Download OHP32 EC130 FOUNDATIONS OF ECONOMIC ANALYSIS Topic 3

EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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EC130 FOUNDATIONS OF ECONOMIC
ANALYSIS
2004- 2005
DEPARTMENT OF ECONOMICS
UNIVERSITY OF WARWICK
Topic 3
• Preferences and Constraints
• Utility Maximisation
• Income and Substitution Effects
• Application to the Supply of Labour
• Market Demand Curves
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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• Preferences and Constraints
Preferences
Suppose your happiness just depends on two items:
Books and Food.
We assume that you have preferences over books and
food and that these preferences satisfy various axioms,
such as:
• Non-satiation
Books
B1
F1
2
F2
Food
EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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• Ordinal ranking
• Transitivity
If some basket or 'bundle' of goods, say α, is
preferred to some other, say β, and if β is
preferred to a further bundle, say ρ, then it
follows by transitivity that α is preferred to ρ.
This is regarded as a necessary axiom for
consumers to be thought of as 'rational'. We write
it as:
Similarly, transitivity pertains to indifference . . .
• Completeness
This means that any two bundles can be
compared (no matter how far apart or how close
together):
Books
B1
F1
3
Food
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Axioms like these enable us to represent individuals'
preferences diagrammatically with what are called
'indifference curves'. It follows from the axioms about
preferences that indifference curves will have the
following key properties:
• Slope downwards
• Every point in the diagram will lie on a
(unique) indifference curve
• Indifference curves cannot cross
Let us see why these properties obtain.
Figure 3.1
Books
B1
F1
Food
Hence, indifference curves slope downwards.
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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Figure 3.2
Books
I2
I1
Food
Hence, indifference curves cannot cross.
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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If we now add one further assumption about the nature of
preferences - the assumption of the diminishing marginal
rate of substitution - then we also know that indifference
cures must have a further property: they must be convex
to the origin.
Figure 3.3
Books
Food
The marginal rate of substitution (MRS) tells us how
many more books we would need to make up for (ie to
leave our level of happiness/utility unaffected by) the
loss of one unit of food.
The MRS is diminishing if it is the case that the less food
we have, the greater the number of extra books we would
need to compensate for the loss of a given amount of
food (the example of diamonds and water is often used
here).
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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Thus, we have the idea of indifference curves to
represent consumer 'utility'. Furthermore, we assume that
the consumer will try to obtain the highest level of utility
possible:
Figure 3.4
Books
Food
The capacity of the consumer to raise their utility
depends upon . . .
. . . . . their budget constraint.
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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The budget constraint
Figure 3.5
Y
M = px X + p yY
X
Total expenditure, E, must not exceed total money
income, M. Or:
E = px X + p yY ≤ M ,
where Y is the number of books bought and X is the
amount of food.
In the absence of savings, we can write this as:
M = px X + p yY
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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In the diagrams we have been drawing in (X,Y)-space,
the equation for the budget constraint can be represented
as:
Figure 3.6
Y
M = px X + p yY
M
py
M
px
X
To see why the intercepts have the values they do, notice
that the budget equation can be re-written as:
Y = (M − px ) / p y
From this, you can work out the slope of the budget
equation . . . do it!
Hence, you can tell how the budget constraint moves
when:
• Money income increases
• Price of food rises
• Price of books falls
• Price of food and books rises by the same percent
• Money income and both prices all rise by 10%
Show each of these in a diagram.
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Now we can bring together the analysis of indifference
curves and that of the budget constraint, and thereby see
what will determine the consumer's 'utility-maximising'
equilibrium:
Figure 3.7
Y
Consumer
Equilibrium . . . why?
X
Notice that in the consumer equilibrium, the budget line
is a tangent to the indifference curve. I.e., the two slopes
are equal:
thus, the MRS = price ratio.
With this model of consumer behaviour, we can work out
how the consumer might respond to changes in income
and/or price . . .
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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Consider first changes in income:
Effects of changes
equilibrium.
Figure 3.8
in
income
on
consumer
What happens to the
consumer's
optimising point
when income falls?
Y
X
Note that the fall in money income is represented by a
parallel shift inwards of the budget line.
• What happens to the level of demand for X and Y?
• Draw the new optimising point.
• Connect the original and new optima and hence derive
the ICC.
• Distinguish between normal and inferior goods.
Also, think about the income elasticity of demand (and
about luxury and necessary goods).
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
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Effects of changes in price on consumer equilibrium.
Figure 3.9
What happens to the
consumer's
optimising point
when price of X falls?
Y
X
Note that the fall in the price of X is represented by an
outward rotation of the budget line: why?
• What happens to the level of demand for X and Y?
• Draw the new optimising point (must it be to the right
of the original?).
• Connect the original and new optima and hence derive
the PCC.
• Distinguish between substitutes and complements.
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Figure 3.10
We can now derive
a demand curve
from first
principles. We do
this by plotting the
PCC into a diagram
with price and
quantity axes:
Y
PCC
M/Px1
M/Px2
X
PX
Now just show
prices on this
lower diagram
and hence plot
the demand
curve.
X1
X2
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X
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The demand curve we have just derived is called the
Constant Money Income Demand Curve (CMIDC).
• Why?
• Must it always have a negative slope?
Typically the CMIDC has a negative slope: as the price
of a good falls, ceteris paribus, the demand for it rises.
This is because two effects are going on when the price
falls.
First, the lower price means it is now cheaper relative to
the other good than was previously the case.
This generates a substitution effect.
Second, with the lower price, the consumer is better off
and so can afford more of all goods (look at the diagram
again).
This is called the income effect.
We can try to distinguish between the income and
substitution effects in a diagram:
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Distinguishing between the income and substitution effects.
Y
To see the substitution
effect of the price fall
on the demand for X,
shift B2 back in a
parallel way until it
just touches I1
I1
B1
B2
X
Y
The income effect
of the price fall is
then the remainder
of the total effect.
To see this, just plot
the new optimum
on B2
I1
S
X1
B1
B2
X
X2
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
We know that if we plot from the PCC in (X, Y)-space
into the diagram in (PX, X)-space, we can derive the
CMIDC. That is, the CMIDC tells us the total effect of a
price change on the demand for X: made up of both the
income and substitution effects. If instead, we just
consider the substitution effect and plot the resulting
demand curve, we obtain the CRIDC:
Constant real income demand curve.
This is the demand curve derived when we consider the
effect of a price change, but exclude the income effect.
As it just traces out the substitution effect, it moves us
along the initial indifference curve. Thus, utility is held
constant. As utility is a measure of real income, the
resulting demand curve is called the CRIDC. (Notice that
money income is not held constant along the initial
indifference curve as we trace out the substitution effect.
Rather, it is as though we are giving the consumer a price
fall with one hand, but taking away money income with
the other so as to keep their level of utility constant.)
To see the CRIDC diagrammatically, just plot down
from the substitution effect in the previous diagram into
the (PX, X) diagram.
Then compare the CMIDC and the CRIDC.
• We said CMIDC could have a positive slope. Is this
true of CRIDC?
• Which of the two demand curves is the more elastic?
Why? What does this depend on?
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EC130 Foundations of Economic Analysis, 2004-5. Notes and OHPs, Topic 3.
• What is a Giffen good? How is it related to an inferior
good?
In lectures, we then consider market demand curves.
And then an application of this analysis to the important
issue of labour supply.
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