Download Chapter 4

Chapter 4: Individual
and Market Demand
• Extends individual theory of
consumer demand
• Start with individual’s budget
constraint/indifference curve
analysis to show how quantity of
good changes as price changes.
• Steps:
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2.
3.
4.
5.
Start at single U-max.
Show es in PF  es in QF
Price-Consumption Curve
Individual Demand Curve
See Figure 4.1.
Individual’s Demand
Curve: 2 Properties
• 1. As move down D curve, level of
attainable utility increases because a
P implies an  in purchasing
power.
• *Utility es as move down D
Curve.
• 2. As move down D curve and PF is
, MRS is falling too.
• Why? Each pt on D curve comes
from U max, where MRS=-PF/PC; so
when PF falls, MRS falls too.
• Explain using MRS = MUF/MUC.
Effect of Income on
Quantity of Food
• Goal: Link es in income to
shifts in the Demand Curve.
• Steps:
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1.
2.
3.
4.
5.
Start at single U-max.
Show es in I  es in QF
Income-Consumption Curve
Shifts in Individual D Curve
See Figure 4.2.
Review Link Between
Income and QF
• Key: Income-Consumption
Curve shows points on different
demand curves.
• If have : I associated with D
curve shifting to right for the
two goods on both axes
Income-Consumption Curve
slopes upward AND the goods
are normal goods and income
elasticity of demand is positive.
More on Income and
Consumption
• Inferior Good: Income 
consumption  . In this case, if this
inferior good on vertical axis:
Income-Consumption curve slopes
downward.
• Income-Consumption curve can be
backward-bending (See Figure 4.3.)
• Engel Curve: shows relationship
between income and consumption
for a specific good. (See Figure
4.4.) This curve can also be
backward-bending.
Substitutes versus
Complements
• If  PA   DB, then the two
goods are substitutes.
– Review:  PA   QD of good A
(Law of Demand),   DB )
• If  PA   DB, then the two
goods are complements.
• Relate to price-consumption
curve:
– If slopes up: complements.
– If slopes down: substitutes.
Exercise
• Considering two goods C and F, with
C on the vertical axis. Sketch
indifference curves and budget
constraints, showing two different
levels of income.
1. Is the slope of the incomeconsumption curve positive or negative
if both F and C are normal goods?
Show.
2. Is the slope positive or negative if F
is normal and C is inferior? Show.
3. With only two goods, can both
goods be inferior in the same income
range? Why or why not?
Decomposing Full Effect
of PA on QA
• Consider a  Price:
– 1)  relative prices: now one good
relatively less expensive so
individual will substitute away
from other goods to this good. 
Substitution Effect
– 2) This  P is an  in real
purchasing power: Like an 
Income so buy more of all normal
goods.  Income Effect
Show Decomposition
Graphically
• Start with Substitution effect: show
the substituting by allowing price
line to change slope but keeping
utility fixed (so stay on original
indifference curve). This new b.c. is
just temporary one to show this
effect.
• Then Income effect: Allow pure
change I as a shift of this new
temporary budget line up to higher
indifference curve. Shows the
increased utility from the increased
income.
Further Details
• From this  Price Food:
– Substitution Effect ALWAYS
leads to  Food due to convexity
of indifference curves. Pure 
relative prices with no  Income.
– Income Effect: If good is normal,
 income causes  consumption.
For normal good: income effect is
positive. (This positive means the
P like a I, which causes QF)
More Details
• Total Effect = Subst Effect + Income
Effect.
• Subst Effect usually large.
• Could have negative income effect if
good is inferior (means increase
income causes decrease demand).
But still get downward sloped
Demand Curve.
• Giffen good: Theoretical case of
negative income effect dominating
the substitution effect. This violates
the Law of Demand.
Exercise
• Consider two normal goods X and Y
with good X on the horizontal axis.
• 1. Sketch and label a graph showing
an initial U-max bundle of X and Y.
• 2. Now a 10% sales tax is imposed
on good X so there is an increase in
the price of X.
– A. Graph the income and substitution
effects.
– B. Label completely.
Example: Gas Tax
w/Rebate
• Why tax gasoline?
– 1) taxes raise revenues for govt.
– 2) gas tax  consumption of gas
by altering relative prices.
• Concern about gas tax: any tax
on such a necessity tends to be
regressive (low-income
individuals pay higher % of
income on the tax).
• See Figure 4.9: first impose tax;
then add in the rebate.
Market Demand Curve
• Derive market demand curve from
set of individual demand curves.
• Horizontal Summation: At each
price, add together the quantity
demanded by each individual.
• This market demand curve can be
for an entire market or some sort of
sub-market.
• Example: market for home
computers can be divided into submarkets, such as households with
young children, etc.
• See Table 4.2 and Figure 4.10
EP and Total Revenue
• Review price elasticity of demand:
• EP = % QD resulting from a
1% P
•
= P/Q * Q/P
• Issue: When price changes by 1%,
what happens to the total
expenditures on the good? (same as
TR = total revenue = P * Q)
• Starting Point: Law of Demand:
Whenever P goes up, Q goes down.
• Issue is BY HOW MUCH does Q
go down?
More on EP and TR
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Inelastic Demand: EP  1
Q relatively unresponsive to P
When P  by 1%, Q   1%
So when P, Q no fall very
much, so TR = P*Q  too.
See example.
Elastic Demand: EP 1
Q very responsive to P
So  P leads to  TR.
See Example.
Example
• Family buys 1,000 gallons of gas per
year at P = $1/gallon.
• EP = -0.5.
• Interpret EP = 1% P causes a 0.5%
 Q.
• Total Revenue = TR = P * Q
• TR = $1 * 1,000 = $1,000.
• Now P  to $1.10, a 10% .
• SO: Causes a 5%  Q, down to 950
gallons.
• New TR = $1.10 * 950 = $1045.
• See that TR has .
Exercise
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Family buys 100 lbs chicken/yr
P = $2/lb and EP = -1.5.
What is total expenditures?
Now P  to $2.20/lb.
What % is this?
What is new Q?
What is new total expenditures?
Isoelastic Demand
• ‘Iso’ means same.
• Isoelastic: when EP is the same
along the entire Demand curve
(so this curve is not straight).
• Special case is Unitary
Isoelastic demand curve, where
EP = -1 along entire curve.
• With unit elastic D curve: TR is
the same at each P,Q
combination
• See Figure 4.11
More on EP
• Point elasticity: defined as EP at a
specific point. We use this.
• EP = P/Q * 1/slope
• So if the demand curve is straight
line, 1/slope is same number. Can
calculate EP for specific value of P,Q
(like at equilibrium values)
• But usually think of measuring EP
over a specific portion of D curve.
This leads to uncertainty: which P,Q
combination to use?
• Arc Elasticity is alternative measure
• = AvgP/AvgQ * 1/slope.
Consumer Surplus
• Important concept that will reoccur repeatedly throughout this
course!
• Definition: the difference
between what a consumer is
willing to pay and what she
actually pays.
• Two basic components:
– Demand Curve reveals
willingness to pay for each Q.
– We assume single market P
Aggregate Consumer
Surplus
• The triangle formed by the
demand curve and the price
line: the area under the demand
curve but above the price line.
• To measure the area of a
triangle:
• AREA = ½ * base * height.
Exercise
• Two individual consumers for one
firm’s long-distance services; each
indiv. with own D curve:
• Indiv. A: Q = 40 – 0.5P
• Indiv. B: Q = 120 – P
• Q = # minutes long distance calls;
• P = cents/minute = 20 cents; (P=20).
• 1. Draw each Demand curve and its
corresponding equilibrium price line.
• 2. Calculate CS for both; calculate
firm’s total revenue.
• 3. If firm adds $10/month flat fee
plus per/minute, what is new TR?