AN INTRODUCTION TOMICROECONOMICS

Dr. Mohammed Migdad

Elasticityand Its Applications

CHAPTER 3

Chapter 3 content:Chapter three is about elasticity and its applications. It includes:

Price elasticity of demand, Point and arc elasticity, Types of elasticity, Factors affecting elasticity, Elasticity and total revenue, Income elasticity of demand, Price elasticity of supply, In addition to elasticity and tax.

3.1 Introduction

Elasticity

Is a general concept that can be used to quantify the response in one variable when another variable changes.

3.2 Price Elasticity of Demand

Elasticity =Change in quantity demanded

÷Change in price

Quantity demanded Price

3.2 Price Elasticity of Demand

Ed=Qd

÷p

Qd P

Ed=Qd

*P

Qd P

Ed=Qd

*P

P Qd

Example 1

Consider the market for sales of ice cream cones at a state fair. The table below gives the market quantity demanded with consideration in giving all the sellers the same price. Calculate the price elasticity of demand for the ice-cram.

Ice-Cream Demand Schedule

Price of Ice Cream ($) Quantity Demanded(millions)

0.50 161.00 131.50 102.00 72.50 43.00 1

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You can calculate the market price elasticity of demand using the information contained in the table above. For instance, suppose you decided to calculate the price elasticity of demand at the price $2.00 by examining a price decrease from $2.00 to $1.50 per cone.

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In this case, the demand for ice cream will increase from 7 million cones to 10 million cones. You can use these figures to calculate the price elasticity of demand as follows:

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This implies the following:• The price elasticity of demand for ice-cream

cones at a price of $2.00, according to the demand schedule provided, is -1.72.

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• The sign here illustrates the negative relation between price and quantity demanded and that we deal here with the absolute number. So the value of the elasticity in this case equals 1.75.

• This elasticity means that the % change in quantity is higher than the % change in price, which indicates that the demand here is an elastic demand.

Example 2

You are a cement producer. You wish to plot your firm's demand curve and to find the price elasticity of demand at various points along the demand curve. You decide to calculate elasticity by examining the effects of price declines from $50 to $40, $40 to $30, etc.

To calculate the price elasticity of demand between a price of $50 and $40 on the demand curve, divide the percentage change in quantity demanded by the percentage change in price.

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Cement Demand Schedule

Price($ per ton)

Quantity(thousands of tons)

50 500

40 600

30 700

20 800

10 900

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• Similarly, you can find the elasticity between prices of $40 and $30, $30 and $20, and $20 and $10.

• To illustrate, here is what you will find when you calculate elasticity between $40 and $30:

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This is the equation of elasticity between $30 and $20:

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This is the equation for elasticity between $20 and $10

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Notice that demand becomes increasingly less as prices fall. Intuitively, this makes sense; consumers can be expected to react much more dramatically to a change in price when prices are high than they are low.

3.3 Arc Elasticity

Arc Elasticity

Supposing we want to measure the elasticity between point A and point B appearing on the same curve in figure (3.1), we assume that:

• P1 = 4, Qd1 = 12 • P2 = 5, Qd2 = 9

If we intend to calculate the elasticity between the two points, A and B, starting from point B and using the elasticity formula as illustrated above, this is what we get:

Ed = Qd X PP Q

Ed = 9-12 X 45-4 12

Ed =-3

X4 = -

1+1 12

If we intend to calculate the elasticity between the two points, A and B, starting from point A and using the elasticity formula as illustrated above, this is what we get:

Ed = 12-9 X 54-6 9

Ed =+3

X5

= -1.7-1 9

We notice some differences in the results because the starting points were different. To avoid this difference in calculating the Arc Elasticity, calculating from the middle point between both points, A and B, could be the best way. This is known as the Midpoint Law which gives an average result.

Price elasticity of demand=

Change in QuantityX

Price 1+ price 2

Change in price Quantity 1+ Quantity 2

Ed =Qd1 – Qd2

Xp1 + p2

P1 – p2 Qd1+ Qd2

Ed =12 – 9

X4 + 5

4 – 5 12 + 9

Ed = 3 x 9 = - 9 = - 1.3-3 21 7

3.4 Point Elasticity and Types of Demand Elasticity

Point Elasticity >>> ….

3.4 Point Elasticity and Types of Demand Elasticity

Types of Demand Elasticity

P

Qd

E ed =

D ed > 1

C ed = 1

B ed < 1

A ed = 0

Types of Demand Elasticity

3.4.1 Types of Price Elasticity of Demand

1. Elastic Demand2. Inelastic Demand3. Unitary Elastic Demand4. Perfectly Elastic Demand5. Perfectly Inelastic Demand/The

Zero Elasticity

Elastic Demand

p

Qd

D

P2

P1

Q2 Q1

Elastic Demand

Inelastic Demand

p

QdD

P2

P1

Q2 Q1

Inelastic Demand

The Unitary-Elastic Demand

p

QdD

P2

P1

Q2 Q1

Unitary-Elastic Demand

Perfectly Elastic Demand

Perfectly Inelastic Demand/The Zero Elasticity

3.4.2 Special Cases for the Negative Demand Elasticity

• Luxury cars, particularly at the higher end, like the Rolls-Royce Phantom pictured here, are often said to be desirable due to their price. As a result, it is argued that luxury cars are Veblen goods.

• In such cases, if we measure the demand elasticity, it will be positive with positive relationship between price and quantity demanded

3.5 Elasticity and Total Revenue

Example Product X1 can be sold for $5. The seller decides to increase the price to $7 in order to earn more money, but finds that he earns less money. This is because he is selling fewer of the products due to the increased price. His/her total revenue is falling, as a result. The demand for this product must be elastic. The producer failed in achieving his/her aim due to the lack of knowledge about the elasticity of the good.

3.5.1The Relationship between (TR) and Elasticity, and (TE) and Elasticity

• If the demand on a product was as follows, the demand on this product will be elastic

Table: Total Revenue when the Price Decreases in the Elastic Demand

• The demand on this product is elastic; therefore, the decrease in price causes an increase in total revenue (TR). The price decreases 20%, the quantity increases 30%, and total revenue increases 8.3%.

P Qd TR6 100 6005 130 650

Ed =130- 100

x5 +6

5 - 6 130 + 100

Ed =30

x11

=330

= -1.4-1 -230 -230

If the demand was unitary-elastic, total revenue remains constant no matter the price changes.

Total Revenue when the Price Decreases in the Unitary Elastic Demand

P Qd TR

6 100 600

5 120 600

The price decreases 20%, the quantity increases 20%, and total revenue remains constant .

Ed =120- 100

x5 +6

5 - 6 120 + 100

Ed =20

x11

=220

= -1-1 220 -220

The Relationship between Elasticity and Total Revenue

Elasticity of demand

Inelastic demand Unitary-demand Elastic demand

Ed <1 Ed = 1 Ed > 1

Change in price

Price increases Revenue increases Revenue constant Revenue decreases

Price decreases Revenue decreases Revenue constant Revenue increases

The Relationship between Price and Total Revenue

Price & revenue

QdA

P2

P1

TR

MR

P3P4

E

GH

F ML

The Relationship between Price

and Total Revenue.

C

3.6 The Relationship between Marginal Revenue, Price, and Elasticity

Marginal revenue can be defined as "the change in total revenue caused by selling an additional new unit".

Marginal revenue =

Change in total revenue

Change in the number of units sold.

3.7 Elasticity and the Slop

The Slope of the Infinity Elastic Demand Curve

P

Qd

D

3 4

Slope =P

=0

=0Q 1

The Slope of the Perfectly Inelastic Demand Curve

P

Qd

D

3

4

2Slope =

P=

1=infinityQd 0

The Slope of the Normal Demand Curve

P

Qd

F

E

C

B

A

6

4

2

2 4 6 8

8 ed=1

xP

Slope

Q

Slope =P

=1 Q

The Slope of the Unitary-Elastic Demand Curve

P

Qd

6

4

2 4

45

When the demand curve slope = 1 Elasticity differs

3.7.1 The Determinants of Price Elasticity of Demand (Factors that Affect Elasticity)

The elasticity differs from one good to another depending on different factors as following:

1) The Availability of Substitutes 2) Necessity of a Product3) Amount of Income Spent on the Good4) Consumer Income (The Wealth of

Consumers)5) Time

3.8 Practical Applications to Price Elasticity of Demand

The Effect of Decreasing Supply on Total Revenue

P

QdD

P1

Q

P

S

S1

Q1

Monopoly ……

Price

QdA

TR

MR

P1

E

D

C

Q1

MC

3.9 Cross Price Elasticity of Demand (CPED)

• CPED is the extent to which the quantity of good (y) is affected by the change in the price of good (x).

Cross elasticity of demand between product y and x =

% change in quantity demanded of product (y)

% change in price of product (x)

Eyx = Qdy %

px %

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Eyx =Qdy

Divided bypx

Qdy Px

Eyx =Qdy

xPx

=Qdy

xpx

Qdy px px Qdy

The more precise equation in calculating cross price elasticity of demand is the mid-point law

Cross elasticity of demand yandx =

% change in quantity demanded of (y)

X

Both prices summed

% change in price of (x) Both quantities summed

3.10 Income Elasticity of Demand Income elasticity of demand could be measured through the following formula:

EI =

Qd %

I %

EI = Qd x I I Qd

EI = Qd x I I Qd

EI = Qd2 – Qd1

xI1 + I2

I2 – I1 Qd1 + Q2

Example Measure the income elasticity of demand from the following data, and then illustrate the level of elasticity and type of the good. (Income increases from 100 to $150, as a result quantity increases from 90 to 110 units).

The income elasticity is positive and less than one that indicates a normal good with an inelastic demand

EI =110 -90

X150 + 100

150-100 110 + 90  

EI =20

x250  

  50 200  

3.11 Price Elasticity of Supply

Its formula is as follows:

 ES =

QS %    p %  

ES= Qs ÷ pQd P

Formula’s also include:

ES=Qs

*P

Qd p

ES=Qs

*P

P Qd

The sign of "price elasticity of supply" is generally positive because there is a positive relationship between prices and

quantity supplied .

3.11.1 Types of "Price Elasticity of Supply"

1) Perfectly Inelastic Supply (Zero Elastic Supply)

2) Infinity Elastic Supply3) Unitary Elastic Supply4) Elastic Supply5) Inelastic Demand

1. Perfectly Inelastic Supply (Zero Elastic Supply)

P

Qs

P1

Q

P

S

Inelastic Supply Curve

2. Infinity Elastic Supply

P

Qs Q2Q1

P S

Infinity Elastic Supply Curve

3. Unitary Elastic Supply

P

Qs

S

Unitary Elastic Supply Curve

4. Elastic Supply

P

Qs

S

Elastic Supply Curve

5. Inelastic Demand

P

Qs

S

Elastic Supply Curve

3.12 Supply Elasticity in the Short Run and the Long Run

Economists usually differentiate between three time periods due to some conditions:

1) Market Period (Very Short Run)2) The Short Run3) The Long Run

The Supply Curve in the Very Short Run

P

Qs

P1

Q

P

S

D

D1

Qd

Supply Easticity(Market Period)

Supply Curve in the Short Run

P

Qs

P1

Q2

P

S

D

D1

Qd

Supply Elasticity(Short Run)

Q1

Supply Curve in the Long Run

P

Qs

P1

Q2

P

S

D

D1

Qd

Supply Elasticity(Long Run)

Q1

3.12 Elasticity and Tax Incidence (Practical Cases)

There are five different cases concerning both supply and demand elasticity

First: Cases of Price Elasticity of DemandSecond: Cases of Price Elasticity of Supply

First: Cases of Price Elasticity of Demand

1. If the demand for product (x) is perfectly inelastic and the government imposes ($1) tax on this product, the consumer bears the full burden of the imposed tax

P

Q

4 E1

3

S

DS1

(Perfectly Inelastic Demand)Customer bear full burden of

imposed tax

E

First: Cases of Price Elasticity of Demand2. If the demand for product (x) is infinity elastic

and the government imposes ($1) tax on this product, the supplier bears the full burden of the imposed tax

P

Q

3

S

D

S1

(Infinity Elasticity)Customer bear full burden of imposed tax.

QQ1

First: Cases of Price Elasticity of Demand3. If the demand on product (x) is unitary elastic and

the government imposes ($1) tax on this product, the supplier bears half the burden of the imposed tax and the consumer bears the other half.

P

Q

3.5E1

3

S

D S1

(Unitary Elastic Demand)Suppliers bear half of the burden of imposed tax, &Customer bear half.

E

N

First: Cases of Price Elasticity of Demand4. If the demand on product (x) is inelastic, and the

government imposes ($1) tax on this product, the customer bears most of the burden of the imposed tax and the supplier bears the remaining few burden of tax.

P

Q

3.75E1

3

S

D

S1

(Inelastic Demand)Suppliers bear least

burden of imposed tax,

&Customer bear most

E

N

First: Cases of Price Elasticity of Demand5. If the demand on product (x) is elastic and the

government imposes ($1) tax on this product, the supplier bears most of the burden of imposed tax and the customer bears the remaining few burden of tax.

P

Q

3.25E1

3

SD

S1

(Elastic Demand)Customer bear least burden of imposed tax, &suppliers bear most.

E

N

Second: Cases of Price Elasticity of Supply

1.If the supply of product (x) is perfectly inelastic and the government imposes ($1) tax on this product, the supplier bears the full burden of imposed tax.

P

Q

3

S

D

E

(Perfectly Inelasticity Supply)Supplier bear the full burdenof tax.

Second: Cases of Price Elasticity of Supply 2. If the supply of product (x) is infinity elastic, and the

government imposes ($1) tax on this product, the consumer bears the full burden of imposed tax. In this case, the supplier is able to increase the prices to cover the burden of tax.

P

Q

4

3 S

D

S1

(Infinity Elastic Supply)Consumers bear the full burden of tax.

E

E1

Second: Cases of Price Elasticity of Supply 3. If the supply of product (x) is unitary elastic and the

government imposes ($1) tax on this product, the consumer bears half the burden of imposed tax and the supplier bares the remaining burden of tax. In this case, the suppliers are not able to increase the prices to cover the full burden of tax.

P

Q

3.5E1

3

S

D S1

(Unitary Elastic Supply)Suppliers bear half of the burden of imposed tax,

&Customer bear half.E

N

Second: Cases of Price Elasticity of Supply 4. If the supply of product (x) is inelastic and the

government imposes ($1) tax on this product, the consumer bears less and the supplier bears more of the burden of imposed tax.

P

Q

N

E

E1

D

S

S1

3

3.25

(Supply Inelastic)Supplier bear most & consumer bear least of the burden of tax

Second: Cases of Price Elasticity of Supply 5. If the supply of product (x) is elastic and the

government imposes ($1) tax on this product, the consumer bears more and the supplier bears less of the burden of imposed tax.

P

Q

N

E

E1

D

S

S1

3

3.75

(Elastic supply)Consumers bear most and suppliers least of the burden of tax

THE END OF CHAPTER 3