Apples and Bananas aren’t
Everything
Composite Goods
Lectures in Microeconomics-Charles W. Upton
Apples and Bananas aren’t
Everything
• What happens if there are more than
two goods?
• Suppose we are making the choice
among
• What happens if there are more than
two goods?
Composite Goods
Extending the Model
• We could write U(A,B,O,G)
paA +pbB + poO +pGG = Y
• Apples
• Bananas
• Oranges
• Grapefruit
Composite Goods
Extending the Model
• We could write U(A,B,O,G)
paA +pbB + poO +pGG = Y
• This is madness. The graphs get too
complicated, even worse when we think
about extending to many different goods
Composite Goods
Composite Goods
The Composite Good
• Let X be the amount we spend on all other
goods.
Composite Goods
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The Composite Good
• Let X be the amount we spend on all other
goods.
• In this case,
X = pbB + poO +pGG
The Composite Good
• Let X be the amount we spend on all other
goods.
• In this case,
X = pbB + poO +pGG
• Our Utility function is now U(X,A)
Composite Goods
The Composite Good
Composite Goods
Other
Goods
An Indifference Curve
• Let X be the amount we spend on all other
goods.
• In this case,
X = pbB + poO +pGG
• Our Utility function is now U(X,A)
• Our budget constraint is now
X + paA = Y
Composite Goods
An Application
• A Consumer has income of $100 a week.
Peaches cost $1 each. Show graphically,
how many peaches she will purchase.
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Composite Goods
Apples
Peaches
Other
Goods
Draw the
Consumer’s
Indifference
Curves
$100
$80
$60
$40
$20
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20
40
Composite Goods
60
80 100
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Peaches
2
Peaches
Other
Goods
Draw the
Consumer’s
Draw the Budget
Indifference
Line
Curves
$100
$80
Peaches
Other
Goods
$100
$80
$60
$60
$40
$40
$20
AlongDraw
this the
budgetConsumer’s
line the
Draw
MRT
ofthe Budget
Indifference
peaches
toLine
Curves
other goods is
1
$20
20
40
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60
80 100
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Peaches
20
Peaches
Other
Goods
$80
$60
$40
Composite Goods
60
80 100
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Peaches
Peaches
Other
Goods
Draw the
Consumer’s
Draw the Budget
Indifference
Line
Find
the point of
Curves
tangency
$100
40
At the point of tangency,
Draw
the
the MRS between
peaches
Consumer’s
and money Draw
spent on
theother
Budget
goodsIndifference
is 1Line
Find
the point of
Curves
tangency
$100
$80
$60
$40
$20
$20
20
40
Composite Goods
60
80 100
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A Peach of a Problem
• She is now offered a chance to
purchase peaches, from another
vendor. The first 20 cost 50 cents
each and others cost $1.50 each.
Should she switch?
Composite Goods
Peaches
20
40
Composite Goods
60
80 100
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Peaches
A Peach of a Problem
• She is now offered a chance to
purchase peaches, from another
vendor. The first 20 cost 50¢ each
and others cost $1.50 each. Should
she switch?
• It is an all or nothing deal.
Composite Goods
3
A Peach of a Problem
A Peach of a Problem
• Some people argue that it makes no
difference. Forty peaches cost $40.
• Some people argue that it makes no
difference. Forty peaches cost $40.
Nonsense!
Composite Goods
Composite Goods
A Peach of a Problem
• Some people argue that it makes no
difference. Forty peaches cost $40.
• At the old prices,
MRS = MRT = $1.
A Peach of a Problem
• Some people argue that it makes no
difference. Forty peaches cost $40.
• But there is a difference. At the old prices,
MRS = MRT = $1.
• If the consumer purchases 40 peaches, the
MRS is still 1.
Composite Goods
A Peach of a Problem
• Some people argue that it makes no
difference. Forty peaches cost $40.
is now
• But thereThe
is a MRT
difference.
At $1.50
the old prices,
MRS = MRT = $1.
• If the consumer purchases 40 peaches, the
MRS is still 1.
Composite Goods
Other
Goods
A Peach of a Problem
The new and
old budget
lines
$100
$80
$60
$40
$20
Composite Goods
20
40
Composite Goods
60
80 100
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Peaches
4
Other
Goods
A Peach of a Problem
If the consumer
The
buysnew
no and
peaches,
old
budget
money for other
lines is the
goods
same. Ditto for
buying 40
peaches.
$100
$80
$60
$40
$20
20
Other
Goods
40
Composite Goods
60
80 100
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$60
$100
$80
If she purchases
more than 40, she
has less for other
goods
$60
$40
$20
Other
Goods
40
Composite Goods
60
80 100
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Peaches
A Peach of a Problem
She will buy
fewer
peaches
At 40
peaches,
the MRS is still
1, but the MRT
is now 1.50
$100
$80
$60
$40
$40
$20
$20
20
Other
Goods
If she purchases
fewer
peaches
The
new
and she
has budget
more for other
old
goods.
lines
20
At 40 peaches,
the MRS is still
1, but the MRT
is now 1.50
$80
A Peach of a Problem
Peaches
A Peach of a Problem
$100
Other
Goods
40
Composite Goods
60
80 100
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Peaches
20
A Peach of a Problem
Other
Goods
Remember why:
when she was
buying 40
peaches, she was
indifferent
between a peach
and $1 to spend
on other goods.
$100
$80
$60
$40
$20
20
40
Composite Goods
60
80 100
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40
Composite Goods
60
80 100
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Peaches
A Peach of a Problem
Remember
why:
Now, she can
get
when
she
was
$1.50 to spend
40
onbuying
other goods
peaches,
she
was
so she is better
indifferent
off!
between a peach
and $1 to spend
on other goods.
$100
$80
$60
$40
$20
Peaches
20
40
Composite Goods
60
80 100
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Peaches
5
A Twist on the Peach Problem
• Suppose she had been offered another
deal. The first twenty would cost $1.50
and the rest 50¢. Should she take that
deal?
A Twist on the Peach Problem
• Suppose she had been offered another
deal. The first twenty would cost $1.50
and the rest 50¢. Should she take that
deal?
• Again this is a take it or leave it deal.
Composite Goods
Composite Goods
A Twist on the Peach Problem
Other
Goods
The new and
old budget
lines
$100
$80
A Twist on the Peach Problem
Other
Goods
If the consumer
The
and
buysnew
no peaches,
old budget
money
for other
lines is the
goods
same. Ditto for
buying 40
peaches.
$100
$80
$60
$60
$40
$40
$20
$20
20
40
Composite Goods
60
80 100
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Peaches
20
A Twist on the Peach Problem
Other
Goods
If she purchases
fewer
peaches
The
new
and she
has
more
old budgetless for
other
lines goods.
$100
$80
If she purchases
more than 40, she
has less more for
other goods.
$60
$40
$20
20
40
Composite Goods
60
80 100
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40
Composite Goods
60
80 100
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Peaches
A Twist on the Peach Problem
Other
Goods
She will buy
more and be
better off.
$100
$80
$60
$40
$20
Peaches
20
40
Composite Goods
60
80 100
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Peaches
6
Other
Goods
The Simple Moral
Other
Goods
As long as the
MRT and MRS
are unequal, it
pays to change
consumption.
$100
$80
$60
$40
The Simple Moral
Utility Maximization
as the
requires As
thatlong
the MRS
MRT
and
= MRT (price)MRS
are unequal, it
pays to change
consumption.
$100
$80
$60
$40
$20
$20
20
40
Composite Goods
60
80 100
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Peaches
20
40
Composite Goods
60
80 100
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Peaches
End
©2004 Charles
W. Upton
Composite Goods
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