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Lecture # 03
Demand and Supply (cont.)
Lecturer: Martin Paredes
Definition: The Market Supply function tells us
how the quantity of a good supplied by the sum
of all producers in the market depends on
various factors
Qs = f (p,po,w,…)
2
Definition: The Supply Curve plots the aggregate
quantity of a good that will be offered for sale at
different prices
Qs = Q (p)
3
Example: Supply Curve for Wheat in Canada
Price (dollars per bushel)
Supply curve for wheat
in Canada
0
0.15
Quantity (billions of
bushels per year)
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Definition: The Law of Demand Curve states that
the quantity of a good offered increases when
the price of this good increases.
 Empirical regularity
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The supply curve shifts when factors other
than own price change…
 If the change increases the willingness of
producers to offer the good at the same price,
the supply curve shifts right
 If the change decreases the willingness of
producers to offer the good at the same price,
the supply curve shifts left
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A move along the supply curve for a good
can only be triggered by a change in the
price of that good.
A shift in the supply curve for a good can
be triggered by a change in any other
factor
A change that affects the producers’
willingness to offer the good.
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Example: Canadian Wheat
• QS = p + .05r
• QS = quantity of wheat (billions of bushels)
• p = price of wheat (dollars per bushel)
• r = average rainfall in western Canada (inches)
• Suppose price is $2
• Quantity supplied no rainfall = $2
• Quantity supplied with rainfall of 3” = $2.15
• As rainfall increases, supply curve shifts right
• (e.g., r = 4 => Q = p + 0.2)
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Price ($)
0
Quantity,
Billion bushels
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Price ($)
r=0
Supply with
no rain
0
Quantity,
Billion bushels
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Price ($)
r=0
r=3
Supply with
no rain
Supply with 3” rain
0 .15
Quantity,
Billion bushels
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Definition: A market equilibrium is a price such
that, at this price, the quantities demanded and
supplied are the same.
 Demand and supply curves intersect at
equilibrium.
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Example: Market for Cranberries
• Suppose
• QD = 500 – 4P
• QS = –100 + 2P
• Where
• P = price of cranberries (euros per barrel)
• Q = demand or supply (in millions of barrels/year)
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Example: Market for Cranberries
• The equilibrium price is calculated by equating
demand to supply:
QD = QS
or
500 – 4P = –100 + 2P
• Solving for P:
P* = 100
• To get equilibrium quantity, plug equilibrium price
into either demand or supply
• Into demand:
Q* = 500 – 4(100) = 100
• Into supply:
Q* = –100 + 2(100) = 100
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Example: The Market For Cranberries
Price
Market Supply: QS = -100 + 2P
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Quantity
15
Example: The Market For Cranberries
Price
125
Market Supply: QS = -100 + 2P
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Market Demand: Qd = 50 – 4P
Quantity
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Example: The Market For Cranberries
Price
125
P*=100
Market Supply: QS = -100 + 2P
•
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Market Demand: Qd = 50 – 4P
Q* = 100
Quantity
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Definition: If at a given price, sellers cannot sell as
much as they would like, there is excess supply.
Definition: If at a given price, buyers cannot
purchase as much as they would like, there is
excess demand.
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Example: Excess Supply in the Market For Cranberries
Price
125
Market Supply
50
Market Demand
Quantity
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Example: Excess Supply in the Market For Cranberries
Price
125
Market Supply
50
Market Demand
Qd Q*
QS
Quantity
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Example: Excess Supply in the Market For Cranberries
Price
125
•
Excess Supply
•
Market Supply
50
Market Demand
Qd Q*
QS
Quantity
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 If there is no excess supply or excess demand,
there is no pressure for prices to change and we
are in equilibrium.
 When a change in an exogenous variable causes
the demand curve or the supply curve to shift,
the equilibrium shifts as well
22
Definition: The own price elasticity of demand is
the percentage change in quantity demanded
brought about by a one-percent change in the
price of the good
Q,P= (% Q) = (Q/Q) = dQ . P
(% P) (P/P)
dP Q
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 Elasticity is not the slope
 Slope is the ratio of absolute changes in
quantity and price. (= dQ/dP).
 Elasticity is the ratio of relative (or
percentage) changes in quantity and price.
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1. Q,P = 0
 Perfectly inelastic demand
 Quantity demanded is completely insensitive
to changes in price
2. Q,P  (-1, 0)  Inelastic demand
 Quantity demanded is relatively insensitive
to changes in price
3. Q,P = -1
 Unitary elastic demand
 Percentage increase in quantity demanded
equals percentage decrease in price
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4. Q,P  (-, -1)  Elastic demand
 Quantity demanded is relatively sensitive to
changes in price
5. Q,P = - 
 Perfectly elastic demand
 Any increase in price results in quantity
demanded decreasing to zero
 Any increase in price results in quantity
demanded increasing to infinity.
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Example: Linear Demand Curve
• Suppose QD = a – bP
• a, b : positive constants
• P: price
• Notes:
• -b is the slope
• a/b is the choke price
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Example: Linear Demand Curve
• The elasticity is
Q,P= dQ . P = – b . P
dP Q
Q
• So for linear demand curves
• Slope is constant.
• Elasticity falls from 0 to - along the demand curve.
• E.g., suppose Q = 400 – 10P
• At P = 30, Q = 100, so
Q,P= dQ . P = – b . P = –10 . 30 = –3 (elastic)
dP Q
Q
100
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Example: Elasticity with a Linear Demand Curve
P
0
Q
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Example: Elasticity with a Linear Demand Curve
P
a/b
a/2b
0
•
a/2
a
Q
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Example: Elasticity with a Linear Demand Curve
P
a/b
Q,P = -
Elastic region
a/2b
•
Q,P
= -1
Inelastic region
Q,P = 0
0
a/2
a
Q
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Example: Constant Elasticity Demand Curve
• Suppose QD = Apε
• A: constant
• P: price
• ε : elasticity of demand
• The elasticity is
Q,P= dQ . P = εApε-1 . P = ε
dP Q
Q
• So for Constant Elasticity demand curves
• Elasticity is constant.
• Slope falls from 0 to - along the demand curve.
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Example: A Constant Elasticity
versus a Linear Demand Curve
Price
•
P
0
Q
Observed price and quantity
Quantity
33
Example: A Constant Elasticity
versus a Linear Demand Curve
Price
•
P
Observed price and quantity
Linear demand curve
0
Q
Quantity
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Example: A Constant Elasticity
versus a Linear Demand Curve
Price
•
P
Observed price and quantity
Constant elasticity demand curve
0
Q
Quantity
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Example: A Constant Elasticity
versus a Linear Demand Curve
Price
•
P
Observed price and quantity
Constant elasticity demand curve
Linear demand curve
0
Q
Quantity
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Example: A Constant Elasticity
versus a Linear Demand Curve
Price
•
0
Quantity
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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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Category
Estimated Q,P
Soft Drinks
-3.18
Canned Seafood -1.79
Canned Soup
-1.62
Cookies
-1.6
Breakfast Cereal -0.2
Toilet Paper
-2.42
Laundry
Detergent
Toothpaste
-1.58
Snack Crackers
-0.86
Frozen Entrees
-0.77
Paper Towels
-0.05
Dish Detergent
-0.74
Fabric Softener
-0.73
Price Elasticity of Demand
for Selected Grocery
Products, Chicago, 1990s
-0.45
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Model
Price
Estimated
Q,P
Mazda 323 $5,039
-6.358
Nissan
Sentra
$5,661
-6.528
Ford
Escort
$5,663
-6.031
Lexus
LS400
$27,544
-3.085
BMW 735i
$37,490
-3.515
Source: Berry, Levinsohn and
Pakes, "Automobile Price in
Market Equilibrium,"
Econometrica 63 (July 1995),
841-890.
Example: Price Elasticities of Demand for Automobile Makes, 1990.
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 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. 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.
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