CHAPTER 4 Elasticity. The Responsiveness of the Quantity Demanded to Price When price rises,...

CHAPTER 4

Elasticity

The Responsiveness of the Quantity Demanded to Price When price rises, quantity demanded

decreases. The question is how much quantity

will decrease in response to a given price increase.

We want a measure that is units free and can be compared across different commodities.

The Responsiveness of Quantity Demanded to Price

The measure we will study that meets the criteria we want is

the price elasticity of demand.

Price Elasticity of Demand

Price elasticity of demand is a measure of the responsiveness of the quantity demanded of a good to a change in its price (ceteris paribus).

Elastic Demand - means demand is sensitive to price

Inelastic Demand - means demand is insensitive to price

Elasticity: A Units-Free Measure

Price elasticity ofdemand =

Percentage change in quantity demanded

Percentage change in price

Calculating Elasticity

Negative sign is ignored for convenience.

The changes in price and quantity are expressed as percentages of the average price and average quantity between the two prices and quantities being compared.– Avoids having two values for the price

elasticity of demand


P

Q

%

%

Price elasticity of demand =Percentage change in quantity demanded



P

Q

%

%



ave

ave

PP

QQ

/

/


P

Q

%

%



ave

ave

PP

QQ

/

/

(Q2 - Q1)/Qave(P2 - P1)/Pave

=

Calculating the Elasticity of Demand - Example

P1 = 410

P2 = 390

Q1 = 36

Q2 = 44

Calculating the Elasticity of Demand

Quantity (millions of chips per year)

Pri

ce (d

olla

rs p

er c

hip)

36 40 44

390

400

410

Da

Originalpoint (P1, Q1)


Pri

ce (d

olla

rs p

er c

hip)

36 40 44

390

400

410

Da


Newpoint (P2, Q2)



Pri

ce (d

olla

rs p

er c

hip)

36 40 44

390

400

410

Da

= 8Q


Newpoint (P2, Q2)


`P =$20


Pri

ce (d

olla

rs p

er c

hip)

36 40 44

390

400

410

Da


Newpoint (P2, Q2)

Pave = $400

= $20P

= 8Q



Pri

ce (d

olla

rs p

er c

hip)

36 40 44

390

400

410

Da


Newpoint (P1, Q1)

Pave = $400

Qave = 40

= $20P

= 8Q



P

Q

%

%



ave

ave

PP

QQ

/

/


=400/20

40/8


P

Q

%

%



ave

ave

PP

QQ

/

/


=400/20

40/8 = 4

Elasticity Using Different Bases

Use P1 and Q1 as base– E = ((44 – 36)/36)/((390 – 410)/410)– = (8/36)/(-20/410) = .222/.0488 = 4.55

Use P2 and Q2 as base– E = ((44 – 36)/44)/((390 – 410)/390)– = (8/44)/(-20/390) = .182/.051 = 3.57

Note that average of these two elasticities is about 4, which is the elasticity obtained using the average Ps and Qs

P1 = 410, Q1 = 36; P2 = 390, Q2 = 44

Inelastic and Elastic Demand

Five demand curves that cover the entire range of possible elasticities of demand:– Perfectly inelastic (Elasticity=0)– Inelastic (0<Elasticity<1)– Unit elastic (Elasticity=1)– Elastic (1<Elasticity< )– Perfectly elastic (Elasticity= )


6

12

Pri

ce

Quantity

D1

Elasticity = 0

Perfectly Inelastic


Perfectly inelastic demand – Implies that quantity demanded remains

constant when price changes occur. – Price elasticity of demand = 0


6

12

Pri

ce

Quantity

D2

0<Elasticity<1

Inelastic


Inelastic demand – Implies the percentage change in quantity

demanded is less than the percentage change in price.

– Price elasticity of demand > 0 and < 1


6

12

Pri

ce

Quantity

D3

1 2 3

Elasticity = 1

Unit Elasticity


Unit elastic demand– Implies that the percentage change in quantity

demanded equals the percentage change in price.

– Price elasticity of demand = 1


6

12

Pri

ce

Quantity

D4

1<Elasticity< ∞

Elastic


Elastic demand –Implies the percentage change in quantity

demanded is greater than the percentage change in price.

–Price elasticity of demand > 1 and <


6

12

Pri

ce

Quantity

D5

Elasticity =

Perfectly Elastic


Perfectly elastic demand– Implies that if price changes by any percentage

quantity demanded will fall to 0.– Price elasticity of demand =

Examples of Elasticity Calculation

(1)

Q1 = 10, P1 = 50, Q2 = 8, P2 = 60

Elasticity = ((8-10)/9)/(60-50)/55) = (-2/9)/(10/55)=-1.22 Therefore demand over this range is

elastic


(2)

Q1 = 30, P1 = 20, Q2 = 28, P2 = 26

Elasticity = ((28-30)/29)/(26-20)/23) = (-2/29)/(6/23)=-.264 Therefore demand over this range is

inelastic


(3)

Q1 = 55, P1 = 9, Q2 = 45, P2 = 11

Elasticity = ((45-55)/50)/(11-9)/10) = (-10/50)/(2/10)=-1.00 Therefore demand over this range is

unitary elastic

The Factors that Influence the Elasticity of Demand

The closer the substitutes for a good, the more elastic is demand.

The higher the proportion of income spent on a good, the more elastic is demand.

The greater the time elapsed since a price change, the more elastic is demand.

Total Revenue Test

The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue that results from a price change (all other things remaining the same).

Unitary Elastic Demand and Total Revenue

If demand is unitary elastic, an increase in price results in an equal percentage decrease in the quantity demanded and total revenue remains constant.

Elastic Demand andTotal Revenue

If demand is elastic, an increase in price results in a larger percentage decrease in the quantity demanded and total revenue decreases.

Inelastic Demand andTotal Revenue

If demand is inelastic, an increase in price results in a smaller percentage decrease in the quantity demanded and total revenue increases.

Exampleof Total Revenue Test

Elasticity Calculation (1)

Q1 = 10, P1 = 50, Q2 = 8, P2 = 60

Elasticity = ((8-10)/9)/(60-50)/55) = (-2/9)/(10/55)=-1.22 (elastic) TR1 = P1xQ1 = 50x10 = 500

TR2 = P2xQ2 = 60x8 = 480

TR falls as P increases Therefore demand is elastic


Elasticity Calculation (2)

Q1 = 30, P1 = 20, Q2 = 28, P2 = 26

Elasticity = ((28-30)/29)/(26-20)/23) = (-2/29)/(6/23)=-.264 (inelastic) TR1 = P1xQ1 = 20x30 = 600

TR2 = P2xQ2 = 26x28 = 728

TR rises as P increases Therefore demand is inelastic


Elasticity Calculation (3) Q1 = 55, P1 = 9, Q2 = 45, P2 = 11

Elasticity = ((45-55)/50)/(11-9)/10) = (-10/50)/(2/10)=-1.00 (unitary elastic) TR1 = P1xQ1 = 9x55 = 495

TR2 = P2xQ2 = 11x45 = 495

TR doesn’t change as P increases Therefore demand is unitary elastic

Elasticity Along a Straight-Line Demand Curve

Elasticity is not the same as slope, but the two are related.

As the price increases, demand becomes more elastic.

Elasticity will equal 1.0 at the midpoint of any linear demand curve.

Other Commonly UsedElasticities

Income Elasticity of Demand Cross Price Elasticity of Demand Price Elasticity of Supply

CHAPTER 4 Elasticity. The Responsiveness of the Quantity Demanded to Price When price rises,...

Documents

Transcript of CHAPTER 4 Elasticity. The Responsiveness of the Quantity Demanded to Price When price rises,...