Microeconomics: Theory and Applications David Besanko and Ronald Braeutigam Chapter 2: Demand and Supply Analysis Prepared by Katharine Rockett

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Lecture 03 Demand and Supply
(cont.) Lecturer Martin Paredes
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Market Supply Function

• 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,)

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Supply Curve

• Definition The Supply Curve plots the aggregate
  quantity of a good that will be offered for sale
  at different prices
• Qs Q (p)

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Example Supply Curve for Wheat in Canada

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The Law of Supply

• 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 Law of Supply

• 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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The Law of Supply

• 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 gt 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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Market Equilibrium

• 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
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Example The Market For Cranberries
Price
Price
125
Market Supply QS -100 2P
50
Market Demand Qd 50 4P
Quantity
Quantity
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Example The Market For Cranberries
Price
125
Market Supply QS -100 2P

P100
50
Market Demand Qd 50 4P
Q 100
Quantity
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Market Equilibrium
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
Q
QS
Qd
Quantity
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Example Excess Supply in the Market For
Cranberries
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Market Equilibrium

• 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

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Elasticity

• 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

• 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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Elasticity Classification

• ?Q,P 0 ? Perfectly inelastic demand
• Quantity demanded is completely insensitive to
  changes in price
• ?Q,P ? (-1, 0) ? Inelastic demand
• Quantity demanded is relatively insensitive to
  changes in price
• ?Q,P -1 ? Unitary elastic demand
• Percentage increase in quantity demanded equals
  percentage decrease in price

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Elasticity Classification

• 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
Q
0
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Example Elasticity with a Linear Demand Curve
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Example Elasticity with a Linear Demand Curve
P
?Q,P -?
a/b
Elastic region

?Q,P -1
a/2b
Inelastic region
?Q,P 0
Q
a
0
a/2
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• Example Constant Elasticity Demand Curve
• Suppose QD Ape
• A constant
• P price
• e elasticity of demand
• The elasticity is
• ?Q,P dQ . P eApe-1 . P e
• 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

Observed price and quantity
P
0
Q
Quantity
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Example A Constant Elasticity versus a Linear
Demand Curve
Price

Observed price and quantity
P
Linear demand curve
0
Q
Quantity
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Example A Constant Elasticity versus a Linear
Demand Curve
Price

Observed price and quantity
P
Constant elasticity demand curve
0
Q
Quantity
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Example A Constant Elasticity versus a Linear
Demand Curve
Price

Observed price and quantity
P
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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Elasticity

• 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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Price Elasticity of Demand for Selected Grocery
Products, Chicago, 1990s
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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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Other Elasticities

• 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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Other Elasticities

• Price elasticity of supply measures curvature of
  supply curve
• (? QS) (?QS/QS) dQS . P
• (? P) (?P/P) dP QS

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Other Elasticities

• 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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Other Elasticities

• 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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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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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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How to Estimate Demand and Supply Equations

• Use Own Price Elasticities and Equilibrium Price
  and Quantity
• Use Information on Past Shifts of Demand and
  Supply

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Use Own Price Elasticities and Equilibrium Price
and Quantity

• Choose a general shape for functions
• Linear
• Constant elasticity
• Estimate parameters of demand and supply using
  elasticity and equilibrium information
• We need information on e, 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 ?Q,P -0.55
• 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
• Suppose demand is QD APe
• Suppose again P 0.7 Q 70 ?Q,P -0.55
• Notice that, if QD APe ? A QP-e
• Then 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

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

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

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

Observed price and quantity
.7
Constant elasticity demand curve
Linear demand curve
0
70
Quantity
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Use Information on Past Shifts of Demand and
Supply

• A shift in the supply curve reveals the slope of
  the demand curve
• 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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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

Old Supply
P2

P1
Old Demand
New Demand
0
Q2
Q1
Quantity
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Summary
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.