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Chapter 4
More Demand Theory
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The Law of Demand
 The
law of demand implies an
inverse relationship between price
and quantity demanded.
 When the price and quantity of a
good are positively related, the good
is called a Giffen Good.
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Income and Substitution Effects
 The
substitution effect of a change
in p1 is associated with the relative
change in the price of good 1.
 The income effect of a change in p1
is associated with the change in real
income.
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Figure 4.1 A Giffen good
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Figure 4.2 Income and substitution
effects for a price increase
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Figure 4.3 Income and substitution
effects for a price decrease
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Income and Substitution Effects
If indifference curves are smooth and
convex and if the consumer buys a
positive quantity of both goods, then the
substitution effect is always negatively
related to the price change.
 For a normal good, the income effect is
negatively related to the price change.
 For an inferior good, the income effect is
positively related to the price change.

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Compensatory Income
 After
a price change, the minimum
income that allows the consumer to
attain the original indifference curve
is called the compensatory income.
 The budget line associated with the
compensatory income is the
compensated budget line.
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Figure 4.4 The nonpositive
substitution effect
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The Compensated Demand Curve
 The
compensated demand curve
identifies the consumer’s utility
maximizing bundle when, as a result
of a price change, the consumer’s
income is adjusted to keep him/her
on the same indifference curve.
 The compensated demand curve
reflects the substitution effect and
cannot be upward sloping.
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Figure 4.5 The compensated demand curve
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Compensating and Equivalent Variation
 Equivalent
variation identifies the
variation in income that is equivalent
to being able to buy good x at a
given price.
 Compensating variation identifies
the variation in income that
compensates for the right to buy
good x at a given price.
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Figure 4.8 Measuring the benefit of a new good
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From Figure 4.8
 Mr.
Polo’s non-member initial
equilibrium is E0 on I0.
 Equilibrium as a member is E1 on I1.
 Equivalent variation is EV. With no
membership, this additional income
would yield indifference curve I1.
 Compensating variation is CV. Given
that he is a member, this reduction in
income yields indifference curve I0.
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Figure 4.9 Measuring the cost of a price change
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From Figure 4.9
 Low
price of P1 gives equilibrium of
E0 on I0.
 Equilibrium with higher price of P1 is
at E1 on I1.
 With a lower price, reducing income
by EV yields I1.
 With a higher price, increasing
income by CV would yield I0.
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Figure 4.10 The case in which CV equals EV
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Figure 4.11 Consumer’s surplus for a new good
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Figure 4.12 Consumer’s surplus
for a price reduction
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Figure 4.13 Marginal values and
marginal rates of substitution
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Figure 4.14 Total value and marginal value
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Figure 4.15 Equal marginal values
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Application: Two Part Tariff
 What
combination of camera price
(pc) and film price (p1) maximize
profits?
 The cost of producing a camera is
$5, the cost of making film is 1$.
 The firm’s profit maximizing strategy
is to sell the film at cost and charge
the corresponding reservation price
for the camera, area GAF (Fig 4.16).
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Figure 4.16 The Polaroid pricing problem
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Figure 4.17 The Paasche quantity index
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Paasche Quantity Index
1
1
1
1
1
0
1
0
P  ( p x  p x ) /( p x  p x )
1 1
2 2
1 1
2 2
1
0
If P exceeds 1 then B is preferred to B
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Laspeyres Quantity Index
0
1
0
1
0
0
0
0
L  ( p x  p x ) /( p x  p x )
1 1
2 2
1 1
2 2
0
1
If L  1, then B is preferred to B
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Price Indices
Paache Pr ice Index
P '  ( p1x1  p1 x1 ) /( p 0 x1  p 0 x1 )
11
2 2
1 1
2 2
Laspeyres Pr ice Index
L'  ( p1x 0  p1 x 0 ) /( p 0 x 0  p 0 x 0 )
11
2 2
1 1
2 2
When L' is less than 1, then P' is also less than 1,
and you are better off in period 1.
When P' is greater than 1, then L' is aslo greater than1,
and you are better off in period 0.
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Figure 4.18 An index-number puzzle
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