Demand and Supply cont 2
Lecturer: Assoc Prof Akalpler

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 Factors that determine price elasticity of
demand
 Demand tends to be more price-elastic when
there are good substitutes for the good
 Demand tends to be more price-elastic when
consumer expenditure in that good is large
 Demand tends to be less price-elastic when
consumers consider the good as a necessity.

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 In general, for the elasticity of “Y” with respect
to “X”:
Y,X= (% Y) = (Y/Y) = dY . X
(% X) (X/X) dX Y

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 Price elasticity of supply: measures curvature
of supply curve
(% QS) = (QS/QS) = dQS . P
(% P) (P/P) dP QS

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 Income elasticity of demand measures degree
of shift of demand curve as income changes…
(% QD) = (QD/QD) = dQD . I
(% I) (I/I) dI QD

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 Cross price elasticity of demand measures
degree of shift of demand curve when the price
of another good changes
(% QD) = (QD/QD) = dQD . P0
(% P0) (P0/P0) dP0 QD

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Cross elasticity of demand
Cross elasticity of demand (XED) measures the percentage change in
quantity demand for a good after the change in price of another.
XED = % change in Q.D. good A
% change in P good B
Cross elasticity of demand for Coffee / Tea
For example: if there is an increase in the price of tea by 10%. and Q.D
of coffee increases by 2%, then XED = +0.2

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Substitute goods
For goods which are substitutes, we expect to see a positive cross elasticity of
demand. If the price of Asda bread increases, people will buy more of an
alternative, such as Mother’s Pride bread.
 Weak substitutes like tea and coffee will have a low cross elasticity of
demand
 Alternative brands of chocolate, e.g. Mars vs Cadbury quite similar, so will
have a higher cross elasticity of demand.

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Complements goods
These are goods which are used together, therefore the cross
elasticity of demand is negative. If the price of one goes up, you will
buy less of both goods.
 For example, if the price of DVD players goes down, you will buy
more DVD players and also there will be a increase in demand for
DVD disks.
 If the price of Samsung mobile phones goes down, we will also buy
more Samsung related phone apps.

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o Complementary goods have a negative cross-price
elasticity: as the price of one good increases, the
demand for the second good decreases.
o Substitute goods have a positive cross-price
elasticity: as the price of one good increases, the
demand for the other good increases.
o Independent goods have a cross-price elasticity of
zero: as the price of one good increases, the
demand for the second good is unchanged.

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substitute
A good with a positive cross elasticity of demand,
meaning the good's demand is increased when
the price of another is increased.
 Complement
A good with a negative cross elasticity of
demand, meaning the good's demand is
increased when the price of another good is
decreased.

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COEFFICIENT ELASTICITY
The coefficient of elasticity is defined as the percentage change in quantity
demanded divided by the percentage change in price.
DQ/Qt-1
DP/Pt-1
The first step is to find percentage changes. The percentage change in any variable
X is
usually defined as
Xnew - Xold
coefficient of elasticity = -----------
Xold
where Xnew is the NEW value of X and Xold is the OLD value of X.

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For example, if price increased from 10 dollars to 12 dollars, the
percentage change, as usually defined, would be:
(12 - 10) / 10 = 2/10 = 20 percent.
If at the same time the quantity demanded fell from 30 to 20 items, the
percentage change in quantity demanded -- again using the usual definition of
percentage -- would be
(20 - 30) / 30 = - 10/30 or - 33 percent.
If we used the usual percentage change formula in our calculation of elasticity,
we would arrive at a coefficient of elasticity of:
-33/20 = - 1.67

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MIDPOINT
The midpoint formula makes only one change to the calculation of percentages:
rather than dividing by the old value of X, it divides by the average value.
That we define the midpoint percentage change as
Xnew - Xold
-----------
Xaverage
Where X average is the sum of the old and new values divided by 2.

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Implementing this is straightforward. In our previous example:
The percentage change in price, calculated by the midpoint formula would be
(12 - 10) / 11 = 2/11 = 18.2 percent
since the average price is 11.
The percentage change in quantity, calculated bye the midpoint formula would
be
(20 - 30) / 25 = -10/25 = -40 percent
since the average quantity is 25.
And the coefficient of elasticity, calculated by the midpoint formula is
-40/18.2 = -2.2

COBWEB THEOREM
THE CLASSIC PAPER ON THE COBWEB THEOREM WAS
PUBLISHED BY EZEKIEL' IN 1938
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THE COBWEB THEORY WAS NAMED BY HUNGARIAN-BORN
ECONOMIST NICHOLAS KALDOR (1908-
1986).
• The Cobweb theory stems from a simple dynamic model of cyclical
demand, which involves time lag (between the response of production and
change in price (most often seen in agricultural sector)
• it is assumed that the demand for a good is a decreasing function of its
current price and
• its supply is an increasing function of last year’s price because of the time
taken to produce, plant and harvest products.
• Especially, this happens in agriculture because the price of agricultural
products has mostly an elastic demand. Not durable and need to be sold in
short period therefore price can be change depends on demand less
demand price reduced more demand price increase
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IF ANY CHANGES IN THE CONDITIONS OF DEMAND AND/ OR
SUPPLY OCCUR, THEN THIS WILL LEAD TO CHANGES IN THE
EQUILIBRIUM VALUES OF PRICE AND QUANTITY.
if difference in price changes between first year product prices
(P0P1) and second year product prices (P0P2) is increasingly
decreased, then output and price tend to approach to the equilibrium
position. This has also meant that the slope of the demand curve is
smaller than the slope of the supply curve (Fig1.1).
P2 P1 P0 P1
Slope of demand curve = -------- < ------ = Slope of supply curve
Q1 Q2 Q1 Q2
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COBWEB THEOREM
In the opposite case, if the supply curve is more elastic than
the demand curve (absolute slope of supply curve is less than
demand curve), then output and price tend to move further away
from the equilibrium position.
Therefore, the slope of the demand curve is expected to be greater
than the slope of the supply curve, which means that price and
output tend to move further from the equilibrium position (Fig1.2).
P2 P1 P0 P1
Slope of demand curve = -------- < ------ = Slope of supply curve
Q1 Q2 Q1 Q2
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COBWEB MODEL
Thecase where supplyand price have the same slope is shown inFigure 1.3.
P p p
P0 P1
P2 P0 p
P1 P2
Q2 Q1 Q 0 Q1 Q2 Q 0 Q1 Q2 Q
Figure1.1:Demandispriceelastic Figure1.2:Supplyisprice elastic Figure1.3:Both havethesameelasticity
(A Stable Cobweb) (An UnstableCobweb)
Source: SextonRobert:Microeconomics, 1995,p.282 (reproducedbythe permission of author andpublisher)
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Sentra Escort LS400 735i
Sentra -6.528 0.454 0.000 0.000
Escort 0.078 -6.031 0.001 0.000
LS400 0.000 0.001 -3.085 0.032
735i 0.000 0.001 0.093 -3.515
Source: Berry, Levinsohn and Pakes, “Automobile Price in Market
Equilibrium," Econometrica 63 (July 1995), 841-890.
Example: The Cross-Price Elasticity of Demand for Cars
(Above -1 is elastic below -1 is inelastic)

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Elasticity Coke Pepsi
Price
elasticity of
demand
-1.47 -1.55
Cross-price
elasticity of
demand
0.52 0.64
Income
elasticity of
demand
0.58 1.38
Source: Gasmi, Laffont and Vuong, "Econometric
Analysis of Collusive Behavior in a Soft Drink Market,"
Journal of Economics and Management Strategy 1
(Summer, 1992) 278-311.
Example: Elasticities of Demand for Coke and Pepsi

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1. Use Own Price Elasticities and Equilibrium
Price and Quantity
2. Use Information on Past Shifts of Demand and
Supply

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1. Choose a general shape for functions
 Linear
 Constant elasticity
2. Estimate parameters of demand and supply
using elasticity and equilibrium information
 We need information on ε, P* and Q*

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Example: Linear Demand Curve
• Suppose demand is linear: QD = a – bP
• Then, elasticity is Q,P = -bP/Q where b = dq /dp
• ǫ = (p /q) .(dq /dp)
• Suppose P = 0.7 Q = 70 Q,P = -0.55
• finding a and b
• Notice that, if  = -bP/Q  b = -Q/P
• Then b = -(-0.55)(70)/(0.7) = 55
• …and a = QD + bP = (70)+(55)(0.7) = 108.5
• Hence QD = 108.5 – 55P

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Example: Constant Elasticity Demand Curve for finding
coefficient
• Suppose demand is: QD = APε
• Suppose again P = 0.7 Q = 70 Q,P = -0.55
• Finding deman equation
• Notice that, if QD = APε then  A = QP-ε
• Then A = (70)(0.7)0.55 = 57.53
• Hence QD = 57.53P-0.55

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Quantity
Price
0 70
.7 •
Observed price and quantity
Example: Broilers in the U.S., 1990

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Quantity
Price
0 70
.7 •
Observed price and quantity
Linear demand curve
Example: Broilers in the U.S., 1990

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Quantity
Price
0 70
.7 •
Observed price and quantity
Constant elasticity demand curve
Example: Broilers in the U.S., 1990

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Quantity
Price
0 70
.7 •
Observed price and quantity
Constant elasticity demand curve
Linear demand curve
Example: Broilers in the U.S., 1990

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1. A shift in the supply curve reveals the slope of
the demand curve
2. A shift in the demand curve reveals the slope of
the supply curve.

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Example: Shift in Supply Curve
• Old equilibrium point: (P1,Q1)
• New equilibrium point: (P2,Q2)
• Both equilibrium points would lie on the same (linear)
demand curve.
• Therefore, if QD = a - bP
• b = dQ/dp = (Q2 – Q1)/(P2 – P1)
• a = Q1 - bP1

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Quantity
Price
0
Market Demand
Supply
Example: Identifying demand by a shift in supply

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Quantity
Price
0
Market Demand
New Supply
Old Supply
Example: Identifying demand by a shift in supply

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Quantity
Price
0
Market Demand
New Supply
Q2
•
•
Q1
Old Supply
P2
P1
Example: Identifying demand by a shift in supply

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This technique only works if the curve we want to estimate
stays constant.
Example: Shift in Supply Curve
• We require that the demand curve does not shift

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Quantity
Price
0
Demand
Supply

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Quantity
Price
0
Old Demand
New Supply
Old Supply
New Demand

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Quantity
Price
0
Old Demand
New Supply
Q2 =
•
•
Q1
Old Supply
P2
P1
New Demand

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1. First example of a simple microeconomic
model of supply and demand (two equations and an
equilibrium condition)
2. Elasticity as a way of characterizing demand and
supply
3. Elasticity changes as market definition
changes (commodity, geography, time)

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4. Elasticity a very general concept
5. Back of the envelope calculations:
Estimating demand and supply from own price
elasticity and equilibrium price and quantity
Estimating demand and supply from information on
past shifts, assuming that only a single curve shifts
at a time.