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Class 3:
Marginal Rate of Substitution
The Budget Constraint
The
budget constraint
states that
expenses
income
:
Remark.
In this course we examine only consumers who have no saving motive. The
consumer thus spends all income so that
expenses
=
income
holds at the optimum.
Formally
: Budget constraint is
p
1
x
1
+
p
2
x
2
m;
where
p
1
and
p
2
are the prices of goods
1
and
2
;
respectively,
x
1
and
x
2
are the quantities
consumed of goods
1
and
2
;
respectively, and
m
is income.
Remark
. Good
2
may stand for the
composite good
"everything else except good
1
"
. If the price of one good is set to
p
2
= 1
it is called the
numeraire good
other prices are in terms of consumption of the numeraire good.
Example
: If good 2 is the numeraire good and
p
1
= 3
then to consumer 1 unit of good 1
the consumer has to forgo
3
units of the numeraire good.
.
Budget set
is all the combinations of
x
1
and
x
2
that satisfy the budget con
straint.
1
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.
Budget line
is the set of combinations of
x
1
and
x
2
that satisfy the budget
constraint exactly:
p
1
x
1
+
p
2
x
2
=
m:
Rearrange budget line to get
x
2
=
m
p
2
p
1
p
2
x
2
:
Remark
. The slope of the budget line is
p
1
p
2
:
This measures the opportunity cost of
consuming good 1: To increase consumption of good 1 by one unit the consumer has to
decrease the consumption of good 2 by
p
1
p
2
units.
FIGURE 3.1 HERE
If income increases the budget line shifts outwards.
FIGURE 3.2 HERE
If price of good 1 increases the budget line becomes steeper.
FIGURE 3.3 HERE
2
Preferences
.
preferences
rank each possible consumption combination
(
x
1
;x
2
)
of goods 1 and 2 relative to any other possible consumption combinations
(
y
1
;y
2
)
of
goods 1 and 2.
Remark
. Notation
(
x
1
;x
2
)
(
y
1
;y
2
)
means that for the consumer the combination
(
x
1
;x
2
)
is strictly preferred to the combination
(
y
1
;y
2
)
i.e. consumer would choose
(
x
1
;x
2
)
over
(
y
1
;y
2
)
if they cost the same amount.
Remark
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This note was uploaded on 05/23/2011 for the course ECON 201 taught by Professor Vandewaal during the Spring '09 term at Waterloo.
 Spring '09
 VANDEWAAL

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