity of the othergood constant. M

UZ,

Marginalutilityofpizza

MUZ

10987654321


0

130

(b) Marginal Utility

20

U,

Utils

(U = 20

Utility function, U (10, Z )

(Z = 1

10987654321


0

350

250

(a) Utility

230Z

UMUZ

(

(!


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Ordinal utility

The indifference map of the utility function U =

XYwill look identical to the indifference map of

the utility function V= (XY)2 = U2 or of the utility

function W= (XY

)2

+ 12 =U2

+ 12 That is, the way a utility function ranks various

goods bundles is unchanged if the utility numbers

given to every bundle are transformed in an

order-preserving manner

The utility numbers themselves are unimportant

Only the implied rankings are important


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Ordinal utility

As was just claimed, the indifference map of

the utility function U = XYwill look identical to

the indifference map of the utility function V=

(XY)2 = U2 or of the utility function W= (XY)2 +12 = U2 + 12

In particular, MRSXY at any goods bundle will

be unaffected if the utility numbers given toevery bundle are transformed in an order-

preserving manner


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Figure 4.12: Perfect Substitutes

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Utility function: U = 2E+ R

MRSRE

=


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Figure 4.13: Perfect Complements

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Utility function: U = min{R,L}


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Quasi-linear utility

U = f(X) + Y

Example: U = X0.5 + Y

MRSXY depends on Xbut

not on Y

That is, at any value ofX, allindifference curves have

the same slope

As all indifference curves

are parallel to each other,

the vertical distancebetween any two

indifference curves is

always the same

We will see later why this

utility function is significant

X

Y

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