Svetlana Danilkina
Lectures, week 1
Topic 1.
Consumer Theory
Econ20002
Intermediate Microeconomics
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Overview
1.
Budget set
a.
b.
c.
d.
e.
f.
g.
2.
bundles
budget set and budget line; how to draw
math: formula for a budget line
the slope of the budget line
what happens if income falls
what happens if price rises
other changes
Preferences
a.
b.
c.
d.
e.
completeness, transitivity and more is better
indifference curves and maps
goods and “bads”
convexity and concavity
the shape of the indifference curves and the
marginal rate of substitution (MRS)
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Consumer choice
problem
• Hungry Jack is always hungry. He likes Big
Macs and Coca-Cola very much but thinks
that eating them all the time may not be very
healthy.
• Recently, he was invited to repeat Morgan
Spurlock’ experience in Supersize me and
eat only Big Macs and drink Coke for a month.
He was allocated income I to spend on the
food.
• Jack accepted the offer with the enthusiasm.
• Can we say how many Big Macs and cups of
Coke he will buy?
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What do we need?
To understand Jack’s purchases
of Big Macs and Coke we need to
know
• his preferences over Big Macs and Coke
(what he likes)
• his budget constraint (what he can
afford)
• how he makes a decision: is he rational?
(Is he choosing, for example, randomly,…?)
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1. Budget constraints
1a. bundles
Jack can buy, for example (per month):
(60 burgers, 60 cups of Coke) or
(180 burgers, 30 cups of Coke) or
(30 burgers, 120 cups of Coke) or
(0 burgers, 150 cups of Coke) or
any other combination of these two goods.
We call them bundles of goods, or market baskets.
A consumer bundle, or market basket,
is a list of specific quantities of goods to buy.
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1b. Budget set
What bundles Jack can buy depends on
• how much money he has to spend (his income I) and
• the prices of the goods he wants to buy (the price of
BigMac and the price of Coke).
Therefore, his choice of bundles is restricted by what he
can afford. He might want to eat a thousand of burgers
and drink a thousand of cups of Coke (and probably die
from too much food), but he may or may not be able to
afford them.
Budget set the set (in other words, collection) of all bundles of
goods that consumer can afford given prices of goods
and his/her income.
It is a set of feasible bundles.
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Jack goes to the McDonalds
• he can spend up to $600 (this is his
income or wealth)
• he can buy Coke at $2.50 per cup
• he can buy BigMacs at $5 each
• We can draw up his budget set (all
bundles of BigMacs and Coke he can
afford)
• The outer boundary of the budget set
is called the budget line. It consists
of all bundles of goods for which he
spends all his income.
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To draw Jack's budget set
• We have two goods and two dimensions
q2 , Coke
30
20
10
10
20
30
q1, BigMacs
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• Find the two intercepts (given by income
divided by price for the relevant good)
q2 , Coke
I/p2=
=600/2.50=
=240
I/p1=600/5=
=120
q1, BigMacs
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• If Jack faces unchanging prices then the
budget line is a straight line
– Every time Jack buys one less BigMac he
‘frees up’ p1=$5. But Coke costs p2=$2.50
so with the extra $5 he can buy 2 cups of
Coke (p1/p2 = $5/$2.50 = 2 Coke)
q2 , Coke
– Thus, the budget line is a straight line with
slope =-2 (i.e. give up 1 BigMac to get 2
240
Coke)
the budget set
?
1
the budget line; the slope = -p1/p2=-2
slope = -2
120
q1, BigMacs
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q2 , Coke
I/p2
=240
the budget set: p1q1 + p2q2 ≤ I
5*q1 + 2.50*q2 ≤ 600
the budget line: p1q1 + p2q2 = I
5*q1 + 2.50*q2 = 600
the slope = -p1/p2=-2
slope = -2
I/p1=120
q1, BigMacs
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1c. math
In general:
q2
the budget set: p1q1 + p2q2 ≤ I
I/p2
The better way
to write down
the budget line
the budget line: p1q1 + p2q2 = I
the slope=-p1/p2
q2 = a + bq1
intercept
slope = -p1/p2
I/p1
the budget line: p1q1 + p2q2 = I
q1
slope
Only
mathematician
would do that!
rearrange: p2q2 = I - p1q1=> q2 = I/p2 – (p1/p2) q1
intercept = I/p2
slope=-p1/p2
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1d. The slope of the budget line
• The slope of the budget line tells us the
marginal rate of transformation (MRT)
of BigMacs for Coke in the market place
(trade off between the two goods on the
market).
– By buying one less BigMac Jack can buy 2
more cups of Coke.
• Alternatively, it tells us the opportunity
cost of a BigMac to Jack in terms of Coke
foregone
– If Jack buys one more BigMac he gives up the
chance of buying an extra 2 cups of Coke.
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When things change …
Change in prices and income can cause the
budget line to shift inward or outward,
rotate inward or outward, become
steeper or flatter...
• A rise in income results in a parallel shift
of the budget line outward
• A fall in income results in a parallel shift
of the budget line inward
• A change in one price causes the budget
line to rotate about one intercept
πάντα χωρεϊ καί ούδέν μένει, Heraclitus as interpreted by Plato
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1e. What happens if Jack's
income falls from $600 to
$500?
q , Coke
2
240
Both end points change.
if Jack only buys BigMacs
then the most he can buy
now is 100 BigMacs, not 120.
He can buy 20 less BigMacs
(he has lost $100 and each
BigMac is $5)
100
120
q1, BigMacs
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What happens if Jack's
income falls from $600 to
$500?
q , Coke
2
240
Both end points change.
If Jack only buys Coke then
the most he can buy now is
200 cups, not 240 cups. He
can buy 40 less cups (he
has lost $100 and each
Coke is $2.50 per cup)
200
100
120
q1, BigMacs
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What happens if Jack's
income falls from $600 to
$500?
q , Coke
2
240
But note that the slope of
Jack's budget line does
not change. The slope is
the negative of the price
ratio – and the prices are
unchanged.
200
Result: a parallel shift of
the budget line inward
100
120
q1, BigMacs
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1f. What happens if the price
of BigMacs rises to $6 each?
q2 , Coke
240
This intercept doesn’t change
– if you buy only Coke, the
price of BigMacs is irrelevant
120
q1, BigMacs
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What happens if the price of
BigMacs rises to $6 each?
q2 , Coke
But this intercept does
change. With $600 Jack can
only buy a maximum of 100
BigMacs at the new higher
price, not 120 BigMacs
240
100
120
q1, BigMacs
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What happens if the price of
BigMacs rises to $6 each?
q2 , Coke
The slope of the budget line also
changes. The slope is -(PBigMac/Pcoke).
240
Initially the slope is -(5/2.5) = -2.
But after the price rise the slope is
-(6/2.5) = -2.4
Results: the budget line rotates
inward and becomes steeper.
100
120
q1, BigMacs
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What happens if the price of
BigMacs rises to $6 each?
• Why does the slope increase?
– If Jack buys one less BigMac after the price
rise, then he frees up $6 and can use this to
buy 2.4 cup of Coke. So the MRT of BigMac for
Coke in the market place is now 2.4.
– Alternatively, note that if Jack buys an extra
BigMac he spends $6 and gives up 2.4 Coke.
So the opportunity cost of a BigMac for Jack
is now 2.4 Coke.
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1g. Other changes
• What happens if Jack's income rises?
• What happens if the price of Coke falls to $1
per cup?
• What happens if both the price of BigMacs
and the price of Coke doubles?
• What happens if both the price of Coke and
the price of BigMacs increase by 50% but
Jack's income also increases by 50%?
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math, please!
q2
I/p2
the budget line: p1q1 + p2q2 = I
the slope=-p1/p2
slope = -p1/p2
I/p1
q1
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Other changes
• What happens if Jack's income rises?
– his budget line shifts out parallel to the original b.l.
• What happens if the price of Coke falls to $1
per cup?
– his budget line rotates outward around the ‘BigMac
intercept’
• What happens if both the price of BigMacs
and the price of Coke doubles?
– This is just like a halving of Jack's income
• What happens if both the price of Coke and
the price of BigMacs increase by 50% but
Jack's income also increases by 50%?
– Nothing happens to his budget set! (no “money
illusion”)
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2. Preferences
We can use a weak preference relation ≿ to
represent the consumer’s preferences: if
A ≿ B,
we say that bundle A is at least as good as bundle
B (you can also say “A is weakly preferred to B” or
“A is weakly better than B”).
Consumers’ preferences usually satisfy some
assumptions. We will discuss some of them.
Assumption 1. Completeness
Any two consumption bundles can be compared: for
any A and B, either A ≿ B or B ≿ A.
• note that “or” here is inclusive (i.e. it could be both)
• does this assumption always hold?
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Strict preference and indifference
Consider two bundles, A and B. When the
consumer compares them, three things could
happen:
• the consumer prefers A to B: A ≻ B, i.e. A is
better than B. This happens when A ≿ B but B is
not ≿ A. This relation, ≻, is a strict preference
relation (the consumer strictly prefers A to B).
• the consumer prefers B to A: B ≻ A. This
happens when B ≿ A but A is not ≿ B.
• the consumer is indifferent between A and B:
A ∼ B, i.e. the consumer is equally satisfied with
either bundle. This happens when A ≿ B and B ≿
A. This relation, ∼, is an indifference relation.
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• We can restate the Assumption 1 in terms of
strict preference and indifference.
Assumption 1’. Completeness
Any two bundles can be compared: for any A and B,
either A ≻ B, or B ≻ A, or A ∼ B.
• Thus, for any two bundles A and B, a consumer
will prefer A to B, will prefer B to A, or will be
indifferent between the two.
• Note that this comparison of bundles is about
preferences (“likes”), not about choices. The prices and
expenditures are completely ignored at this point.
When the consumer is making an actual choice, he will
need to take into account his budget constraint, for
example, Jack can prefer steak to BigMac but buy
BigMac because it is cheaper.
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Assumption 2. Transitivity
if bundle 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:
if A ≿ B and B ≿ C then A ≿ C.
• money pump: pink ≻ blue ≻ green ≻ pink ≻ … (if your
preferences do not satisfy transitivity)
• You can prove (in more advanced Micro subjects)
that A2. Transitivity implies the following:
• if A ≻ B and B ≻ C then A ≻ C
• if A ∼ B and B ∼ C then A ∼ C
• if A ≻ B and B ∼ C then A ≻ C
• if A ∼ B and B ≻ C then A ≻ C
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Assumption 3.
More is better than less
Consumers always prefer more of any good to less.
• Goods are assumed to be desirable—i.e., to be
good.
• In addition, consumers are never satisfied or
satiated; more is always better, even if just a
little better.
• There are many examples where “more is better”
assumption is not satisfied. There are “bads” you
prefer to avoid; it could be “too much” of a good
thing and so on.
In more advanced subjects, a slightly different assumption is usually
made – strict monotonicity. It is weaker than “more is better”. This
means that preferences that satisfy “more is better” are strictly
monotonic, but the opposite is not true: strictly monotonic preferences
may or may not satisfy “more is better”.
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2b. Indifference Curves
FIGURE 3.1
DESCRIBING INDIVIDUAL
PREFERENCES
Ann’s preferences
Because more of each good
is preferred to less, we can
compare market baskets in
the shaded areas.
Basket A is clearly preferred
to basket G, while E is clearly
preferred to A.
However, A cannot be
compared with B, D, or H
without additional information.
● indifference curve A curve representing all combinations
of market baskets that provide a consumer with the same level
of satisfaction.
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FIGURE 3.2
AN INDIFFERENCE CURVE
Ann’s preferences
The indifference curve U1
that passes through market
basket A shows all baskets
that give the consumer the
same level of satisfaction as
does market basket A; these
include baskets B and D.
Our
consumer
prefers
basket E, which lies above
U1, to A, but prefers A to H
or G, which lie below U1.
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Indifference Maps
● indifference map Graph containing a set of
indifference curves showing the market baskets among
which a consumer is indifferent.
FIGURE 3.3
AN INDIFFERENCE MAP
Tomasz’ preferences
An indifference map is a
set of indifference curves
that describes a person's
preferences.
Any market basket on
indifference curve U3, such
as basket A, is preferred to
any basket on curve U2
(e.g., basket B), which in
turn is preferred to any
basket on U1, such as D.
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FIGURE 3.4
If preferences satisfy
assumptions 1 to 3, then
INDIFFERENCE CURVES
CANNOT INTERSECT
If indifference curves U1 and
U2 intersect, one of the
assumptions of consumer
theory is violated. According
to
this
diagram,
the
consumer
should
be
indifferent among market
baskets A, B, and D. Yet B
should be preferred to D
because B has more of both
goods.
What if preferences do not satisfy “more is better”?
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2c. Goods and “bads”
• If you prefer more of a product, then
it is a ‘good’
• If you prefer less of a product then it
is a bad (e.g. sewerage, rubbish,
nuclear waste)
• Some products can start as goods
and then become bads as you get
more
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Here Curry and Sushi are both
goods
Hinata’s preferences
Qcurry
Direction of higher
preference
Qsushi
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Curry is a good, sewerage is a bad
Svetlana’s preferences
Qcurry
Direction of higher
preference
Qsewerage
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Curry is a good if less than 10 curries
but a bad if more than 10
Arjun’s preferences
Qcurry
Direction of
increasing
preference
10
Qsushi
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If there is a ‘free disposal’, then you can
just ‘throw away’ any excess of a product
Mirna’s preferences
Qcurry
10
When curry
becomes a ‘bad’
after 10 (as in
the previous
slide), you can
throw excess
away
Qsushi
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2d. Convexity and concavity
• If preferences are convex then
indifference curves are ‘bowed
inward’
– Prefer mixtures
– Convex and strictly convex preferences
are very common
• If preferences are ‘concave’ then
indifference curves are bowed out
– Prefer extremes
– Concave preferences are less common;
the term is rarely used
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Convex preferences
Qcurry
Direction of higher
preference
Qsushi
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Convex preferences
Direction of higher
preference
Qcurry
8
A
Alex’ preferences
Mixtures lie on a
higher
indifference curve
and are preferred
to extremes:
C
C ≻ A, C ≻ B.
B
2
2
10
Qsushi
50%-50% mixture of bundles A and B is a bundle (6,5).
70%-30% mixture of bundles A and B is a bundle 0.7(2,8)+0.3(10,2)=
(1.4+3, 5.6+0.6)=(4.4, 6.2)
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Convex preferences: formal definition
Qc
A
strictly convex
preferences
C
B
Qs
Qc
A
C
strictly convex
preferences
B
Qs
Qc
convex, but not strictly
convex preferences
Qs
Preferences are convex, if for any two
bundles A and B such that bundle B is at
least as good as A (i.e. B ≿ A),
any bundle C that is a mixture of A and
B (i.e. lies on the line segment between
the two bundles) is at least as good as
A:
if B ≿ A and C is a mixture of the two,
then C ≿ A.
Preferences are strictly convex, if for
any two distinct bundles A and B such
that bundle B is at least as good as A
(i.e. B ≿ A),
any bundle C that is a mixture of A and
B, is better than A:
if B ≿ A and C is a mixture of the two,
then C ≻ A.
Strict convexity is a stronger property than convexity:
strictly convex preferences are convex; convex
preferences may or may not be convex.
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Concave preferences
Qcurry
Betty’s preferences
Qsushi
Alex: convex preferences over curry and sushi (previous slide)
Betty: concave preferences (this slide)
Svetlana: vodka and chocolate
The term “concave preferences” is not commonly used
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2e. The Shape of Indifference Curves
FIGURE 3.5
THE MARGINAL RATE
OF SUBSTITUTION - MRS
The magnitude of the
slope of an indifference
curve
measures
the
consumer’s marginal rate
of
substitution
(MRS)
between two goods.
Slope is negative; MRS is
positive – it is an absolute
value of the slope.
In this figure, the MRS
between clothing (C) and
food (F) falls from 6
(between A and B) to 4
(between B and D) to 2
(between D and E) to 1
(between E and G).
Pindyck/Rubinfeld: the MRSFC of food F for clothing
C; we will use the following notation: MRSFC
Danger! Note that
economists managed to
disagree on the
terminology. Don’t even
ask – I have no idea why.
Perloff calls the same
slope MRSFC of clothing
for food.
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diminishing marginal rate of
substitution, a bit more precise
Direction of higher
preference
Clothing
MRSFC
at
bundle A
MRSFC
at
bundle B
MRSFC is the absolute value of the
slope of the indifference curve = the
absolute value of the slope of the
tangent line.
A
MRSFC decreases
when we move down
the indifference curve.
B
C
Food
MRSFC at
bundle C
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The Marginal Rate of Substitution
● marginal rate of substitution (MRSxy) of good
X for good Y:
Maximum amount of good Y (which is on the
vertical axis) that a consumer is willing to give up
in order to obtain one additional unit of good X
(which is on the horizontal axis).
Assumption 4. Convexity
If indifference curves exhibit diminishing MRS, then
preferences are strictly convex;
if MRS is weakly decreasing, i.e., it either decreases
or stays the same, then preferences are convex.
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• Often we will assume that preferences are
convex and smooth so that there are no
‘kinks’ in indifference curves
• To summarise, the common
assumptions about preferences are:
1. completeness
2. transitivity
3. more is better
4. convexity
• Preferences of any particular person may fail
some of the above 4 assumptions, but, in
most cases, we will be assuming that all four
of them are satisfied.
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Consumer choice?
Utility maximisation?
It isn't normal to know what we
want. It is a rare and difficult
psychological achievement.
Abraham Maslow
There are only two tragedies in
life: one is not getting what one
wants, and the other is getting it.
Oscar Wilde
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