Transcript Consumer Theory Made Much Too Simple

Consumer Theory
Made Much Too
Simple
The basics of the Theory of
Demand
7/20/2015
(c) 1998 Peter Berck
1
Bundles
Definition: A Bundle is a
collection of goods (e.g., 2
apples, 3 green beans).
 In an economy with n goods,
a bundle has n elements,
some of which may be zero.
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Preferences
Behavioral Assumption: Each
person has his/her own
preferences over bundles.
A person can rank two bundles
A and B. Either
A is preferred to B
B is preferred to A
A is indifferent to B
One person may prefer A to B
whilst another prefers B to A.
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Individual Preference?
 Meditation XVII. John Donne.

"The bell doth toll for him that thinks it doth: and though it intermit
again, yet from that minute that that occasion wrought upon him, he is
united to G_d. Who casts not up his eye to the sun when it rises? but
who takes off his eye from a comet when that breaks out? Who bends
not his ear to any bell which upon any occasion rings? but who can
remove it from that bell which is passing a piece of himself out of this
world? No man is an island, entire of itself; every man is a piece of the
continent, a part of the main. If a clod be washed away by the sea,
Europe is less, as well as if a promontory were, as well as if a manor of
thy friend's or thine own were.. Any man's death diminishes me
because I am involved in mankind, and therefore never send to know
for whom the bell tolls; it tolls for thee. (page 1213 of the Norton
Anthology of English Literature. Volume 1. WW Norton & Co. 1974)
 Leviticus. XIX-7.

And when you reap the harvest of your land, thou shalt not wholly
reap the corner of thy field, neither shalt you gather the gleaning of
thy harvest. And thou shalt not glean thy vineyard, neither shalt thou
gather the fallen fruit of thy vineyard: thou shalt leave them for the
poor and the stranger. I am the Lord your G_d. (Hertz)
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Respect Preferences?
 Would you use the word, prefer, to describe the
actions of an alcoholic or a drug addict. Would
you say, "she prefers alcohol to food?" If you said
that, would you still want to influence the addict
to change their behavior? Does your answer
depend upon the damage addicts do to other
people? If it does, consider the poster-girl addict:
she hurts no-one but herself and dies with
enough money in her pocket for her own burial.
Do you subscribe to the view that if a person
thinks their choice makes them better off then
you (and the rest of society) ought also think that
the person's choice makes them better off? Do
you have the same problems answering these
questions for a person who chooses cauliflower
rather than broccoli?
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Properties
The preferences are assumed to
have the following reasonable
properties:
 I. More is better. If bundle A has
strictly more of one good and does
not have less of any good than
bundle B, then all consumers prefer
A to B.
 II. Transitivity. A better than B
better than C means A better than
C.
 III. A preferred to B means B is
not preferred to A.
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More is Better
Bread
?
These points have
more bread or wine
or both.
Every consumer prefers
them to
A
A
Worse than
A
for all.
?
Wine
Point, A, in Bread-Wine space is a bundle
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Level Set
A set of points that have the
same height.
Examples
All the locations on Mt. Rose
that are 8,000 feet.
z = xy; {(x,y)| k = xy} is a level
set, where k is a constant
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Same colored squares are all the same height.
They are in the same level set.
Light Blue squares are 50 units off the “floor”
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Indifference curves.
Two bundles are indifferent (for
a particular consumer) if the
consumer is equally happy with
either bundle.
 (If one added the teeniest bit of
any good to one of the bundles,
then the consumer would prefer it.)
Let A be a bundle. There is an
indifference curve through A.
The indifference curve through
A is the set of all bundles that
makes the consumer just as
happy as bundle A.
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Utility
Think of Utility as height and
amount of goods as x1 and x2
All bundles same height =
level set = indifference curve
Theory only requires
indifference curves not utility
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Properties.
Indifference curves slope down.
They do not cross.
 Higher indifference curves are
better.
For reasons that I don't care to
discuss, I always draw them so
that they look like a crescent
moon.
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A Demonstration
c
B
b
a
W
Every point on the higher indifference
curve is better because b is preferred to a
by more is better, c is indifferent
to b because they are on the same
indifference curve and therefore c is
preferred to a.
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Indiff. Curves Don’t
Cross
Use more is better
and transitivity to
construct the proof
B
a
c
b
W
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Choosing a Bundle
Consumers can choose anything
on or under their budget
constraints.
Those are the only things that
they can afford.
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Which Bundle?
Of the bundles a consumer can
afford, the consumer chooses
the one the consumer
likes most.
B e
Remember: Higher
indifference curve, like
more.
c
f
d
W
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Which??
Choice will occur where an
indifference curve is tangent to
the budget constraint.
No point on the upper
indifference curve lies on the
budget the constraint. The
consumer might like it but
can't afford any such bundle.
All points on the lower
indifference curve are inferior
to the middle indifference
curve.
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Find the bundle
How much bread and
how much wine are purchased?
B
If income is 2, what are the
prices of bread and wine?
6
4
2
2
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W
18
Change in income
An increase in income shifts
budget constraints up in a
parallel fashion.
 (x2 = y/p2 -p1/p2 x1; slopeintercept. change in y does not
change slope but increases
intercept.)
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Inferior and Normal
When income increases the
quantity purchased of a normal
good also increases.
When income increases, the
quantity purchased of an inferior
good decreases
B
W
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5. The food stamp
example
Pay $A to buy $C worth of
stamps
food stamp food FB and food
bought with cash OB.
total food B = OB +FB >=
$C/Pb = FB,
after purchase of stamps
y - $A left to spend so
y - $A= Pb OB + Pw W,
where OB >= 0.
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Algebra Concludes
 Subsitute B - FB for OB
 and $C/Pb for FB
, to get the new budget
constraint,
 y - $A +$C = Pb B + Pw W ,
where B >= $C/Pb
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Food stamp picture
Let the price of wine be 1. What is y?
slope of the budget constraints? Price of bread?
Quantity of food stamps, $c,
and cost of food stamps $a?
120
100
Wine
80
60
40
20
0
0
10
20
30
Bread
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Participate? Cash?
120
100
Wine
80
60
40
20
0
0
10
20
30
Bread
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