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Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes. Other Elasticities. In general, for the elasticity of “Y” with respect to “X”:  Y,X = ( % Y) = ( Y /Y) = d Y . X ( % X ) ( X /X) d X Y. Other Elasticities.

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Lecture # 04a

Demand and Supply (end)

Lecturer: Martin Paredes

slide2

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
slide3

Other Elasticities

  • Price elasticity of supply: measures curvature of supply curve
  • (% QS) = (QS/QS) = dQS . P
  • (% P) (P/P) dP QS
slide4

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 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 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 = APε
  • Suppose again P = 0.7 Q = 70 Q,P = -0.55
  • Notice that, if QD = APε A = QP-ε
  • 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

slide20

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

slide24

Price

New Supply

Old Supply

P2

P1

Old Demand

New Demand

0

Q2 =

Q1

Quantity

slide25

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.
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