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 ...
(
)
1
2
1
2
1
1
2
2
,
,...,
max
,
,...,
subject to
...
n
n
n
n
x
x
x
u x
x
x
p x
p x
p x
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:
{
}
{
}
1
2
1
2
,
,
,
p
p
m
x
x
→
z
Keep this up and you’ll map out the
Marshallian Demand
Functions
{
}
{
}
{
}
{
}
1
2
1
2
1
2
1
2
,
,
,
ˆ
ˆ
ˆ
ˆ
ˆ
,
,
,
p
p
m
x
x
p
p
m
x
x
→
→
%
%
%
%
%
(
)
(
)
1
1
2
2
1
2
,
,
,
,
x
p
p
m
x
p
p
m
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
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2
Measuring the Effects of Change –
“Elasticities”
z
y
depends upon
x:
z
Change
x
a bit:
Look at the change in
y:
(
)
y
f
x
=
(
)
x
x
x
′
Δ
=
−
(
)
y
y
y
′
Δ
z
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
y
y
y
x
y
x
x
x
ε
Δ
=
=
Δ
=
−
y
Δ
x
Δ
Measuring the Effects of Change –
“Elasticities”
Take a Marshallian demand function:
1
1
1
1
1
1
/
The own price elasticity of demand :
/
x p
x
x
x
p
p
p
p x
ε
Δ
Δ
=
=
Δ
Δ
(
)
1
1
2
,
,
x
p
p
m
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
/
The cross price elasticity of demand :
/
/
The income elasticity of demand :
/
x p
x m
x
x
x
p
p
p
p
x
x
x
x
m
m m
m x
ε
ε
Δ
Δ
=
=
Δ
Δ
Δ
Δ
=
=
Δ
Δ
x
2
Measuring the Effects of Change –
Income Elasticities
1
1
1
/
0
0
/
0
/
0
x m
x
x
m m
x
x
ε
Δ
>
=
=
>
Δ
>
Δ
>
0
x
1
1
x
Δ
2
x
Δ
2
2
2
0
/
0
x m
m m
ε
=
=
>
Δ
>
Both are “
Normal goods
”
x
2
Measuring the Effects of Change –
Income Elasticities
1
1
1
/
0
0
/
0
/
0
x m
x
x
m m
x
x
ε
Δ
<
=
=
<
Δ
>
Δ
>
x
1
0
1
x
Δ
2
x
Δ
2
2
2
0
/
0
x m
m m
ε
=
=
>
Δ
>
is a normal good
Is an
“Inferior Good”
x
1
x
2
Measuring the Effects of Change –
Income Elasticities
“Necessities”
“Luxuries”
0
1
i
x m
ε
<
<
1
i
x m
ε
<
0
Inferior Goods
1
Normal Goods
Income Elasticities
0
i
x m
ε
<
0
i
x m
ε
>
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
1
1
1
1
1
1
/
0
0
/
0
x p
x
x
p
p
ε
Δ
>
=
=
<
Δ
<
Good 1 is an
“Ordinary Good”