Market
Demand
Chapter 5
Slides by Pamela L. Hall
Western Washington University
©2005, Southwestern
Introduction

Demand for a commodity is differentiated from a
want
 In terms of society’s willingness and ability to pay for
satisfying the want

This chapter determines total amount demanded
for a commodity by all households
• Called market demand or aggregate demand


Sum of individual household demands
 Assuming individual household demands are independent of
each other
Will explore network externalities
 Independence assumption does not hold
2
Introduction

Major determinants of market demand for a commodity are
 Its own price
 Price of related commodities
 Households’ incomes


Elasticity of demand is a measure of influence each parameter has on
market demand
We investigate own-price elasticity of demand
 Classify market demand as elastic, unitary, or inelastic

• Depending on its degree of responsiveness to a price change
Relating own-price elasticity to households’ total expenditures for a
commodity
 Demonstrate how this determines whether total expenditures for a
commodity will increase, remain unchanged, or decline, given a price
change
3
Introduction





Define income elasticity of demand and elasticity of demand
for the price of related commodities
 Called cross-price elasticity
Applied economists are active in estimating elasticities for
all determinants (parameters) of market demand
Knowledge of the influence these determinants provides
information for firms’ decisions
Government policymakers also use estimates of elasticities
With reliable estimates of elasticities based on economic
models
 Economists can explain, predict, and control agents’ market behavior
4
Market Demand




One arm of Marshallian cross
Conveys individual household preferences for a commodity
given a budget constraint
Sum of all individual households’ demands for a single
commodity
Consider only two households—Robinson, R, and Friday,
F—and two commodities
• xR1 and xF1 are household Robinson’s and household Friday’s demand for
commodity x1, respectively
 Both households face same per-unit prices for the two commodities
• Each household is a price taker
 Both households are bound by budget constraints
• IR and IF represents income for Robinson and Friday, respectively
5
Market Demand

Market demand, Q1, is sum of amounts demanded by the
two households
 Holding p2, IR, and IF constant, we obtain market demand curve for x1
in Figure 5.1
 For a private good, market demand curve is horizontal summation of
individual household demand curves
6
Figure 5.1 Market demand for
commodity Q1 …
7
Market Demand

At p*1 Robinson demands 5 units of Q1 and Friday demands 3
 For a total market demand of 8 units
 Varying price will result in other associated levels of market demand
• Will trace out market demand curve for Q1




Will have a negative slope
 For market demand to have a positive slope, a large portion of households would
have to consider x1 a Giffen good
Assume market demand for a commodity is inversely related to its own
price
Shifts in market demand will occur if there is a change in household
preferences, income, price of another commodity, or population
As illustrated in Figure 5.2, market demand curve will shift outward for
an increase in




Income
Population
Price of substitute commodities, or
A decrease in prices of complement commodities
8
Figure 5.2 Shift in market
demand
9
Network Externalities


Horizontal summation of households’ demand functions
assumes individual demands are independent of each other
For some commodities, one household’s demand does
depends on other households’ demands
 Example of network externalities
• Exist when a household’s demand is affected by other households’
consumption of the commodity

Positive network externalities result when
 Value one household places on a commodity increases as other
households purchase the item

Negative network externalities exist if household’s
demand decreases as a result of other households’ actions
10
Bandwagon Effect





Specific type of positive network externality
Individual demand is influenced by number of other
households consuming a commodity
The greater the number of households consuming a
commodity
 More desirable commodity becomes for an individual household
Key to marketing most toys and clothing is to create a
bandwagon effect
Results in market demand curve shifting outward
 Individual household demand increases in response to increased
demand by numerous other households
11
Market Effect

If positive network externalities exist, summation of individual
household demands does not take into account households’
increase in demand when other households increase their
demand for the commodity
 Will underestimate true market demand
• Shown in Figure 5.3

Individual household demand curves are positively influenced
by other households’ level of demand for commodity
 Results in a further outward shift of individual household demand
curves, and market demand curve

Instead of market demand being sum of 5 plus 3 units at p*1
 Positive network externalities result in a market demand of 7 plus 6
units
12
Figure 5.3 Market demand for
commodity Q1 …
13
Market Effect

If negative network externalities exist
 Summation of individual household demands will
overestimate true market demand
• Shown in Figure 5.4

Results in inward shift of individual household demand
curves
 With a corresponding inward shift in market demand
curve
14
Figure 5.4 Market demand for
commodity Q1 …
15
Elasticity



Market demand function provides a relationship between
price and quantity demanded
 Quantity demanded is inversely related to price
Of greater interest to firms and government policymakers is
how responsive quantity demanded is to a change in price
Downward-sloping demand curve indicates
 If a firm increases its price, quantity demanded will decline
• Does not show magnitude of decline

To measure magnitude of responsiveness use derivative or
slope of curve
 The larger the partial derivative, the more responsive is y
16
Units Of Measurement


One problem in using derivative is units of measure
By changing units of measure—say from dollars to
cents or pounds to kilograms
 Cause magnitude of change or value of derivative to vary
• For example, if y is measured in pounds, x in dollars, and ∂y/∂x =
2



Measurement is 2 pounds per dollar
 For each $1 increase in x, y will increase by 2 units
However, if change scale used to measure y to ounces, then ∂y/∂x =
32
 For each $1 increase in x, y will increase by 32 units
Just changing scale makes it appear that y is more responsive to a
given change in x
17
Unit-free Measure Of
Responsiveness


Prior failure to convert from English to metric system of
measurement caused loss of Mars Climate Orbiter
To avoid making such errors in comparing responsiveness
across different factors with different units of measurement
in economics
 Use a standardized derivative, elasticity
• Removes scale effect

Derivative is standardized (converted into an elasticity)
 By weighting it with levels of variables under consideration
• Results in percentage change in y given a percentage change in x

Provides a unit-free measure of the responsiveness
• Partial derivative is not as useful as elasticity measurement
18
Logarithmic Representation

As a percentage change measure, elasticity
can be expressed in logarithmic form
19
Price Elasticity Of Demand
For market quantity, Q is defined as
 Q,p(∂Q/∂p)(p/Q) = ∂ ln Q/∂ ln p
 Elasticity of demand indicates how Q
changes (in percentage terms) in response
to a percentage change in p
 Ordinary good: ∂Q/∂p < 0

• Implies Q,p < 0 given that p and Q are positive

Examples of demand elasticities are provided in Table 5.1
20
Table 5.1 Estimates of price
elasticities of demand
21
Perfectly Inelastic Demand

A change in price results in no change in
quantity demanded
 Q,p = 0
 Represented in Figure 5.5
• Results in a vertical demand curve

At every price level quantity demanded is the same
 Examples are difficult to find due to the lack of
households with monomania preferences
 For example, alcoholics and drug addicts would have
highly inelastic demands over a broad range of quantity
22
Figure 5.5 Perfectly inelastic
demand curve
23
Perfectly Elastic Demand


Smallest possible value of Q,p is for it to approach
negative infinity
If Q,p = - demand is perfectly elastic
 Very slight change in price corresponds to an infinitely
large change in quantity demanded
• Illustrated in Figure 5.6

Many examples of perfectly elastic demand curves
 Whenever a firm takes its output price as given it is
facing a perfectly elastic demand curve
• For example, agriculture
24
Figure 5.6 Perfectly elastic
demand curve
25
Classification of Elasticity

Between elasticity limits from - to 0, elasticity may
be classified in terms of its responsiveness
 Q,p < -1, elastic, |∂Q/Q| > |∂p/p|
• Absolute percentage change in quantity is greater than absolute
percentage change in price

Quantity is relatively responsive to a price change
 Q,p = -1, unitary, |∂Q/Q| = |∂p/p|
• Absolute percentage change in quantity is equal to absolute
percentage change in price
 Q,p > -1, inelastic, |∂Q/Q| < |∂p/p|
• Absolute percentage change in quantity is less than absolute
percentage change in price

Quantity is relatively unresponsive to a price change
26
Linear Demand


Linear demand curve will exhibit all three elasticity
classifications
Consider linear demand function for commodity x1
 x1 = 120 – 2p1
• Plotted in Figure 5.7
 Elasticity of demand represented as
• 11 = (∂x1/∂p1)(p1/x1)
 Size of elasticity coefficient increases in absolute value for
movements up this linear demand curve
• Because slope is remains constant while weight is increasing



At point B
 11 = (∂x1/∂p1)p1/x1 = -2(45/30) = -3, elastic
At D
 11 = (∂x1/∂p1)p1/x1 = -2(15/90) = -1/3, inelastic
At point C (A) [E] elasticity of demand is unitary (-) [0]
27
Figure 5.7 Linear demand curve
…
28
Linear Demand

General functional form for a linear market
demand function
 Q1 = a + bp1, b<0
• Q1 denotes market demand for commodity 1
• p1 is associated price per unit
• Partial derivative is equal to constant b
Elasticity of demand is not constant along a linear demand
curve
 As p1/Q1 increases, demand curve becomes more elastic
 In the limit, as Q1 approaches zero, elasticity of demand
approaches negative infinity, perfectly elastic
 p1 = 0 results in perfectly inelastic elasticity of demand

29
Linear Demand
 A straight-line
(linear) demand curve is
certainly the easiest to draw (Figure 5.8)
 However, such behavior is generally
unrealistic
• Because linear demand curve assumes
(∂Q1/∂p1) = constant
 Implies
that a doubling of prices will have same
effect on Q1 as a 5% increase
30
Figure 5.8 Linear demand curve
31
Proportionate Price Changes


Assuming households respond to proportionate
rather than absolute changes in prices
May be more realistic to consider the demand
function
 Q1 = apb1, a > 0, b > 0 or
 ln Q1 = ln a + b ln p1
• Elasticity of demand is


11 = (∂Q1/∂p1)(p1/Q1) = bap1b-1(p1/Q1) = b or
11 = (∂ ln Q1/∂ ln p1) = b
 Elasticity of this demand curve is constant along its entire
length
 Constant elasticity of demand curve, with b = -1 is illustrated in
Figure 5.9
32
Figure 5.9 Constant unitary
elasticity of demand …
33
Price Elasticity and Total
Revenue

Valuable use of elasticity of demand
 Predict what will happen to households’ total expenditures on a
commodity or to producers’ total revenue when price changes


Total revenue (TR) and total expenditures are defined as
price times quantity (p1Q1)
A change in price has two offsetting effects
 Reduction in price has direct effect
• Reduces total revenue for the commodity
• Results in an increase in quantity sold

Increases total revenue
 Considering these two opposing effects, total revenue from a
commodity price change may rise, fall, or remain the same
• Effect depends on how responsive quantity is to a change in price

Measured by elasticity of demand
34
Price Elasticity and Total
Revenue


Relationship between total revenue and elasticity of demand
may be established by differentiating total revenue (p1Q1)
with respect to p1
Using product rule of differentiation, dividing both sides by
Q1 and multiplying left-hand-side by p1/p1 yields total
revenue elasticity
 TR, p = 1 + 11
• Measures percentage change in total revenue for a percentage change
•
in price
Sign depends on whether 11 is > or < -1



If 11 > -1, demand is inelastic and TR,p > 0
 Price and total revenue move in same direction
If 11 < -1, demand is elastic, and TR,p < 0
 An increase in p1 is associated with a decrease in total revenue
If elasticity of demand is unitary, Q,p = -1, then TR,p = 0
35
Price Elasticity And Total
Revenue

If elasticity of demand is elastic
 Quantity demanded will increase by a larger percentage than price
decreases
• Total revenue will increase with a price decline

Opposite occurs when demand is inelastic
 A price decline results in total revenue declining
• Because quantity demanded increases by a smaller percentage than
price decreases


In elastic portion of demand curve
 Price and total revenue move in opposite directions
In inelastic portion
 Price and TR move in same direction
36
Table 5.2 Response of total
revenue to a price change
37
Figure 5.10 Elasticity of demand
and total revenue …
38
Price Elasticity and the Price
Consumption Curve


Setting p2 as numeraire price, p2 = 1
 Then p1x1 + x2 = I
Solving for total revenue (expenditures) for x1 yields
 p1x1 = I – x2
 On vertical axis in Figure 5.7, at p1 = $45,
• Income I is initially allocated between total expenditures for x2,
x2, and total expenditure on x1, I - x2
 Decreasing p1 from $45 to $30 results in a decline in total
expenditure for x2 and an increase in total expenditure for
x1
• Movement from B to C in indifference space results in a
negatively sloping price consumption curve
39
Price Elasticity and the Price
Consumption Curve



Declining price consumption curve is associated with an
increase in total expenditures on x1
 Indicating elastic demand
Negatively sloping portion of price consumption curve is
associated with elastic portion of demand curve
Positively sloping price consumption curve is associated
with inelastic portion of demand curve
 Decreasing p1 from $30 to $15 results in total expenditures for x2
increasing and total expenditures for x1 declining
 Indicating inelastic demand

If price consumption curve has a zero slope, unitary
elasticity exists
40
Price Elasticity and the Price
Consumption Curve

Slope of price consumption curve is determined by
magnitude of income and substitution effects
 Total effect of a price change is sum of these two effects
 Closeness of substitutes for a commodity directly influences
substitution effect
• The more closely related substitutes are to the commodity, the larger will
be the substitution effect
• A relatively large substitution effect will decrease slope of price
consumption curve

Will make demand curve more elastic
• If a commodity has a close substitute and if price of substitute remains
constant

A rise in price of commodity will divert households’ expenditures away from
product toward substitute
41
Price Elasticity and the Price
Consumption Curve

Other important determinants of slope of price
consumption curve
 Proportion of income allocated for a commodity


• And whether commodity is normal or inferior
The smaller the proportion of income allocated for a
commodity, the larger the slope of price consumption
curve
• The more inelastic the demand
Income effect is relatively small for a commodity
requiring a small fraction of income
 Results in a more inelastic demand
42
Price Elasticity and the Price
Consumption Curve

An inferior commodity will tend to result in a
positively sloping price consumption curve
 Inelastic demand curve
 If inferior nature of a commodity results in a Giffen good,
result is
• Backward-bending price consumption curve
• Positively sloping demand curve

A final major determinant of demand elasticity is
time allowed for adjusting to a price change
 Elasticities of demand tend to become more elastic as
time for adjustment lengthens
• The longer the time interval after a price change, the easier it
may become for households to substitute other commodities
43
Income Elasticity Of Demand


Relationship between change in quantity demanded and
change in income may be represented by the slope of an
Engel curve
Weighting this slope with income divided by quantity results
in income elasticity
 ηQ = (∂Q/∂I)(I/Q)
 Measures percentage change in quantity to a percentage change in
income
• Classified as follows
44
Table 5.3 Estimated income
elasticities
45
Cross-Price Elasticity of Demand



Demand for a commodity such as an automobile will depend
on its own price and income and
 Prices of other related commodities
Measure responsiveness of demand to a price change in a
related commodity by cross-price elasticity
Cross-price elasticity of demand for commodities x1 and x2
 When Q1 is a gross substitute for Q2
• 12 = (∂Q1/∂p2)(p2/Q1) = ∂ ln Q1/∂ ln p2 > 0
 When Q1 is a gross complement for Q2
• 12 = (∂Q1/∂p2)(p2/Q1) = ∂ ln Q1/∂ ln p2 < 0
 Cross-price elasticity can be either positive or negative
• Depending on whether Q1 is a gross substitute or gross complement for
Q2
46
Table 5.4 Estimated cross-price
elasticities of demand …
47
Slutsky Equation in Elasticities

Slutsky equation from Chapter 4

Substitution elasticity
• Indicates how demand for x1 responds to proportional compensated price
changes
48
Slutsky Equation in Elasticities

Slutsky equation in elasticity form
 Where α1 = p1x1/I is proportion of income spent on x1
• Indicates how price elasticity of demand can be disaggregated
into substitution and income components


Relative size of income component depends on proportion of total
expenditures devoted to commodity in question
 Given a normal good, the larger the income elasticity and
proportion of income spent on the commodity, the more elastic
is demand
Income effect will be reinforced by substitution effect
 Larger the substitution effect, the more elastic is demand
49