AND ITS APPLICATION
Chapter 3 Comparative
Statics AnalysisDemand
This chapter studies how
people change their choices when conditions such as income or changes in the
prices of goods affect the amount that people choose to consume.
This type of investigation
is sometimes called comparative statics analysis because it compares two
utility-maximizing choices.
Demand Functions
If we knew a persons
preferences and all the economic forces that affect his or her choices, we
could predict how much of each good would be chosen.
This summarizes this
information in a demand function: a representation of how quantity
demanded depends on prices, income, and preferences.
The three elements that
determine the quantity demanded are the prices of X and Y, the persons income
(I), and the persons preferences for X and Y.
Preferences appear to the
right of the semicolon because we assume that preferences do not change during
the analysis.
Homogeneous Demand Function
Individual demand functions
are homogeneous since quantity demanded does not change when prices and income
increase in the same proportion.
The budget constraint PXX
+ PYY = I is identical to
the budget constraint 2PXX + 2PYY = 2I.
Graphically the lines are
the same.
Changes in Income
When a persons income
increase, while prices remain the same, the quantity purchased of each good
might increase.
This situation is shown in
Figure 3.1 where the increase in income is shown as the budget line shifts out
from I1 to I2 to I3.
The slope of the budget
lines are the same since the prices have not changed .
FIGURE 3.1: Effect
of Increasing Income on Quantities of X and Y Chosen
In response to the increase
in income the quantity of X purchased increases from X1 to X2
and X3 while the quantity purchased of Y also increases from Y1
to Y2 to Y3.
Increases in income make it
possible for a person to consume more reflected in the outward shift in the
budget constraint that allows an increase in overall utility.
Normal Goods
A normal good is one
that is bought in greater quantities as income increases.
If the quantity increases
more rapidly than income the good is called a luxury good as with good Y in
Figure 3.1.
If the quantity increases
less rapidly than income the good is called a necessity good as with good X in
Figure 3.1.
APPLICATION 3.1:
Engels Law
One important generalization
about consumer behavior is that the fraction of income spent on food tends to
decline as income increases.
This finding was discovered
by Prussian economists Ernst Engel (1821-1896).
Table 1 show Engels data
with Table 2 showing recent data for U.S. consumers.
TABLE 1:
Percentage of Total Expenditures of Various Items in Belgian Families in 1853
TABLE 2:
Percentage of Total Expenditures by U.S. Consumers on Various Items, 1997
Inferior Goods
An inferior good is one that
is bought in smaller quantities as income increases.
In Figure 3.2 as income
increases from I1 to I2 to I3, the consumption
of inferior good Z decreases.
Goods such as rotgut
whiskey, potatoes, and secondhand clothing are examples of inferior goods.
FIGURE 3.2:
Indifference Curve Map Showing Inferiority
Changes in a Goods Price
A change in the price of one
good causes both the slope and an intercept of the budget line to change.
The change also involves
moving to a new utility-maximizing choice on another indifference curve with a
different MRS.
The quantity demanded of the
good whose price has changed changes.
Substitution Effect
The part of the change in
quantity demanded that is caused by substitution of one good for another is
called the substitution effect.
This results in a movement
along an indifference curve.
Consumption has to be
changed to equate MRS to the new price ratio of the two goods.
Income Effect
The part of the change in
quantity demanded that is caused by a change in real income is called the income
effect.
The
price change also changes real purchasing power and consumers will move to a
new indifference curve that is consistent with this new purchasing power.
Substitution and Income Effects from a Fall in Price
As shown in Figure 3.3, when
the price of good X falls, the budget line rotates out from the unchanged Y
axis so that the X intercept lies father out because the consumer can now buy
more X with the lower price.
The flatter slope means that
the relative price of X to Y (PX/PY) has fallen.
Substitution Effect from a Fall in Price
The consumer was originally
maximizing utility at X*, Y* in Figure 3.3.
After the fall in the price
of good X, the new utility maximizing choice is X**, Y**.
The substitution effect is
the movement on the original indifference curve to point B.
FIGURE 3.3: Income
and Substitution Effects of a Fall in Price
If the individual had to
stay on the U1 with the new price ratio, the consumer would choose B
since that is the point where the MRS is equal to the slope of the new budget
line (shown by the dashed line).
Staying on the same
indifference curve is the same as holding real income constant.
The consumer buys more good
X.
Income Effect from a Fall in Price
The movement from point B to
X**, Y** results from the increase in purchasing power.
Because PX falls
but nominal income (I) remains the same, the individuals real income
increases so that he or she can be on utility level U3.
The consumer buys more good
X.
The Effects Combined
Using the hamburger-soft
drink example from Chapter 2, suppose the price of soft drinks falls from $.50
to $.25.
Previously the consumer
could purchase up to 20 soft drinks, but now he or she can purchase up to 40.
This price decrease shifts the
budget line outward and increases utility.
If the consumer bought his
or her previous choice it would now cost $7.50 so that $2.50 would be unspent.
If the individual stayed on
the old indifference curve he or she would equate MRS to the new price ratio
(consuming 1 hamburger and 4 soft drinks).
This move is the
substitution effect.
Even with constant real
income the consumer will buy more soft drinks since the opportunity cost of
eating a burger in terms of the soft drinks forgone is now higher.
Since real income has
increased the person will choose to buy
more soft drinks so long as soft drinks are a normal good.
Substitution and Income Effects from an Increase in
Price
An increase in PX
will shift the budget line in as shown in Figure 3.4.
The substitution effect,
holding real income constant, is the move on U2 from X*,
Y* to point B.
Because the higher price
causes purchasing power to decrease, the movement from B to X**, Y**
is the income effect.
FIGURE 3.4: Income
and Substitution Effects of an Increase in Price
In Figure 3.4, both the
substitution and income effects cause the individual to purchase less soft
drinks do to the higher price of soft drinks.
Substitution and Income Effects for a Normal Good:
Summary
As shown in Figures 3.3 and
3.4, the substitution and income effects work in the same direction with a
normal good.
When the price falls, both
the substitution and income effects result in more purchased.
When the price increases,
both the substitution and income effects result in less purchased.
This provides the rational
for drawing downward sloping demand curves.
This also helps to determine
the steepness of the demand curve.
If either the substitution
or income effects are large, the change in quantity demanded will be large with
a given price change.
If the substitution and
income effects are small, the effect of a given price change in the quantity
demanded will also be small.
This kind of analysis also
offers a number of insights about some commonly used economic statistics.
APPLICATION 3.2: The Consumer Price Index and Its
Biases
The Bureau of Labor
Statistics monthly calculates the Consumer Price Index (CPI) which is a
principal measure of inflation in the U.S..
To construct the CPI, a
typical market basket of commodities purchased by consumers in the base year
(currently 1982) is calculated.
The ratio of the current
cost of the basket to the base year price is the measure of the value of the
CPI.
The rate of change in the
CPI between two periods is the reported rate of inflation.
An Algebraic Example
Suppose the 1982 typical
market basket contained X82 of good X and Y82 of good Y.
The prices of these goods
are and
The cost of this bundle in
the 1982 base year would be written as
To compute the cost of the
same bundle of goods in, say 2000, requires that we compute the cost of the
bundle using current prices
The CPI is defined as the
ratio of the costs of these two market baskets
If the basket cost $100 in
1982 prices and $175 in 2000, the value of the CPI would be 1.75 and with a
measured 75 percent increase in prices over the 18 year period.
Substitution Bias in the CPI
The CPI does not take into
account the real possibility that consumers would substitute among commodities
because of changes in relative prices.
In Figure 1, the typical
individual is initially consuming X82, Y82 maximizing
utility on U1 with 1982 constraint I.
FIGURE 1:
Substitution Bias of the Consumer Price Index
Suppose the 2000 relative
prices change so that PX/PY falls.
The cost of the 1982 bundle
in terms of 2000 prices is reflected in the constraint I which is flatter and
goes though the 1982 bundle.
The consumer would
substitute X for Y and stay on U1 on budget line I.
Since I is inside I
(which is used to compute the CPI), the CPI tends to overstate the inflation
rate.
Unfortunately, adjusting the
CPI to take such substitution into account is difficult because it would
require that we know the utility function of the typical consumer.
New Product Bias in the CPI
New products typically
experience sharp declines in prices and rapidly grow in rates of acceptance.
If the CPI does not include
these new products, this source of welfare increase is omitted.
The CPI basket is revised
but not rapidly enough to eliminate this bias.
Outlet Bias in the CPI
The typical basket is bought
at the same retail outlets every month.
This method can omit the
benefits of sales or other bargains.
The CPI does not currently
take such price-reducing strategies and thus tends to overstate inflation.
Consequences of the CPI Biases
Measuring and correcting for
these biases is not an easy task.
The CPI is such a widely
used measure of inflation that any change becomes a hot political issue.
However, there is a general
agreement that the CPI overstates inflation by as much as 0.75 to 1.0 percent
per year.
Politicians have proposed
caps on Cost of Living Adjustments (COLAs) tied to the CPI on government
programs, but none have yet been enacted.
However, the private sector
has adjusted so that few private COLAs provide full offsets to inflation
measured by the CPI.
Substitution and Income Effects for Inferior Goods
With an inferior good, the
substitution effect and the income effects work in opposite directions.
The substitution effect
results in decreased consumption for a price increase and increased consumption
for a price decrease.
The income effect results in
increased consumption for a price
increase and decreased consumption for
a price decrease.
Figure 3.5 shows the two
effects for an increase in PX.
The substitution effect,
holding real income constant, is shown by the move from X*, Y*
to point B both on U2.
FIGURE 3.5: Income
and Substitution Effects for an Inferior Good
The income effect reflects
the reduced purchasing power due to the price increase.
Since X is an inferior good,
the decrease in income results in an increase in the consumption of X shown by
the move from point B on U1 to the new utility maximizing point X**,
Y** on U1.
Since X** is less
than X* the price increase in X results in a decrease in the
consumption of X.
This occurs because the
substitution effect, in this example, is bigger than the income effect.
Thus, if the substitution
effect dominates, the demand curve is negatively sloped.
Giffens Paradox
If the income effect of a
price change is strong enough with an inferior good, it is possible for the
quantity demanded to change in the same direction as the price change.
Legend has it that this
phenomenon was observed by English economist Robert Giffen.
When the price of potatoes
rose in Ireland the consumption of potatoes also increased.
Potatoes were not only an
inferior good but constituted the source of a large portion of Irish peoples
income.
The situation I which an
increase in a goods price leads people to consume more of the good is called Giffens
paradox.
The Lump Sum Principle
The lump-sum principle
hold that taxes that are imposed on general purchasing power will have a
smaller welfare costs than will taxes imposed on a narrow selection of
commodities.
Consider Figure 3.6 where
the individual initially has I dollars to spend and chooses to consume X*
and Y* yielding U3 utility.
FIGURE 3.6: The
Lump-Sum Principle
A tax on only good X raises
its price resulting in budget constraint I and consumption reduced to X1,
Y1 and utility level U1.
A general income tax that
generates the same total tax revenue is represented by budget constraint I
that goes though X1, Y1.
The utility maximizing
choice on I is X2, Y2 yielding utility level U2.
The lump-sum general income
tax generates the same amount of tax revenue but leaves the consumer on a
higher utility level (U2) than the utility level associated with the
tax only on good X (U1).
The intuitive explanation of
the lump-sum principle is that a single-commodity tax affects people in two
ways:
it reduces their purchasing
power,
it directs consumption away
from the good being taxed.
The lump-sum tax only has
the first of these two effects.
Generalizations of the Lump-Sum Principle
The utility lass associated
with the need to collect a certain amount of tax revenue will be minimized by
taxing goods for which the substitution effect is small.
Even though the tax will
reduce purchasing power, it will minimize the impact of directing consumption
away from the good being taxed.
APPLICATION 3.3:
The Lump-Sum Principle in Practice
The most commonly proposed
real-world approximation to a lump-sum tax is a general tax on income.
However, such tax still
effects the choice of how much to work and other income influencing decisions.
Estimates suggest as much as
a 22 percent loss in utility from an income tax rather than a pure lump-sum
tax.
A income subsidy (negative
tax) is also subject to the lump-sum principle.
Studies suggest that
subsidies on food, housing and medical generate $.88, $.56, and $.68 for $1
subsidy respectively.
Changes in the Price of Another Good
When the price of one good
changes, it usually has an affect on the demand for the other good.
In Figure 3.3, the increase
in the price of X (a normal good) caused both an income and substitution effect
that caused a reduction in the quantity demanded of X.
In addition, the
substitution effect caused a decrease in the demand for good Y as the consumer
substituted good X for good Y.
However, the increase in
purchasing power brought about by the price decrease causes an increase in the
demand for good Y (also a normal good).
Since, in this case, the
income effect had a dominant effect on good Y, the consumption of Y increased
due to a decrease in the price of good X.
With flatter indifference
curves as shown in Figure 3.7, the situation is reversed.
A decrease in the price of
good X causes a decrease in good Y, as before.
FIGURE 3.7: Effect
on the Demand for Good Y of a Decrease in the Price of Good X
However, in this case, the
income effect is much smaller than the substitution effect so that the consumer
ends up consuming less of good Y at Y** after the decrease in the
price of X.
Thus, the effect of a change
in the price of one good has an ambiguous effect on the demand for the other
good.
Complements
Complements are goods that
go together in the sense that people will increase their use of both goods
simultaneously.
Two goods are complements
if an increase in the price of one causes a decrease in the demanded of the
other or a decrease in the price of one good causes an increase in the demand
for the other.
Substitutes
Substitutes are goods that
are goods that are used for essentially the same purpose.
Two goods such that if the
price of one increases, the demand for the other rises are substitutes.
If the price of one good
decreases and the demand for the other good decreases, they are also
substitutes.
APPLICATION 3.4: Gas Prices and Automobiles
Gasoline and automobiles are
complements as fuel costs constitute between 10 and 20 percent of the total
cost of operating a car.
Fluctuating gas prices can
have important impacts on the types of cars people drive in the long run.
Between 1973 and 1980
gasoline prices increase nearly four-fold in the U.S. resulting in smaller more
fuel-efficient cars being purchased.
With the decline of gasoline
prices in the 1980s, consumers again bought larger cars.
In 1991 a gas guzzler tax
on automobiles was instituted which can rise to $7,700 for automobiles getting
less than 12.5 miles per gallon.
However, sport utility
vehicles (SUVs) are exempt from the tax which may help to explain the increased
popularity of such vehicles.
Construction of Individual Demand Curves
An individual demand
curve is a graphic representation between the price of a good and the
quantity of it demanded by a person holding all other factors (preferences, the
prices of other goods, and income) constant.
Demand curves limit the
study to the relationship between the quantity demanded and changes in the own
price of the good.
In Panel a of Figure 3.8 an
individuals indifference curve map is drawn using three different budget
constraints in which the price of X decreases.
The decreasing prices are PX,
PX, and PX respectively.
The individuals utility
maximizing choices of X are X, X, and X respectively.
FIGURE 3.8:
Construction of an Individuals Demand Curve
These three choices show
that the quantity demanded of X increases as the price of X falls.
Panel b shows how the three
price and quantity choices can be used to construct the demand curve.
The price of X is shown on
the vertical axis and the quantity of X is shown on the horizontal axis.
The demand curve (dX)
is downward sloping showing that when the price of X falls, the quantity
demanded of X increases.
As previously shown, this
result follows from the substitution and income effects.
Shape of the Demand Curve
If a good, say X, has close
substitutes, a increase in its price will cause a large decrease in the
quantity demanded as the substitution effect will be large.
The demand curve for a type
of breakfast cereal will likely be relatively flat due to the strong
substitution effect.
If the good has few
substitutes, the substitution effect of a price increase or decrease will be
small and the demand curve will be relatively steep.
Water is an example of a
good with few substitutes.
Food has no substitutes so
it might be thought that no change in consumption would occur with a price
increase.
But food constitutes a large
part of an individuals budget so that price changes will cause relatively
larger effects on the quantity demanded that might be thought due to the income
effect.
Shifts in an Individuals Demand Curve
When one of the variables
that are held constant (price of another good, income or preferences) on a
demand curve changes, the entire curve shifts.
Figure 3.9 shows the kinds
of shifts that might take place.
If X is a normal good and
income increases, demand increases as shown in Panel a.
FIGURE 3.9: Shifts
in Individuals Demand Curve
If X and Y are substitutes
and the price of Y increases, the demand for X increases as shown in Panel b.
Alternatively, if X and Y
are complements, the increase in the price of Y will cause a decrease in the
demand for X as shown in Panel c.
Changes in preferences can also
shift demand curves.
Panel b could represent an
increased preference for cold drinks when a sudden hot spell occurs.
Increased environmental
consciousness during the 1980s and 1990s increased the demand for recycling
and organic food.
APPLICATION 3.5: Fads, Seasons, and Health Scares
Fads (sometimes termed bandwagon
effects) are when preferences cause extremely large increases in demand
followed later by large decreases in demand.
While fads are hard to
predict, seasonal items are easy to predict.
Increased demand for turkeys
in November and Christmas trees are examples.
Health scares can cause
large decreases in the demand for products.
Examples include the long
term decline in smoking and the decreased demand for Chinese food because of
the concern for its fat content.
Recent scientific studies
have also affected demand such as the increase in the demand for tomatoes in
1998.
Demand Curve Terminology
A movement downward along a
stationary demand curve in response to a fall in price is called an increase in
quantity demanded while a rise in the price of the good results in a
decrease in quantity demanded.
A rightward shift in a
demand curve is called an increase in demand while a leftward shift is a
decrease in demand.
Compensated Demand Curves
Since nominal income is held
constant along a demand curve, a decline in the price of the good increases
purchasing power and increases the utility of the consumer.
An alternative would be to
hold utility constant and examine reactions to changes in the price of a good.
In Panel a of Figure 3.10
the price of good X is decreased from PX to PX to PX
causing the decline in the relative price of X (PX/PY).
This generates tangency
points between the slope of indifference curve U2 (MRS) and the
slope of the relative prices (shown by the tangent lines).
FIGURE 3.10:
Construction of a Compensated Demand Curve
In Panel b the vertical axis
is the price of good X and the horizontal axis is the quantity of good X
demanded.
The tangency points in Panel
a generate the curve hx shown in panel b.
In this curve utility
(instead of nominal income) is held constant.
The curve hX is
called a compensated demand curve since the effects of the price changes on
purchasing power are compensated so as to prevent the individuals welfare to
increase from the price declines.
Price increases would have
to be compensated by increased income.
A demand curve drawn on the
assumption that other prices and utility are held constant is a compensated
demand curve.
Income effects of price changes
are compensated for along the curve, and it reflects only substitution effects.
Consumer Surplus
The extra value individuals
receive from consuming a good over what they pay for it is called consumer
surplus.
Consumer surplus is also what people would
be willing to pay for the right to consume a good at its current price.
This concept is used to
study the welfare effects of price changes.
The compensated demand curve
is shown in Figure 3.11.
At the price P0
the individual chooses to consume X0 as shown at point E0.
If the price were to
increase to P1 the consumer would choose zero consumption but would
be compensated with income to keep utility constant.
Suppose, starting at X0,
the price of X were increased very slightly (DP) so that the consumer
still consumed approximately X0.
To compensate for this price
increase, his or her purchasing power would have to be increased by DP·X0 if utility is to remain
constant.
FIGURE 3.11:
Consumer Surplus
This compensation would
allow the individual to continue to consume the original set of goods consumed
before the price rise.
Repeating this experiment
many times would result in a movement up along hX.
Summing all of these
compensations as price increases from P0 to P1 would
yield the shaded area P1E0P0.
This is the total increase
in purchasing power that must be provided to this person to make him or her
equally well off at P1 (where no X is consumed) as at P0
(where X0 is consumed).
Thus the shaded triangle in
Figure 3.11 shows what this individual would voluntarily pay for the right to
be allowed to choose to consume X0 at its current price P0.
Hence, at E0this
person is receiving consumer surplus in the amount of P1E0P0.
Lower prices increase
consumer surplus while higher prices lower it.
APPLICATION 3.6: Valuing Clean Air
By looking at the ceteris
paribus relationship between air pollution levels in various locations and
the prices of houses in these locations, it is possible to infer the amount
that people will pay to avoid dirty air.
This information allows the
computation of a compensated demand curve for clean air.
In Figure 1, the vertical
axis shows the price home buyers are willing to pay to avoid air pollution and
the horizontal axis shows the quantity of clean air purchased.
The national average is reflected
at point E as home buyers pay $50 and consume an average of 55 micrograms of
suspended particulates per cubic meter.
FIGURE 1:
Compensated Demand Curve for Clean Air
Consumers are paying $2,250
($50 times 45 micrograms) extra to avoid dirty air.
At E0 consumers
also receive a consumer surplus equal to the shaded area in Figure 1.
This consumer surplus of 788
per household can be multiplied by the total number of households to estimate
total consumer surplus from clean air.