Download Market Demand and Elasticity

AAEC 3315
Agricultural Price Theory
Chapter 3
Market Demand and Elasticity
Market Demand

To Gain an Understanding of:


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
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Derivation of Market Demand
Demand Functions
Own Price Elasticity of Demand
Cross Price Elasticity of Demand
Income Elasticity of Demand
Market Demand



Earlier, we derived the demand
curve for an individual
consumer that will maximize
their utility based upon their
preferences and budget
constraint.
Remember that we derived an
individual consumer’s demand
curve from his/her Price
Consumption curve (PCC).
The Demand Curve represents
quantity demanded at various
price levels.
P
P1
P2
Individual Demand
Curve
Q1
Q2
Q
Market Demand Curve

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D1 is the demand curve
for consumer 1.
For every single
consumer there will be a
separate demand curve.
If we have two
consumers in the
market, then we will
have two individual
demand curves, D1 and
D2.
P
P1
P2
D2
D1
Q1
Q2
Q
Market Demand

Given the two demand curves
D1 and D2



Note that
at price=$2,
Consumer 1 buys 10 units
Consumer 2 buys 20 units
Thus the market demand at
P=$2 is 30 units
At price=$1,
Consumer 1 buys 22 units
Consumer 2 buys 30 units.
Thus the market demand is
52 units.
Thus, the aggregate or market
demand is obtained by the
horizontal summation of all
individual consumer’s demand
curves.
P
Market Demand
$2
$1
D2
D1
10
20 22
30
52 Q
Market Demand


Market Demand - a
schedule showing the
amounts of a good
consumers are willing
and able to purchase in
the market at different
price levels during a
specified period of time.
Change in its own price
results in a movement
along the demand curve.
P
P1
P2
Market Demand
Q1
Q2
Q
Factors that Shift the Demand Curve
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Population
Tastes
Income

Normal good

Inferior good
Price of Related Goods

Substitutes - increase in the price of
a substitute, the demand curve for
the related good shifts outward (&
vice versa)

Complements - increase in the price
of a complement, the demand curve
for the related good shifts inward
(& vice versa)
Expectations

Expectations about future prices,
product availability, and income
can affect demand.
P
D1
D2
D
Q
Functional Relationship for Demand

Market Demand FunctionQd = f (P, T, I, R, N)
Where,
P = Own Price
T = Tastes of consumers
I = Consumer Income
R = Price of related goods
N = # of consumers in the market place
P
P1
P2

An example demand function for beer;
Qb = 100 – 30 Pb – 20 Pc + .005I
Where,
Qb = Quantity demanded of beer in
billion 6-packs
Pb = Price of beer per 6-pack
Pc = Price of a pack of chips
I = Annual household income
Market Demand
Q1
Q2
Q
Working with a Demand Function

Suppose the demand function for beer is given by:
Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity
demanded of beer in billion 6-packs, Pb = Price of beer per 6pack, Pc = Price of a pack of chips, and I = Annual household
income.

If the price of a 6-pack of beer is $5, price of a bag of chips
is $1, and the annual household income is $25,000 per year,
what would be the total quantity of beer that will be sold per
year?
Qb = 100 – 30*(5) – 20*(1) + .005*(25000)
Qb = 100 – 150 – 20 + 125
Qb = 55 billion 6-packs.
Responsiveness of the Quantity
Demanded to a Price Change


Earlier, we indicated that, ceteris paribus, the
quantity of a product demanded will vary inversely
to the price of that product. That is, the direction
of change in quantity demanded following a price
change is clear.
What is not known is the extent by which quantity
demanded will respond to a price change.

To measure the responsiveness of the quantity
demanded to change in price, we use a measure called
PRICE ELASTICITY OF DEMAND.
Own Price Elasticity of Demand (ED)

Own Price Elasticity of demand is defined as the
percentage change in the quantity demanded
relative to a percentage change in its own price.

Calculating Own Price Elasticity of Demand from a Demand
Function:

Using calculus: Ed 
Q P

P Q
Own Price Elasticity of Demand (ED)



Given a demand function:
Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity
demanded of beer in billion 6-packs, Pb = Price of beer
per 6-pack ($5), Pc = Price of a pack of chips ($1), and I
= Annual household income ($25,000).
Qb = 100 – 30*(5) – 20*(1) + .005*(25000) = 55
Taking partial derivative of the demand function with
respect to price and substituting values for P and Q we
get:
Ed 
Q P
5

 (30) 
 2.7272
P Q
55
Using Own Elasticity of Demand


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Elasticity is a pure ratio independent of
units.
Since price and quantity demanded
generally move in opposite direction, the
sign of the elasticity coefficient is generally
negative.
Interpretation: If ED = - 2.72: A one percent
increase in price results in a 2.72%
decrease in quantity demanded
Classifications of Own-Price
Elasticity of Demand

Classifications:

Inelastic demand ( |ED| < 1 ): a change in price
brings about a relatively smaller change in
quantity demanded (ex. gasoline).

Unitary elastic demand ( |ED| = 1 ): a change
in price brings about an equivalent change in
quantity demanded.

Elastic demand ( |ED| > 1 ): a change in price
brings about a relatively larger change in
quantity demanded (ex. expensive wine).
Cross Price Elasticity of Demand

Shows the percentage change in the quantity
demanded of good Y in response to a change in
the price of good X.

Calculating Cross Price Elasticity of Demand from a
Demand Function:

Using calculus: Edyx 
Qy Px

Px Qy
Cross Price Elasticity of Demand (Edyx)



Given a demand function:
Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity
demanded of beer in billion 6-packs, Pb = Price of beer
per 6-pack ($5), Pc = Price of a pack of chips ($1), and I
= Annual household income ($25,000).
Qb = 100 – 30*(5) – 20*(1) + .005*(25000) = 55
Taking partial derivative of the demand function for beer
with respect to price of chips and substituting values for
Pc and Q we get:
Edbc 
Qb Pc
1

 (20) 
 0.3636
Pc Qb
55
Classification of
Cross-price elasticity of Demand

Interpretation:


If Edyx = - 0.36: A one percent increase in price of chips results
in a 0.36% decrease in quantity demanded of beer
Classification:
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If (Edyx > 0): implies that as the price of good X increases, the
quantity demanded of Good Y also increases. Thus, Y and X
are substitutes in consumption (ex. chicken and pork).
(Edyx < 0): implies that as the price of good X increases, the
quantity demanded of Good Y decreases. Thus Y & X are
Complements in consumption (ex. bear and chips).
(Edyx = 0): implies that the price of good X has no effect on
quantity demanded of Good Y. Thus, Y & X are Independent
in consumption (ex. bread and coke)
Income Elasticity of Demand (EI)

Shows the percentage change in the quantity
demanded of good Y in response to a percentage
change in Income.

Calculating Income Elasticity of Demand from a Demand
Function:

Using calculus: EI 
Qy
I

I
Qy
Income Elasticity of Demand (EI)



Given a demand function:
Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity
demanded of beer in billion 6-packs, Pb = Price of beer
per 6-pack ($5), Pc = Price of a pack of chips ($1), and I
= Annual household income ($25,000).
Qb = 100 – 30*(5) – 20*(1) + .005*(25000) = 55
Taking partial derivative of the demand function with
respect to income and substituting values for Q and I we
get:
EI 
Qb
I
25000

 (0.005) 
 2.2727
I
Qb
55
Income Elasticity of Demand (EI)

Interpretation:


If EI = 2.27: A one percent increase income results in a
2.27% increase in quantity demanded of beer
Classification:
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If EI > 0, then the good is considered a normal good (ex.
beef).
If EI < 0, then the good is considered an inferior good
(ex. roman noodles)
High income elasticity of demand for luxury goods
Low income elasticity of demand for necessary goods
Market Demand
from the Seller’s Perspective



Consumer demand or consumer expenditure is the
receipt or revenue for the seller.
So, let us look at demand from the other side of the
market, i.e., the seller side of the market.
Total Revenue: From the market demand, we can
easily determine the total revenue of the seller at each
price by multiplying the price per unit by the quantity
sold a that price


TR = P. Q
And let’s say TR = 20 Q – 0.5 Q2
Market Demand
from the Seller’s Perspective

Average Revenue: Average revenue is simply the total
revenue divided by quantity.



AR = P. Q / Q = P
Or, for
TR = 20 Q – 0.5 Q2
AR = 20 – 0.5 Q
Marginal Revenue: Marginal revenue is the amount of
change or addition to the total revenue attributed to the
addition of 1 unit to sales.


MR = ∂TR/∂Q
Or, for
TR = 20 Q – 0.5 Q2
MR = 20 – 1Q
Market Demand
from the Seller’s Perspective

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Given that
AR = 20 – 0.5 Q
MR = 20 – 1Q
Note that both AR and MR
have the same y-intercept.
Also note that the MR has a
slope twice as that of the
slope of the AR.
Graphically, this means that
both the AR and MR curves
have the same price-axis
intercept and the MR curve is
twice as steep as the AR or
the demand curve.
P
AR or
Market Demand
MR
Q
Relationships Among AR, MR, and TR
$/unit
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AR = Demand
MR curve is twice as steep as
the AR Curve
MR is the slope of the TR
Curve
As long as MR is + ve, TR is
increasing with output
When MR = 0, TR is at its
maximum
When MR is – ve, TR
declines
When AR = 0, TR = 0
AR or
Market Demand
MR
Q
$
TR
Q
Relationships Among Price, MR, and
Elasticity of Demand
 (TR )
 ( P.Q )

Q
Q
Q
P
MR  P
 Q
Q
Q
P
MR  P  Q
Q
MR 



Q
P 
MR  P 1 
.
 P 1 

P
Q 





1 
MR  P 1 
 




1

Q
P 
.
P
Q 

Note that the price elasticity of demand is always negative; thus in using this
relationship, the elasticity coefficient must always be entered as a negative
number.
Relationships Among Price Elasticity of
Demand, MR and TR
$/unit
Remember that :

1
MR  P 1 



Elastic
Unitarily Elastic
Inelastic
When η is elastic MR is positive
 When η is unitary MR = 0
 When η is inelastic MR is negative
Now Let us look at TR
MR > 0

η
MR
TR when P
TR when P
Elastic
Positive
Increases
Decreases
Unitary
Zero
Constant
Constant
Inelastic
Negative
Decreases
Increases
AR or
Market Demand
Q
MR < 0
MR = 0
$
TR
Q