Transcript Chapter 1

Chapter Four
Demand
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Demand
• In this chapter, we examine five main topics.
– Deriving Demand Curves
– Effects of an Increase in Income
– Effects of a Price Increase
– Cost-of-living adjustments
– Revealed Preference
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4-2
Deriving Demand Curves
• System of Demand Equation
We used calculus to maximize utility subject to a budget
constraint. In doing so, we solved for the optimal
quantities that a consumer chooses as functions of prices
and income. That is, we solved for the consumer’s system
of demand functions for these goods.
q1  Z  p1 , p2 , Y 
q2  B  p1 , p2 , Y 
where p1 is the price of pizza, p2 is the price of burritos,
and Y is her income.
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Deriving Demand Curves
• Graphical Interpretation
An individual chooses an optimal bundle of
goods by picking the point on the highest
indifference curve that touches the budget
line. When a price changes, the budget
constraint the consumer faces shifts, so the
consumer choose a new optimal bundle.
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4-4
Deriving Demand Curves
• By varying one price and holding other
prices and income constant, we can
determine how the quantity demanded
changes as the price changes, which is the
information we need to draw the demand
curve.
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4-5
Deriving Demand Curves
• We derive a demand curve using the
information about tastes from indifference
curves.
• These indifference curves are convex to the
origin: Mimi views beer and wine as
imperfect substitutes. We can construct
Mimi’s demand curve for beer by holding her
budget, her tastes, and the price of wine
constant at their initial levels and varying the
price of beer.
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Deriving Demand Curves
• Price-consumption curve, is the line through
the equilibrium bundles, such as e1 , e2 ,
and e3 , that Mimi would consume at each
price of beer, when the price of wine and
Mimi’s budget are held constant.
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Figure 4.1(a)
Deriving Mimi’s Demand Curve
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4-8
Figure 4.1(b)
Deriving Mimi’s Demand Curve
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Effects of an Increase in
Income
• How Changes in Income Shift
Demand Curves
– We illustrate the relationship between the
quantity demanded and income by
examining how Mimi’s behavior changes
when her income rises, while the prices of
beer and wine remain constant.
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Figure 4.2(a)
Effect of a Budget Increase
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Figure 4.2(b)
Effect of a Budget Increase
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Figure 4.2(c)
Effect of a Budget Increase
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Effects of an Increase in
Income
• The income-consumption curve through
bundles e1 , e2 , and e3 in panel a shows how
Mimi’s consumption of beer and wine
increases as her income rises. As Mimi’s
income goes up, her consumption of both
wine and beer increases.
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Effects of an Increase in
Income
• Engel curve
– the relationship between the quantity
demanded of a single good and income,
holding prices constant
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Consumer Theory and
Income Elasticities
• Income elasticities tell us how much the
quantity demanded changes as income
increases. We can use income elasticities to
summarize the shape of the Engel curve, the
shape of the income-consumption curve, or
the movement of the demand curves when
income increases.
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Income Elasticities
• We defined the income elasticities of demand
in Chapter 3 as
percentage change in quantity demanded Q / Q


percentage change in income
Y / Y
where  is the Greek letter xi
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4-17
Consumer Theory And
Income Elasticities
• normal good
– a commodity of which as much or more is
demanded as income rises
• inferior good
– a commodity of which less is demanded as
income rises
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Income-Consumption Curves
and Income Elasticities
• The shape of the income-consumption curve
for two goods tells us the sign of the income
elasticities: whether the income elasticities
for those goods are positive or negative.
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Some Goods Must Be Normal
• It is impossible for all goods to be inferior.
• If both goods were inferior, Peter would buy
less of both goods as his income rises-which
makes no sense.
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Figure 4.3
Income-Consumption Curves and Income
Elasticities
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Figure 4.4
A Good That Is
Both Inferior and
Normal
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Weighted Income Elasticities
• The weighted sum of a consumer’s income elasticities
equals one.
p1q1  p2 q2  ...  pn qn  Y
dqn
dq1
dq2
p1
 p2
 ...  pn
1
dY
dY
dY
pn qn dqn Y
p1q1 dq1 Y p 2 q2 dq2 Y

 ... 
1
Y dY q1
Y dY q2
Y dY qn
11   2 2  ...   n n  1
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4-23
Effects of a Price Increase
• An increase in a price of a good, holding
other prices and income constant, has two
effects on an individual’s demand. One is the
substitution effect: If utility is held constant,
as the price of the good increases,
consumers substitute other, now relatively
cheaper goods for that one.
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Effects of a Price Increase
• The other is the income effect: An increase in
price reduces a consumer’s buying power,
effectively reducing the consumer’s income
and causing the consumer to buy less of at
least some goods.
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Income and Substitution
Effects with a Normal Good
• The substitution effect is the change in the
quantity of a good that a consumer demands
when the good’s price changes, holding
other prices and the consumer’s utility
constant
• The income effect is the change in the
quantity of a good a consumer demands
because of a change in income, holding
prices constant.
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4-26
Income and Substitution
Effects with a Normal Good
• The total effect from the price change is the
sum of the substitution and income effects,
as the arrows show. Mimi’s total effect (in
gallons of beer per year) from a drop in the
price of beer is
Total effect= substitution effect + income effect
32.2=3.9+28.3
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4-27
Income and Substitution
Effects with a Normal Good
• Because indifference curves are convex to
the origin, the substitution effect is
unambiguous: More of a good is consumed
when its price falls. A consumer always
substitutes a less expensive good for a more
expensive one, holding utility constant.
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4-28
Income and Substitution
Effects with a Normal Good
• The direction of the income effect depends
on the income elasticity. Because beer is a
normal good for Mimi, her income effect is
positive. Thus both Mimi’s substitution effect
and her income effect go in the same
direction.
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Figure 4.5
Substitution and Income Effects with
Normal Goods
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4-30
Income and Substitution
Effects with an Inferior Good
• If a good is inferior, the income effect goes in
the opposite direction from the substitution
effect. For most inferior goods, the income
effect is smaller than the substitution effect.
As a result, the total effect moves in the
same direction as the substitution effect, but
the total effect is smaller.
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4-31
Income and Substitution
Effects with an Inferior Good
• A good is called a Giffen good if a decrease
in its price causes the quantity demanded to
fall.
• The Law of Demand was an empirical
regularity, not a theoretical necessity.
Although it’s theoretically possible for a
demand curve to slope upward, economists
have found few, if any, real-world examples
of Giffen goods.
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4-32
Compensated Demand Curve
• We could derive a compensated demand curve,
where we determine how the quantity demanded
changes as the price rises, holding utility constant,
so that the change in the quantity demanded
reflects only pure substitution effects when the
price changes.
• It is called the compensated demand curve because
we would have to compensate an individual-give the
individual extra income- as the price rises so as to
hold the individual’s utility constant.
q1  H  p1 , p2 ,U 
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4-33
Figure 4.6
Deriving Jackie’s
Compensated
Demand Curve
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Slutsky Equation
• The usual price elasticity of demand,  , captures
the total effect of a price change. We can break this
price elasticity of demand into two terms involving
elasticities that capture the substitution and
income effects.
• We measure the substitution effect using the pure
*

substitution elasticity of demand,
, which is the
percentage that the quantity demanded falls for a
given percentage increase in price if we
compensate the consumer to keep the consumer’s
utility constant.
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4-35
Slutsky Equation
• This relationship among the price elasticity
of demand,  , the substitution elasticity of
*
demand,  , and the income elasticity of
demand,  , is the Slutsky equation.
Total effect= substitution effect + income effect


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
*

  
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Cost-of-Living Adjustments
• By knowing both the substitution and effects,
we can answer questions that we could not if
we knew only the total effect.
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4-37
Inflation Indexes
• The price of most goods rise over time. We
call the increase in the overall price level
inflation.
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4-38
Real Versus Nominal Prices
• The actual price of a good is called the
nominal price. The price adjusted for
inflation is the real price.
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4-39
Calculating Inflation Indexes
• The CPI for the first year is the amount of
income it takes to buy the market basket
actually purchased that year:
Y1  p C1  p F1
1
C
1
F
The cost of buying the first year’s bundle in
the second year is
Y2  p C1  p F1
2
C
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2
F
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Calculating Inflation Indexes
• To calculate the rate of inflation, we
determine how much more income it would
take to buy the first year’s bundle in the
second year, which is the ratio of Y2 to Y1 :
Y2 p C1  p F1

Y1 p C1  p F1
2
C
1
C
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2
F
1
F
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Calculating Inflation Indexes
• The CPI is a weighted average of the price
2
1
2
1
p
/
p
increase for each good, C C and pF / pF ,
where the weights are each good’s budget
share in the base year,  C and  F .
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4-42
CPI adjustment
• CPI adjustment to income does not keep an
individual on his original indifference curve.
• Indeed, this person is better off in the second
year than in the first. The CPI adjustment
overcompensates for the change in inflation
in the sense that his utility increases.
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Figure 4.7
CPI Adjustment
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4-44
Revealed Preferences
• If we observe a consumer’s choice at many
different prices and income levels, we can
derive the consumer’s indifference curves
using the theory of revealed
preferences( Samuelson, 1947).
• The basic assumption of the theory of
revealed preference is that a consumer
chooses bundles to maximize utility subject
to a budget constraint: The consumer
chooses the best bundle that the consumer
can afford.
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4-45
Substitution Effect
• One of the clearest and most important
results from consumer theory is that the
substitution effect is negative: The Law of
Demand holds for compensated demand
curves.
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4-46
Figure 4.8
Revealed Preference
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4-47
Consumer Price Indices (CPI)
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4-48
Consumer Price Indices (CPI)
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