Lecture # 04aLecture # 04a

Demand and Supply (end)Demand and Supply (end)

Lecturer: Martin ParedesLecturer: Martin Paredes

2

In general, for the elasticity of “Y” with respect to “X”:

Y,X= (% Y) = (Y/Y) = dY . X (% X) (X/X) dX Y

3

Price elasticity of supply: measures curvature of supply curve

(% QS) = (QS/QS) = dQS . P (% P) (P/P) dP QS

4

Income elasticity of demand measures degree of shift of demand curve as income changes…

(% QD) = (QD/QD) = dQD . I (% I) (I/I) dI QD

5

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

6

Sentra Escort LS400 735i

Sentra -6.528 0.454 0.000 0.000

Escort 0.078 -6.031 0.001 0.000

LS400 0.000 0.001 -3.085 0.032

735i 0.000 0.001 0.093 -3.515

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

7

Elasticity Coke Pepsi

Priceelasticity ofdemand

-1.47 -1.55

Cross-priceelasticity ofdemand

0.52 0.64

Incomeelasticity ofdemand

0.58 1.38

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

8

1. Use Own Price Elasticities and Equilibrium Price and Quantity

2. Use Information on Past Shifts of Demand and Supply

9

1. Choose a general shape for functions Linear Constant elasticity

2. Estimate parameters of demand and supply using elasticity and equilibrium information We need information on ε, P* and Q*

10

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

11

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

12

Quantity

Price

0 70

.7 • Observed price and quantity

Example: Broilers in the U.S., 1990

13

Quantity

Price

0 70

.7 • Observed price and quantity

Linear demand curve

Example: Broilers in the U.S., 1990

14

Quantity

Price

0 70

.7 • Observed price and quantity

Constant elasticity demand curve

Example: Broilers in the U.S., 1990

15

Quantity

Price

0 70

.7 • Observed price and quantity

Constant elasticity demand curve

Linear demand curve

Example: Broilers in the U.S., 1990

16

1. A shift in the supply curve reveals the slope of the demand curve

2. A shift in the demand curve reveals the slope of the supply curve.

17

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

18

Quantity

Price

0

Market Demand

Supply

Example: Identifying demand by a shift in supply

19

Quantity

Price

0

Market Demand

New Supply

Old Supply

Example: Identifying demand by a shift in supply

20

Quantity

Price

0

Market Demand

New Supply

Q2

••

Q1

Old Supply

P2

P1

Example: Identifying demand by a shift in supply

21

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

22Quantity

Price

0

Demand

Supply

23Quantity

Price

0

Old Demand

New Supply

Old Supply

New Demand

24Quantity

Price

0

Old Demand

New Supply

Q2 =

••

Q1

Old SupplyP2

P1

New Demand

25

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

3. Factors that determined elasticity

4. Estimating demand and supply a. From own price elasticity and equilibrium price

and quantityb. From information on past shifts, assuming that

only a single curve shifts at a time.