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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



  • Example: Elasticities of Demand for Coke and Pepsi


How to Estimate Demand and Supply Equations Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.

Use Own Price Elasticities and Equilibrium Price and Quantity

Use Information on Past Shifts of Demand and Supply


Use Own Price Elasticities and Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.

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 Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.: 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 Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.: 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: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Broilers in the U.S., 1990

Price

Observed price and quantity

.7

0

70

Quantity


Example: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Broilers in the U.S., 1990

Price

Observed price and quantity

.7

Linear demand curve

0

70

Quantity


Example: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Broilers in the U.S., 1990

Price

Observed price and quantity

.7

Constant elasticity demand curve

0

70

Quantity


Example: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. 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 Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.

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 Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.: 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: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Identifying demand by a shift in supply

Price

Supply

Market Demand

0

Quantity


Example: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Identifying demand by a shift in supply

Price

New Supply

Old Supply

Market Demand

0

Quantity


Example: Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. Identifying demand by a shift in supply

Price

New Supply

Old Supply

P2

P1

Market Demand

0

Q2

Q1

Quantity



Price stays constant.

Supply

Demand

0

Quantity


Price stays constant.

New Supply

Old Supply

Old Demand

New Demand

0

Quantity


Price stays constant.

New Supply

Old Supply

P2

P1

Old Demand

New Demand

0

Q2 =

Q1

Quantity


Summary stays constant.

  • 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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