Topic 3 – Individual and Market Demand
Outline:
I)
II)
III)
IV)
V)
VI)
The Effects of Changes in Price
The Effects of Changes in Income
Income and Substitution Effects
Market Demand Curves
Elasticities of Demand
Consumer Surplus
I)
The Effects of Changes in Price
Q: Holding income, preferences, and the prices of
other goods constant, how will a change in the price
of X affect the quantity of X purchased?
Begin with the Price-Consumption Curve (PCC)…
A) Price-Consumption Curve
Price-Consumption Curve (PCC) – Holding income,
preferences, and the price of Y constant, the PCC for
X is the set of optimal bundles that are traced out as
the price of X varies.
It is found by connecting the locus of tangencies
(between indifference curves and the budget line) that
results as the budget line is rotated. (see diagram)
Use this information to plot the individual’s demand
curve…
B) Individual Demand Curve
Individual Demand Curve – A curve that plots the
relationship between the quantity of X consumed and
the price of X, holding income, preferences, and the
prices of other goods constant.
To derive the demand curve for a particular
consumer,
- Record the price-quantity combinations from the
PCC in a table
- Plot these points in price-quantity space (see
diagram)
II) The Effects of Changes in Income
Q: Holding preferences and the prices of X and Y
constant, how will a change in income affect the
quantity of X purchased?
Begin with the Income-Consumption Curve (ICC)…
A) Income-Consumption Curve
Income-Consumption Curve (ICC) – Holding
preferences and the prices of X and Y constant, the
ICC for X is the set of optimal bundles that is traced
out as income varies. (see diagram)
Use this information to plot the individual’s Engel
curve…
B) Engel Curve
Engel Curve – A curve that plots the relationship
between the quantity of X consumed and income,
holding preferences and prices constant.
To derive the Engel curve for a particular consumer,
- Record the income-quantity combinations from the
ICC in a table
- Plot these points in quantity-income space (see
diagram)
- Upward sloping for normal goods; downward
sloping for inferior goods
III) Income and Substitution Effects of a Price
Change
- When a price changes, there are actually two
distinct things going on.
- Consider the case of a price increase.
(i)
The Income Effect: The increase in price
reduces the consumer’s purchasing power
(since M/Px falls).
(ii)
The Substitution Effect: The increase in price
gives the consumer an incentive to substitute
away from the good whose price has risen.
- The substitution effect is always away from the
good whose price has risen.
- The direction of the income effect depends on
whether the good is normal or inferior.
- The total effect of the price change is the sum of
the income and substitution effects.
Graphically, we isolate the two effects
constructing a hypothetical budget line that is:
by
Parallel to the “new” budget line, but tangent to the
“old” indifference curve
Income effect is shown as the difference between the
hypothetical budget line and the new budget line.
Note that since these budget lines are parallel to one
another, they represent the effect of a change in
income, holding prices (the slope of the budget line)
constant.
Substitution effect is shown as a movement along the
original indifference curve after the income effect has
been “canceled out” by (hypothetically) giving the
consumer just enough income to return them to their
original indifference curve (or hypothetically taking
income away in the case of a price decrease).
Example 1 – Price increase (see diagram)
Example 2 – Price decrease (see diagram)
Giffen Goods
- The overwhelming majority of goods have
downward sloping demand curves.
- However, the theory does not rule out the
possibility that demand curves could be upward
sloping.
- Goods with upward sloping demand curves are
called Giffen Goods.
- Since the substitution effect of a price increase is
always negative, a good can only be Giffen if:
(1) It is an inferior good.
(2) The income effect
substitution effect.
is
larger
than
the
- For this reason, Giffen goods are most likely to
arise in cases where consumers spend a large
fraction of their income on an inferior good (so that
the income effect will necessarily be large).
Example? The potato in 19th century Ireland.
Q: Is there a condition that we can impose that will
guarantee a downward-sloping demand curve?
Applications – Income and Substitution Effects
A) Biases in the Consumer Price Index
- Goal is to calculate changes in “cost of living,” (i.e.
the amount that must be spent to maintain one’s
standard of living).
- Measured by change in cost of buying a fixed
bundle of goods.
- Determines cost-of-living adjustments for Social
Security and other government programs.
- Two types of bias:
a) Quality change.
b) Substitution bias.
- Focus on the second one.
- Problem: Prices of different goods change by
different proportions (inflation is not uniform
across products).
- This leads people to substitute away from goods
whose price has risen (the substitution effect).
- Cost of living adjustments based on the CPI are
designed to allow consumers to purchase their
original bundle at the new prices.
- This ignores the substitution effect and results in
over compensation.
B) “Shipping the Good Apples Out.”
- Old paradox.
- Washington state is premier region for apple
growers.
- Yet, residents report higher quality apples are
available in other parts of the country than are
available locally.
- Why?
IV) Market Demand Curves
The market demand curve gives the total quantity
demanded by all consumers at each price, holding
constant total income and the prices of other goods.
Graphically, the market demand curve is the
horizontal sum of the individual demand curves.
It is the horizontal sum because we want to add up
the total quantity demanded at each price.
Caveat: In calculating the market demand curve, you
must take into account the different “choke” prices of
the individual demand curves, i.e. the lowest price at
which zero units are purchased.
Example: Consider three consumers: Alice, Betty,
and Cindy. Their individual demand curves are given
by
qa 10  P (vertical intercept = 10)
q  20  6P (vertical intercept = 3.33)
b
qc  50 4P (vertical intercept = 12.5)
Letting market demand be denoted by Q, we have

Q0
Q  qc
Q  qc  qa
Q  qc  qa  q
b
for P  12.5
for 10  P 12.5
for 3.33  P 10
for P  3.33
Q=0
Q = 50 – 4P
Q = 60 – 5P
Q = 80 – 11P
for P  12.5
for 10  P 12.5
for 3.33  P 10
for P  3.33
V) Elasticities of Demand
Measure of the responsiveness of quantity demanded
to some variable (own-price, cross-price, or income)
Expressed in percentage terms to provide a “unitless” measure
Terminology:
Elastic:
Greater than 1 in absolute value
Inelastic:
Less than 1 in absolute value
Unitary:
Absolute value of exactly 1
A) Own-Price Elasticity of Demand
%Qx Qx Px
E


Qx, Px %Px P Q
x x
First term in product is the inverse of the slope of the
demand curve (when price is expressed as a function
of quantity)
Negative according to the law of demand
Elasticity varies along a linear demand curve (due to
second term in the product)
Example: Linear demand curves
Q = 10 – 2P
Qx Px
Px
E

 2
Qx, Px P Q
Qx
x x
Suppose P = 1: then Q = 8 and the own-price
elasticity of demand at (P = 1; Q = 8) is -0.25
Polar Cases: (see diagram)
(a) Perfectly (infinitely) elastic
(b) Perfectly (infinitely) inelastic
Relationship between own-price elasticity of demand
and total revenue (P*Q)
Elastic portion of curve: Increase in price leads to a
decrease in total revenue (and vice-versa).
Inelastic portion of curve: Increase in price leads to
an increase in total revenue (and vice-versa)
Unitary elasticity: Total revenue is maximized at
point where demand is unit elastic.
Factors affecting own-price elasticity:
a) Available substitutes – the more substitutes
available, the more elastic the demand
Example – gasoline vs. rare paintings
b) Time – Demand tends to be more inelastic in the
short term than in the long term. Time allows
consumers to seek out available substitutes
Example – same day airline tickets vs. tickets
purchased a month in advance
c) Expenditure share – Goods that comprise a small
share of consumers’ budgets tend to less elastic
(i.e., less price sensitive) than goods that
comprise a large share.
Example: toothpicks vs. automobiles
B) Cross-Price Elasticity of Demand
%Qx Qx Py
E


Qx, Py %Py P Q
y x
+ Substitutes
- Complements
C) Income Elasticity
%Qx Qx M
E


Qx, M %M M Q
x
+ Normal Good
- Inferior Good
D) Some Business Applications
Application 1 – Pricing and Cash Flows
According to an FTC Report by Michael Ward,
AT&T’s own price elasticity of demand for long
distance services is –8.64.
AT&T needs to boost revenues in order to meet it’s
marketing goals.
Q: To accomplish this goal, should AT&T raise or
lower its price?
A: Lower price.
Since demand is elastic, a reduction in price will
increase quantity demanded by a greater percentage
than the price decline, resulting in more revenues for
AT&T.
Application 2 – Quantifying the effect of a change in
price
Q: If AT&T lowered price by 3 percent, what would
happen to the volume of long distance calls routed
through AT&T?
A: Calls would increase by 25.92%
%Qx
E
 8.64 
Qx, Px
%Px
8.64 
%Qx
 3%
%Qx  3%*(8.64)  25.92%
Application 3 – Impact of a change in a competitor’s
price
According to a FTC report by Michael Ward,
AT&T’s cross price elasticity of demand for long
distance services is 9.06.
Q: If MCI and other competitors reduced their prices
by 4 percent, what would happen to the demand for
AT&T services?
A: AT&T’s demand would fall by 36.24 percent.
%Qx
E
 9.06 
Qx, Py
%Py
9.06 
%Qx
 4%
%Qx   4%*(9.06)  - 36.24%
VI) Consumer Surplus
Definition: Consumer Surplus – The value consumers
receive from a good but do not have to pay for.
- Demand curve indicates willingness to pay
(marginal benefit) at each quantity
- If this exceeds price for some units, the consumer
earns a surplus on these units.
- Summing the surplus per unit up over the number
of units purchased gives the consumer surplus
- Graphically, it is the area under the demand curve,
above the price paid, out to the quantity purchased
(see diagram).
Business Application – Two-Part Pricing
- Many businesses (such as amusement parks and
popular nightclubs) charge an up-front free for the
right to purchase goods or services at a particular
price.
- What is the rationale for these two-part pricing
policies?
- Why don’t all businesses do this?