Post on 20-Dec-2015
transcript
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
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
The Ranking Principle
• A consumer can rank, in order of preference, all potentially available alternatives
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’
Indifference
Indeed, for any consumption bundle, it is possible to find other bundles that are equally good
Origin
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 bundles—such as B, C, and D—that are equally good as A.
W2
Z2
D
An Indifference Curve
An indifference curve is a set of consumption bundles that the consumer prefers equally
Origin
K is inferior and L is superior to the bundles on the indifference curve
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.
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.
B, B
urr
itos
per
sem
est
er
Z, Pizzas per semester
I1
I0a
be
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.
B, B
urr
itos
per
sem
est
er
Z, Pizzas per semester
I
a
b
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 consumer’s willingness to pay Y for a unit of X
curve ceindifferen of slope
XY
XY
MRS
XYMRS
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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 slope—and its negative, the
MRS—at 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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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
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
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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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 consumer’s preferences
• The number assigned to a bundle is called its utility
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 consumer’s preference ranking, then the formula is a utility function.
CONSUMER PREFERENCES
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:
• 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
u(F,C) = FC
Marginal Utility
• Marginal utility is the increase in a consumer’s utility resulting from the addition of a very small amount of some good, per unit of the good
XUMU X
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MU and MRS• Consider changes in
consumption, X and Y, that leave utility unchanged
• A small change in X, X, causes utility to change by MUXX
• Small change in Y, Y, causes utility to change by MUYY
• If we stay on same indifference curve, then MUXX + MUYY = 0. Therefore,
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XYY
X
Y
X
YX
YX
MRSX
Y
MU
MU
YXMU
MU
YMUXMU
YMUXMU
0
Utility and Marginal Utility
• 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. M
UZ,
Mar
gina
l util
ity o
f pi
zza
MUZ
10987654321
Z, Pizzas per semester
0
130
(b) Marginal Utility
20
U,
Util
s
U = 20
Utility function, U (10, Z)
Z = 1
10987654321
Z, Pizzas per semester
0
350
250
(a) Utility
230
Z
UMU Z
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
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
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
X
Y