Lecture # 04a
Demand and Supply (end)
Lecturer: Martin Paredes
 In general, for the elasticity of “Y” with respect
to “X”:
Y,X= (% Y) = (Y/Y) =
(% X) (X/X)
dY . 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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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
0.001
0.093
0.000
-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
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Elasticity
Coke
Pepsi
Price
-1.47
-1.55
elasticity of
demand
Cross-price 0.52
0.64
elasticity of
demand
Income
0.58
1.38
elasticity of
demand
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
• Suppose P = 0.7
Q = 70
• Notice that, if  = -bP/Q
• Then
• …and
Q,P = -0.55
 b = -Q/P
b = -(-0.55)(70)/(0.7) = 55
a = QD + bP = (70)+(55)(0.7) = 108.5
• Hence QD = 108.5 – 55P
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Example: Constant Elasticity Demand Curve
• Suppose demand is: QD = APε
• Suppose again
P = 0.7
• Notice that, if QD = APε
• Then
Q = 70
Q,P = -0.55
 A = QP-ε
A = (70)(0.7)0.55 = 57.53
• Hence QD = 57.53P-0.55
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Example: Broilers in the U.S., 1990
Price
•
.7
0
70
Observed price and quantity
Quantity
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Example: Broilers in the U.S., 1990
Price
•
.7
Observed price and quantity
Linear demand curve
0
70
Quantity
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Example: Broilers in the U.S., 1990
Price
•
.7
Observed price and quantity
Constant elasticity demand curve
0
70
Quantity
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Example: Broilers in the U.S., 1990
Price
•
.7
Observed price and quantity
Constant elasticity demand curve
Linear demand curve
0
70
Quantity
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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:
• New equilibrium point:
(P1,Q1)
(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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Example: Identifying demand by a shift in supply
Price
Supply
Market Demand
0
Quantity
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Example: Identifying demand by a shift in supply
Price
New Supply
Old Supply
Market Demand
0
Quantity
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Example: Identifying demand by a shift in supply
Price
New Supply
Old Supply
•
P2
P1
•
Market Demand
0
Q2 Q1
Quantity
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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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Price
Supply
Demand
0
Quantity
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Price
New Supply
Old Supply
Old Demand
New Demand
0
Quantity
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Price
New Supply
•
•
P2
P1
Old Supply
Old Demand
New Demand
0
Q 2 = Q1
Quantity
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1. Example of a simple micro model of supply and demand
(two equations and an equilibrium condition)
2. Elasticity as a way of characterizing demand and supply
3. Factors that determined elasticity
4. Estimating demand and supply
a. From own price elasticity and equilibrium price and
quantity
b. From information on past shifts, assuming that only a
single curve shifts at a time.
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