Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes

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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

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

Other Elasticities

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

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

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

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

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

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

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*

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

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

Example: Broilers in the U.S., 1990

Price

Observed price and quantity

.7

0

70

Quantity

Example: Broilers in the U.S., 1990

Price

Observed price and quantity

.7

Linear demand curve

0

70

Quantity

Example: Broilers in the U.S., 1990

Price

Observed price and quantity

.7

Constant elasticity demand curve

0

70

Quantity

Example: Broilers in the U.S., 1990

Price

Observed price and quantity

.7

Constant elasticity demand curve

Linear demand curve

0

70

Quantity

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.

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

Example: Identifying demand by a shift in supply

Price

Supply

Market Demand

0

Quantity

Example: Identifying demand by a shift in supply

Price

New Supply

Old Supply

Market Demand

0

Quantity

Example: Identifying demand by a shift in supply

Price

New Supply

Old Supply

P2

P1

Market Demand

0

Q2

Q1

Quantity

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

Price

Supply

Demand

0

Quantity

Price

New Supply

Old Supply

Old Demand

New Demand

0

Quantity

Price

New Supply

Old Supply

P2

P1

Old Demand

New Demand

0

Q2 =

Q1

Quantity

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.