Consumers preferences

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Consumers preferences

• ECO61
• Udayan Roy
• Fall 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 bundles
  consumed 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 all
  possible 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
  equally good
• Transitivity for any three bundles A, B, and C,
  if A is 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 not better than less. Such
  goods are jokingly referred to as bads

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Indifference
W is worse than A. Z is better than A. So, on the
line joining W and 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 bundlessuch
as B, C, and Dthat are equally good as A.
Z2
D
W2
Indeed, for any consumption bundle, it is
possible to find other bundles that are equally
good
Origin
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An Indifference Curve
An indifference curve is a set of consumption
bundles that the consumer prefers equally
K is inferior and L is superior to the bundles on
the indifference curve
Origin
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Part of an Indifference Map
Origin
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Properties of Indifference Maps

• Bundles on indifference curves farther from the
  origin are preferred to those on indifference
  curves closer to the origin.
• There is an indifference curve through every
  possible bundle.
• Indifference curves cannot cross.
• Indifference curves slope downward.

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Impossible Indifference Curves

• Lisa is indifferent between e and a, and also
  between e and b
• so by transitivity she should also be indifferent
  between a and b
• but this is impossible, since b must be preferred
  to a given it has more of both goods.

itos per semester
r
, Bur
B
e
b
1
I
a
0
I
Z
, Pizzas per semester
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Impossible Indifference Curves

• Lisa is indifferent between b and a since both
  points are in the same indifference curve
• But this contradicts the more is better
  assumption. Can you tell why?
• Yes, b has more of both and hence it should be
  preferred over a.

itos per semester
b
r
, Bur
B
a
I
Z
, Pizzas per semester
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Impossible Indifference Curves
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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 is willing
  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 by
  adding 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 from bundle A to C
• Consumer loses 1 soup (?S -1) gains 2 bread
  (?B 2)
• A and C are equally desirable
• Slope of indifference curve ?B/?S -2
• Consumer is willing to substitute for soup with
  bread at 2 ounces per pint

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Marginal Rate of Substitution

• The marginal rate of substitution for X with Y,
  MRSXY, is the rate at which a consumer must
  adjust Y to maintain the same level of well-being
  when X changes by a tiny amount, from a given
  starting point
• Tells us how much Y a consumer needs to
  compensate for losing a little bit of X, per unit
  of X
• Tells us the maximum amount of Y a consumer would
  be willing to pay per additional unit of X
• That is, MRSXY is the consumers willingness to
  pay Y for a unit of X

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Figure 4.9 Marginal Rate of Substitution

• Slope DB/DS 3/(-2) -3/2
• MRSSB -DB/DS-3/(-2) 3/2
• The slopeand its negative, the MRSat bundle A
  can be approximated by the slope of the line AD,
  or the line AE, or the line AF, etc.
• But the precise value is obtained from the slope
  of the line that is tangent to the indifference
  curve at bundle A.

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What Determines Rates of Substitution?

• Tastes
• Preferences for one good over another affect the
  slope of an 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 of Y required to compensate
  for a given change 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 if it
  is sunny and food delivered tomorrow if there
  is a hurricane are different goods

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Figure 4.11 MRS along an Indifference Curve
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Perfect Substitutes and Complements

• Two products are perfect substitutes if their
  functions are identical in such a case, a
  consumer is willing to swap one for the other at
  a fixed rate
• Two products are perfect complements if they are
  valuable only when used together in fixed
  proportions

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Figure 4.12 Perfect Substitutes
MRSRE ½
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Figure 4.13 Perfect Complements
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Utility

• Recall that under the completeness and
  transitivity assumptions, the ranking principle
  is true
• the consumer can rank all bundles according to
  her preference
• Therefore, the consumer can assign a number to
  each bundle such that the numbers assigned to the
  bundles represent the consumers preferences
• The number assigned to a bundle is called its
  utility

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Utility functions

• If the utility numbers assigned by a consumer to
  the various consumption bundles can be
  represented by a mathematical formula, that
  formula is called a utility function
• Example
• Consider two goods, food and clothing and let the
  quantities consumed be F and C.
• Then, the formula U(F,C) F ? C can be used to
  assign a number to any bundle. (For example, if F
  11 and C 3, then U 33.)
• And if the assigned numbers agree with the
  consumers preference ranking, then the formula
  is a utility function.

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CONSUMER PREFERENCES

• Utility and Utility Functions

? utility Numerical score representing the
satisfaction that a consumer gets from a given
market basket.
? utility function Formula that assigns a
level of utility to individual market baskets.
Utility Functions and Indifference Curves
A utility function can be represented by a set of
indifference curves, each with a numerical
indicator. This figure shows three indifference
curves (with utility levels of 25, 50, and 100,
respectively) associated with the utility
function
u(F,C) FC
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Indifference Curves for the Utility Function U
F ? S
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Marginal Utility

• Marginal utility is the increase in a consumers
  utility resulting from the addition of a very
  small amount of some good, per unit of the good

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MU and MRS

• Consider changes in consumption, DX and DY, that
  leave utility unchanged
• A small change in X, DX, causes utility to change
  by MUXDX
• Small change in Y, DY, causes utility to change
  by MUYDY
• If we stay on same indifference curve, then MUXDX
  MUYDY 0. Therefore,

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Utility and Marginal Utility
(a) Utility
350
Utility function,
U
(10,
Z
)
, Utils
U
250
DU 20
230

• As Lisa consumes more pizza, holding her
  consumption of burritos constant at 10, her total
  utility, U, increases
• and her marginal utility of pizza, MUZ, decreases
  (though it remains positive).
• Marginal utility is the slope of the utility
  function as we hold the quantity of the other
  good constant.

DZ 1
10
9
8
7
6
5
4
3
2
1
0
Z
, Pizzas per semester
(b) Marginal Utility
130
, Marginal utility of pizza
Z
MU
20
MU
Z
10
9
8
7
6
5
4
3
2
1
0
Z
, Pizzas per semester
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Ordinal utility

• The indifference map of the utility function U
  XY will 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 XY will 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 to every
  bundle are transformed in an order-preserving
  manner

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Figure 4.12 Perfect Substitutes
Utility function U 2E RMRSRE ½
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Figure 4.13 Perfect Complements
Utility function U minR, L
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Quasi-linear utility

• U f(X) Y
• Example U X0.5 Y
• MRSXY depends on X but not on Y
• That is, at any value of X, all indifference
  curves have the same slope
• As all indifference curves are parallel to each
  other, the vertical distance between any two
  indifference curves is always the same
• We will see later why this utility function is
  significant

Y
X