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1
Introduction to
Microeconomics
Lecture 5
Choices in Action
Ian Crawford
Review
z
Consumers choose the set of goods they most prefer, out
of the set of goods they can afford.
z
We use utility functions/indifference curves to give
formal content to “most prefer”
z
We use budget sets/constraints to give formal content to
“can afford”.
Review
z
In due course this becomes a
constrained maximisation
problem which you can solve mathematically
“Maximise utility, subject to the budget constraint.”
z
So far you’ve learned how to solve the problem
graphically for two goods .
..
(
)
12
1
1
2
2
,
,...,
max
,
,...,
subject to
...
n
nn
n
xx
x
ux x
x
px px
px m
++
+≤
Review
x
2
Optimal choice
(
)
*
2
*
1
,
x
x
0
x
1
*
1
x
*
2
x
Sub
‐
optimal choice #2
Sub
‐
optimal choice #1
Review
z
Given an indifference curve map you can change prices
and income and work out the demands each time:
{
}
{
}
,,
,
ppm
→
z
Keep this up and you’ll map out the
Marshallian Demand
Functions
{
}
{
}
{}{}
,
ˆˆ ˆ
ˆ
ˆ
,
→
→
%%%
%%
()
(
)
112
212
x ppm
Outline
z
Properties of Marshallian Demands
z
Measuring changes
‐
elasticities
z
Income Changes
z
Price Changes
z
Decomposing price changes
z
Substitution and income effects
z
The Slutsky Equation
z
Modelling the labour supply (leisure demand) decision
‐
the Working Tax Credit [we may not get this far today]
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Measuring the Effects of Change –
“Elasticities”
z
y
depends upon
x:
z
Change
x
a bit:
z
Look at the change in
y
(
)
yf
x
=
(
)
x
xx
′
Δ= −
yyy
′
Δ
y:
z
We could compare
and
to measure responsiveness,
but the answer would depend on the units.
z
Economists use “elasticities” instead
/
Proportional change in
The
elasticity of
:
/
Proportional change in
yx
yy
y
xy
x
ε
Δ
==
Δ
(
)
=−
y
Δ
x
Δ
Measuring the Effects of Change –
“Elasticities”
Take a Marshallian demand function:
11
1
1
1
1
/
The own price elasticity of demand :
/
xp
x
p
pp
px
ΔΔ
(
)
112
,,
x ppm
12
1
1
2
22
2
1
1
1
/
The cross price elasticity of demand :
/
/
The income elasticity of demand :
/
xm
x
p
mm
mx
x
2
Measuring the Effects of Change –
Income Elasticities
1
/0
0
Δ>
>
0
x
1
1
x
Δ
2
x
Δ
2
0
=
=>
Both are “
Normal goods
”
x
2
Measuring the Effects of Change –
Income Elasticities
1
0
Δ<
<
x
1
0
1
x
Δ
2
x
Δ
2
0
>
is a normal good
Is an
“Inferior Good”
x
1
x
2
Measuring the Effects of Change –
Income Elasticities
“Necessities”
“Luxuries”
0
1
i
<<
1
i
<
0
Inferior Goods
1
Normal Goods
Income Elasticities
0
i
<
0
i
>
x
2
Measuring the Effects of Change –
Price Elasticities
The price of good 1 falls.
Demand for good 1 rises
x
1
0
1
x
Δ
0
<
Good 1 is an
“Ordinary Good”
3
x
2
Measuring the Effects of Change –
Price Elasticities
The price of good 1 falls.
Demand for good 1 falls (!)
x
1
0
1
x
Δ
11
/0
0
xp
xx
pp
ε
Δ>
==
>
Δ<
Good 1 is a
“Giffen Good”
Measuring the Effects of Change –
Own Price Elasticities
Giffen
“Price Elastic”
“Price Inelastic”
1
ii
< −
10
−
<<
0
Ordinary Goods
‐
1
Goods
Own Price Elasticities
0
>
0
<
x
2
Measuring the Effects of Change –
Price Elasticities
The price of good 1 falls.
Demand for good 2 falls
22
0
>
x
1
0
2
x
Δ
Goods 1 & 2 are
“Substitutes”
21
x
2
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This note was uploaded on 04/12/2010 for the course ECON DEAM taught by Professor Vines during the Spring '10 term at Oxford University.
 Spring '10
 Vines
 Economics, Utility

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