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 e, 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 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

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.