Lecture 5 Elasticity

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# Lecture 5 Elasticity - PowerPoint PPT Presentation

Lecture 5 Elasticity. Required Text: Frank and Bernanke – Chapter 4. Market Demand Curve. For every single consumer there is a separate demand curve. If we have two consumers in the market, then we will have two individual demand curves, D1 and D2. P. P 1. P 2. D2. D1. Q 1. Q 2. Q.

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### Lecture 5Elasticity

Required Text:

Frank and Bernanke – Chapter 4

Market Demand Curve
• For every single consumer there is a separate demand curve.
• If we have two consumers in the market, then we will have two individual demand curves, D1 and D2.

P

P1

P2

D2

D1

Q1

Q2

Q

Market Demand
• Given the two demand curves D1 and D2
• Note that , at price=\$2,

Consumer 1 buys 10 units

Consumer 2 buys 20 units

Thus the market demand at P=\$2 is 30 units

• At price=\$1,

Consumer 1 buys 22 units

Consumer 2 buys 30 units.

Thus the market demand is 52 units.

• Thus, the aggregate or market demand is obtained by the horizontal summation of all individual consumer’s demand curves.

P

Market Demand

\$2

\$1

D2

D1

10

22

20

30

Q

52

Market Demand
• Market Demand - a schedule showing the amounts of a good consumers are willing and able to purchase in the market at different price levels during a specified period of time.
• Change in its own price results in a movement along the demand curve.

P

P1

P2

Market Demand

Q1

Q2

Q

Factors that Shift the Market Demand Curve
• Population
• Tastes
• Income
• Normal good
• Inferior good
• Price of Related Goods
• Substitutes - increase in the price of a substitute, the demand curve for the related good shifts outward (& vice versa)
• Complements - increase in the price of a complement, the demand curve for the related good shifts inward (& vice versa)
• Expectations
• Expectations about future prices, product availability, and income can affect demand.

P

D1

D

D2

Q

Responsiveness of the Quantity Demanded to a Price Change
• Earlier, we indicated that, ceteris paribus, the quantity of a product demanded will vary inversely to the price of that product. That is, the direction of change in quantity demanded following a price change is clear.
• What is not known is the extent by which quantity demanded will respond to a price change.
• To measure the responsiveness of the quantity demanded to change in price, we use a measure called PRICE ELASTICITY OF DEMAND.
Price Elasticity of Demand (ED)
• Price Elasticity of demand for a good is defined as the percentage change in the quantity demanded relative to a percentage change in the good’s own price.

Algebraically:

Classifications of Own-Price Elasticity of Demand
• Classifications:
• Inelastic demand ( |Ed| < 1 ): a change in price brings about a relatively smaller change in quantity demanded (ex. gasoline).
• Total Revenue = P×Q rises as a result of a price increase
• Unitary elastic demand ( |Ed| = 1 ): a change in price brings about an equivalent change in quantity demanded.
• TR= P×Q remains the same as a result of a price increase
• Elastic demand ( |Ed| > 1 ): a change in price brings about a relatively larger change in quantity demanded (ex. expensive wine).
• TR = P×Q falls as a result of a price increase
Using Price Elasticity of Demand
• Elasticity is a pure ratio independent of units.
• Since price and quantity demanded generally move in opposite direction, the sign of the elasticity coefficient is generally negative.
• Interpretation: If Ed = - 2.72: A one percent increase in price results in a 2.72% decrease in quantity demanded
Price Elasticity along Linear Demand Curves

P

• Linear Demand Curve:

Q = a – bP

• Price elasticity of this demand

Ed = (∂Q/ ∂P)(P/Q) = − b(P/Q)

• Any downward sloping demand curve has a corresponding inverse demand curve.
• Inverse linear Demand Curve: P = a/b – (1/b)Q

a/b

M

a/2b

Q

0

a/2

a

• At P= a/b, Ed = − ∞;atP = 0, Ed = 0; at P= a/2b, Ed = −1
• In the region of the demand curve to the left of the mid-point M, demand is elastic, that is − ∞ ≤ Ed < – 1
• In the region to the right of the mid-point M, demand is inelastic, – 1 < Ed ≤ 0
Cross Price Elasticity of Demand
• Shows the percentage change in the quantity demanded of good Y in response to a change in the price of good X.
• Edyx = % Change in Qdy / % change in Px
• Algebraically:

Read as the cross-price elasticity of demand for commodity

Y with respect to commodity X.

Units of Y demanded Price of X Edyx

60 \$10

40 \$12 (-20/2)x(10/60) = - 1.66

Classification of Cross-price elasticity of Demand
• Interpretation:
• If Edyx= - 0.36: A one percent increase in price of chips results in a 0.36% decrease in quantity demanded of beer
• Classification:
• If (Edyx > 0): implies that as the price of good X increases, the quantity demanded of Good Y also increases. Thus, Y and X are substitutes in consumption (ex. chicken and pork).
• If (Edyx < 0): implies that as the price of good X increases, the quantity demanded of Good Y decreases. Thus Y & X are complements in consumption (ex. bear and chips).
• If (Edyx = 0): implies that the price of good X has no effect on quantity demanded of Good Y. Thus, Y & X are Independent in consumption (ex. bread and coke)
Income Elasticity of Demand (EI)
• Shows the percentage change in the quantity demanded of good Y in response to a percentage change in Income.
• EI = % Change in QY / % change in I
• Algebraically:

Units of Y demanded Income EI

100 \$1200

150 \$1600 (50/400)x(1200/100) = 1.5

Income Elasticity of Demand (EI)
• Interpretation:
• If EI= 2.27: A one percent increase income results in a 2.27% increase in quantity demanded of beer
• Classification:
• If EI> 0, then the good is considered a normal good (ex. beef).
• If EI< 0, then the good is considered an inferior good (ex. ramen noodles)
• High income elasticity of demand for luxury goods
• Low income elasticity of demand for necessary goods
Price Elasticity of Supply (ED)
• Price Elasticity of supply of a good is defined as the percentage change in the quantity supplied relative to a percentage change in the good’s own price.

Algebraically:

• Perfectly inelastic supple – A vertical supply curve
• Perfectly elastic supply – a horizontal supply curve.