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Lecture 5 Elasticity

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Lecture 5Elasticity

Required Text:

Frank and Bernanke – Chapter 4

- 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

- 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.

- Note that , at price=$2,
- 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 - 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

- 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

- 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 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:
- 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

- Inelastic demand ( |Ed| < 1 ): a change in price brings about a relatively smaller change in quantity demanded (ex. gasoline).

- 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

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

- 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 demandedPrice of XEdyx

60 $10

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

- 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)

- 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 IncomeEI

100 $1200

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

- 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 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.