It measures the responsiveness of

consumer for a good to the changes in its determinants.

As per determinants, there are three type of Elasticity:

Price Elasticity Cross Elasticity Income Elasticity

It is defined as : Percentage change in quantity demanded of

the commodity divided by percentage change in price holding other determinants constant in demand function.

Ep = Q/Q = Q X P P/P P Q

Price elasticity indicates that the percentage change in quantity demanded for a percentage change in price.

Example: A firm increases price of its product by 2% and quantity demanded decreases by 3% .

Ep = - 3% = -1.5 2%

Important features:

Ep is always negative except in rare cases.

Price elasticity of demand is negative

because of law of demand or inverse relationship between price and demand.

If price falls from Rs. 50 to 48 and consequently demand increases from 100-110. What would be Ep.

Ep = Q X P P Q = 10 x 50 = 2.5 2 100

Commodity

Original Price

New Price Original Demand

New Demand

X 10 11 50 45

Y

2 12 10 8

Z 92 92 40 35

W 5 6 25 22

Find the elasticity of demand for each commodity.

Which commodity has the greatest elasticity and which the least.

Ans. X =1 Y = 0.04 Z =5.62 W= 0.60

There are two important methods to measure elasticity:

Point Method Arc Method

It is also known as elasticity at a given point on the demand curve.

This approach evaluates the effect of very small price change. Point elasticity formula:

Q/ P x P/Q Q/ P = dQ/dP

6

5

4

3

2

100 200 300 400

A

B

C

F

G

H

500

0

P$

Dx 1

0600

J

Q/ P x P/Q Q/ P = -100/$1 at

every point on Dx

Since Dx is linear.

Price elasticity at various points:

Q/ p x P__ = -100/$1 X 5/100

Q = -5 A Point = -1( 6 __) =∞ 0 B Point = -1( 5 _) =-5 Ep > 1 (above 1 the midpoint) C Point = -1( 4__) = -2 Ep>1 2

F Point = -1( __3___) = -1 Ep =1 ( 3 )

G Point = -1( 2__) =-1/2 Ep<1 ( 4 ) (Inelastic)

H Point = -1 ( 1__) = - 1/5 Ep<1 ( 5) (Inelastic)

J Point = -1 (_0__) = 0 (perfectly ( 6 ) Inelastic)

Q/

P is given by a1, the estimated coefficient of P.

Formula for Point Elasticity can be rewritten:

Ep = a1 P_ Q

a1 = -1606/$1

QS = 8604 at Ps $7

Ep=1606(7/8064) - 1.39

1 percent increase in Ps leads to 1.39 percent decline in Qs.

Ep >1 above the geometric midpoint on Linear Demand Curve DX .

Ep = 1 above the geometric midpoint on Linear Demand Curve DX

Ep < 1 below the geometric midpoint on Linear Demand Curve DX.

6

5

4

3

2

100 200 300 400

A

B

C

F

G

H

500

0

P$

Dx 1

0600

J

Ep > 1

Ep =1

Ep < 1

Qd = 100-4P

Find point Price elasticity of demand if price is Rs. 10.

Ep = a1 P_ Q a1 = -4/Rs.1Qd = 100-4*10 = 60

Ep = -4 x _10___ = -0.67 60

It is also known as price elasticity of demand between two points on the demand curve.

It analyzes measurable change in price.

Ep = Q2- Q1 X P2 +P1

P2-P1 Q2+Q1

Measure Arc Elasticity of Dx for a movement from point C to Point F (for a price decline) and F to C (price increase)

6

5

4

3

2

100 200 300 400

A

B

C

F

G

H

500

0

P$

Dx 1

0600

J

Solution:Ep = Q2- Q1 X P2 +P1 = P2-P1 Q2+Q1

200-300 x $4+$3 = -7 = - 1.4 $4-$3 200+300 5

Solution:Ep = Q2- Q1 X P2 +P1 = P2-P1 Q2+Q1

300-200 x $3+$4 = 7 = - 1.4 $3-$4 300+200 5

Suppose market demand for Playing Cards:

Q = 60,00,000 – 10,00,000P

Price increases from Rs. 2 to Rs. 3 Per deck,

What is the arc elasticity?

(Q2-Q1)/(P2-P1) = Q/ P

Q/ P = 1 Rs. Price increase causes a 10,00,000 decrease in quantity demanded.

Q/ P = - 10,00,000

p

Ep = 10,00,000 x______2+3________ 40,00,000+30,00,000

= - .71

1% increase in price will reduce the Quantity demanded by 0.71%

TR = P x Q

MR = T R Q

With a decline in price:

TR increases if Ep > 1TR remain unchanged if Ep =1TR declines if Ep<1

(1) P

(2) Q

(3) Ep

(4) TR= P.Q

(5) MR= TR/ Q

$6 0 -∞ $0 ----

5 100 -5 500 $5

4 200 -2 800 3

3 300 -1 900 12 400 -1/2 800 -1

1 500 -1/5 500 -3

0 600 0 0 -5

MR = P 1 + 1___ Ep

Since TR = PQ , Taking the derivative of total revenue with respect to quantity give MR:

MR = d (PQ) = P+Q dP dQ dQ

= P =P 1+ 1

Ep MR =$41+ 1 = $4 1- 1 = 2 -2 2

MR =$3 1+1 =0 -1

1+ dP x Q dQ P

If MR = 0 or Ep = 1, A price change would have no effect on total revenue.

If MR is Positive or Ep>1, by increasing quantity demanded price reduction would increase total revenue.

If MR is negative or Ep< 1 price reduction would decrease total revenue.

Find the MR of a firm that sells a product of $10 and the price elasticity of the demand for the product (-2).

MR = $10 1- 1 = $5 2

Nature of the Commodity:

Necessities (like food grains) and Prestige goods = Ep <1 demand.

Luxuries and comforts goods = Ep> 1 demand.

Number of Substitutes:Poor substitutes (wheat and rice) =

low Ep

Close substitute (Tea ,coffee, butter)= EP>1

No Substitute (Salt) = Ep<1

Price Level of the Commodity:

Goods are very costly and very Cheap = Ep<1

Goods are in middle range priced = Ep>1

Position of Commodity in Consumer’s Budget :

Higher the proportion of income spent on a commodity = Ep>1 (cloth)

Lower the proportion of income spent on commodity (Salt, soap, match

Boxes, ink) = Ep<1

Postponement of Demand:

The greater the time period (long Run)= Ep>1 (if the demand can be postponed consumer can subs-titute goods).

Lesser the time period (Short Run)= Ep<1.

Joint Demand:Demand of Complementary Goods

(Petrol & car, Pen & ink) = Ep<1

Consumer’s Behaviour:Frequent purchase of goods =

Ep>1 & Vis-à-visAddicted with goods = Ep<1 &

Vis-a-vis

CommodityShort Run

EpLong Run

Ep

Butter (India) 1.478 2.78

Petrol(India) 0.3 0.9

Tea (India) 0.712 1.14

Coffee (India) .292 0.685

Clothing(India)Beer (India)

1.10.85

2.881.18

Clothing (US)Electricity

(household)

0.900.13

2.901.89

It is measure of responsiveness in the demand for a commodity to a

change in consumer income.

EI = % change in the demand % change in Income

When other factors are held constant, the Income Elasticity of good or services is:

The percent change in demand associated with a 1 % change in income .

Two type of EI: Point EI & Arc EI

I/I come Elasticity

Point Income Elasticity:

EI = Q/Q = Q X I I / I = I Q

Point Elasticity measures the shift in Demand curve at each price level.

Q / P is given by ai, the estimated coefficient of I.

Formula for Point Elasticity of EI can be rewritten:

EI = ai _I_ Q

Q = 50,000+5I (Each one unit increase in income

associated with five unit increase in demand).

For I = Rs. 10500/- Q = 1,02500What is Point EI.

ai = 5

EI = ai _I_ Q

= 5x 10500 = 0.512

102500

The coefficient of income in a regression of the quantity demanded of a commodity on Income is 10.

Calculate the income elasticity of demand at income of $10,000 and sales of 80,000 units.

EI = ai _I_ Q

10(10,000/80,000) = 1.25

Point EI gives different results based on income rises or falls.

To avoid this, Arc EI provides same result whether income rises or falls.

EI= Q2 – Q1 X I2+I1 I2 - I1 Q2+Q1

Demand function for automobile as function of Per capita income is:

Q =50,000 +5(I)

What is the EI as income increases from Rs. 10,000 to Rs. 11,000

At Rs. 10000/- income 100000 car demanded.

I1 = 10000 & Q1 = 100000

At Rs. 11000/- income 105000 car demanded.

I2 = 11000 & Q2 = 105000

EI= Q2 – Q1 X I2+I1 I2 - I1 Q2+Q1

EI= 105000 – 100000 X 11000+10000 = 0.512 11,000-10,000 105000+100000

The coefficient of income in a regression of the quantity demanded of a commodity on Income is 10.

Calculate the income elasticity of demand if income increases from $10,000 to 11000 and sales of 80,000 units t 90,000 units.

EI= Q2 – Q1 X I2+I1

I2 - I1 Q2+Q1

90,000-80,000 x 11000+10000 $11000-$10000 90,000-80,000

= 1.24

EI is positive for Normal Goods◦EI is low (between 0 and 1) for necessities

(clothing, food & housing)◦EI is >1 for luxuries (health care, education

recreation◦

EI is negative for inferior goods

EI<1 for Wheat grain, cheap washing powder.

The responsiveness in the demand for commodity X to a change in the price of commodity Y can measure with Point Cross-price Elasticity :

QX/QX = QX * PY PY/PY PY Qx

QX/ PY refers to the change in quantity of X to the change in price of Y.

Value of QX and PY is given by

as, the estimated coefficient of PY.

Point Cross–Price Elasticity formula can be rewritten:

EXY = as x PY QX

As per given demand function: Qx = 100+0.5PY

Calculate Point Cross Price

Elasticity if price of Y commodity is Rs. 20

EXY = 0.5 X 20 = 0.09 110Per one % increase in price of Y

caused demand increase of X by 0.09%

Analyzed demand change of X in the change of price of Y while rising as well as falling price. Formula:

EXY = Qx2-QX1 = Py2+Py1 Py2-Py1 QX2+QX1 = as x Py2+Py1 QX2+QX1

As per given demand function :

100+0.5PYCalculate the Arc cross price

elasticity if PY increase from

Rs 50 to 100 and Qx increases from 125 unit to 150 units.

EXY = as x PY2+PY1

QX2+QX1

= 0.5 X 100+50 = 0.27 150+125

If EXY > 0 or positive , the two products are said to be substitute.

(Hamburger &Hot dogs, coca cola& Pepsi, Electricity & gasoline).

If EXY< 0 or negative, the two produtcs are said to complementary products. (Petrol &car, Sugar &coffee)

If ExY = 0 or close to 0 the both the goods (X&Y)not related.

Example : Books & Beer, pencil and potatoes, Car & candy

Maruti Suzukhi Corporation can use the cross price Elasticity of demand to measure the effect of change in the price of Swift on the demand of Wagon R.

The reduced price of Swift will reduce demand of Wagon R.

Manufacture of razors and razor blades can use cross elasticity and measure the increase in demand of razor blades if firm reduced the price of Razor.

% Change in quantity Demanded =

Ed x Percentage change in Price

Predict the effects of the change in Price of Beer on drinking and highway deaths among young adults.

Price Elasticity of demand of Beer among adult is about 1.30.

If state imposes beer tax that increase the price of beer by 10%.

What will be the beer consumption?

% change in quantity demanded = % change in price x Ed.

10% X 1.30 = 13%

Demand will decrease by 13 %

5 chang r e in

It measures the responsiveness of the producer to quantity supplied of goods and services.

Percentage change in quantity supplied of a commodity . Percentage in the price of the commodity.

Q X P P Q

If Ajit Singh trader is willing to supply 10 Rims at the rate of Rs.50 per Rim.

When the price of Rim increases to Rs.60 per Rim, he is ready to supply 12 Rims.

Es = 2 X 50 = 1 10 10

Elasticity of supply = 1 implies that 10% increase in price will push up the 10%

increase in supply.

% Change in quantity Supplied =

Es x Percentage change in Price

Elasticity of Supply – 0.80 Price increases by 5% How Much Quantity supplied will change?

% change in quantity supplied = Es x % change in price

= 0.80 X 5% = 4%

Applying Demand and Supply elasticity together magnitude of price change can be calculated. As:

% change in equilibrium Price =% change in demand /Es+Ed

If the quantity demanded of Milk increases from 100 million gallon per year to 135 million gallon per year at a price of $ 1.00.

If Demand changed by 35% and supply & demand elasticity is 2.5 & 1.0 respectively.

What will be the equilibrium price?

% change in equilibrium Price =

35% / 2.5+1.0 = 10%

Suppose the demand for a product decrease by 12 percent.

If the supply elasticity is 1.6 and the demand elasticity is o.40.

What change is possible in equilibrium Price?

% change in equilibrium price =

% change in demand / Es+Ed

= - 12% /1.6 + 0.4

= - 12% /2.0 = 6%

Consider the effect of population growth on housing prices.

The Portland metropolitan area is expected to grow by 12 percent in the next decade.

Suppose planners want to predict the effects of population growth on the equilibrium price of housing.

At the metropolitan level, the price elasticity of supply is about 0.5 and the price elasticity of demand is 1.0.

what will be affect on equilibrium price of housing due to increase in population?

% change in equilibrium Price = 12%/5.0+1.0

= 12% /6.0 = 2%