Microeconomics:%20Theory%20and%20Applications%20%20David%20Besanko%20and%20Ronald%20Braeutigam%20%20Chapter%202:%20%20Demand%20and%20Supply%20Analysis%20%20Prepared%20by%20Katharine%20Rockett

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Lecture 04a Demand and Supply
(end) Lecturer Martin Paredes
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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. 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
• Factors that determined elasticity
• Estimating demand and supply
• From own price elasticity and equilibrium price
  and quantity
• From information on past shifts, assuming that
  only a single curve shifts at a time.