Elasticity of demand

ELASTICITY OF DEMAND REPRENSTED BY PROF. S.D. BHARDWAJREGISTER OF B.M.I.E.T FAZILPUR ,

SONEPAT ASSISTANT PROFESSOR BHAWANA

BHARDWAJ OF G.V.M.GIRLS COLLEGE SONEPAT.

INTRODUCTION OF ELASTICITY OF

DEMANDElasticity of demand explain the quantitative relationship between price(x) and q(d)x. to measure the quantitative relationship between price X and Q(D)x, french economist Cournot and British Economist J. S. Mill propounded the concept of elasticity of demand. Dr. Marshall developed it as the elasticity of wants in his famous book, “Principles of Economics” published in 1890. But later on he called it elasticity of demand or price elasticity of demand.

ELASTICITY OF DEMAND

ACCORDING TO DR.MARSHALL, “THE ELASTICITY OF DEMAND IN GREATER OR SMALLER ACCORDING AS THE AMOUNT

DEMANDED INCREASES MUCH OR LITTLE FOR GIVEN FALL IN PRICES AND DIMINISHES

MUCH OR LITTLE FOR A GIVEN RISE IN PRICES.”

ACCORDING TO PROF. STONIER AND HAGUE, “ ELASTICITY OF DEMAND IS THEREFORE A

TECHNICAL TERM USED BY ECONOMISTS TO DESCRIBE THE DEGREE OF RESPONSIVENESS

OF DEMAND DUE TO FALL IN PRICES.”

TYPES OF ELASTICITY OF DEMAND Price elasticity of demand(Epx)=+(% or

propotionate change in Q(D)x/ % or proportionate change in price)

Income elasticity of demandEix or Eyx=% change in Q(D)x/%change in

the income of the consumer.o Cross elasticity of demandEcx=% change in Q(D)x (TEA)/% change in

Py(coffee).o Elasticity of substitutionEsx=% change in the combination of two

commodities/ % change in their price ratio

DEGREES OF ELASTICITY OF DEMAND

Perfectly elastic demand y

11

10

0 Quantity demanded of X X

HIGHLY ELASTIC DEMAND y

10

Price of x

8 0 x 100 200 QUANTITY DEMANDED OF X COMMODITY

HIGHLY INELASTIC DEMAND OR LESS ELASTIC DEMAND.

Y D

10 8 Price of x

6

4 D

0 50 100 110 X QUANTITY DEMANDED OF X(Qx)

PERFECTLY INELASTIC DEMAND y

12

10

price of x(Px)

8

6

4

2

X

0 50 100 200

Quantity demanded of X ( Qx)

UNITARY ELASTIC DEMAND Y Y D

D

rectangular hyperbola

Q Q shaped curve.

10 Priceof x P 10

Q1 MM1=PP1 epx=1 D

Price OF X 8 Q1 P1 8

6 D 6

4 4

2 2

M M1

0 50 100 120 x 0 50 100 120 x

QUANTITY DEMANDED OF X QUANTITY DEMANDED OF X

MEASUREMENT OF ELASTICITY OF DEMAND GRAPHIC METHOD EpX<1 Epx=0

Y Epx=1

Epx>1

Px

O Q(D)x x

GRAPHIC METHOD Y D4 Epx

Px D D D1 D2 D3 0 Q(D)x X

TOTAL OUTLAY METHOD T3 P3 Q1 Epx> 1(Luxurygoods) P2 T2 Px(Rs.) Epx=1 comforts

P1 T1 Q P T Epx<1(neccessity)

x 0 M M1 T.O.(Rs.)

FLUX METHODEpx=±(% or proportionate change in

Q(D)x / % or propotionate change in Px)Epx=±(change in Q(D)x/original or intial

Q(D) X 100)/ (change in Px/ Original or intial Px) X 100.

Epx=±(∆Q/Q X100)/(∆P/P X100).Epx=±(∆Q/Q/∆P/P)Epx=±(∆Q/Q X P/∆P)Epx=±(∆Q/∆P X P/Q)

POINT METHOD

Y D

Px P Q

P1 Q1

O M M1 D X Q(D)x

This method was propounded by Dr. Alfred Marshall to measure Epx at different points of the same demand curve.

According to Leftwitch, “ elasticity computed at single point on the demand curve for an infinitely small change is point elasticity.” this method is based on percentage method.

Epx=±(∆Q/∆P X P/Q) -----------------------------(i)

In the diagram: Q=OM ∆Q= MM1 P=OP ∆P =PP1

By putting these values in eq(i),we getEpx=±(MM1/PP1 X OP/ OM)---------------------

(ii)In the diagram we know that: OM= P1R=PQ MM1= RQ1 OP=QM (Opposite sides of rectangle are

always equal).PP1=QRBy putting these values in Eq(ii),we getEpx=±(RQ1/QR X QM/PQ)----------------------

(iii)In ∆QRQ1 and ∆QMD1<1=<4 (RIGHT ANGLE)

<2= <5(<corresponding)<6=<9 180◦-(<4+<5)=180◦-(<7+<8) therefore , ∆s are similar, hence,the ratios of

their sides will be equal.MD1/PQ=QD1/QD=QM/DP ---------------------(vi)We known from Eqn.(v) that MD1/PQ= Epx Epx=MD1/PQ=QD1/QD=QM/DP.Epx at Q= QD1/QD= Lower sector of the

demand curve from Q/Upper sector of the demand curve from Q.

WHEN A DEMAND CURVE IS LINEAR.

y Epx at any point lies between Q and D( Epx>1)

Epx at Q=QD1/QD=4CM/4CM=1

Epx at any point lies between Q

and D

(Epx<1)

0 Epx=0/D1D=0

/8=1 x

WHEN DEMAND CURVE IS A CURVILINEAR. y D

Q

D1

0 x

REVENUE METHOD. e= A/ A-M y Epx= AR/AR-MR

PP1,R

0 M (MR) D1(AR) X

BY POINT METHOD WE KNOW THAT Epx at Q=QD1/QD ----------------

(i)IN ∆QMD1 and∆DPQ <1=<4(RIGHT ANGLES) <2=<5(Corresponding angles) <3=<6 (Corresponding angles)∆s are similar, hence, the ratio of their

sides are equal. QD1/QD=QM/DP=MD1/PQ Epx=QD1/QD=QM/DP=MD1/PQ

-----------------(ii)Epx= QM/DP------------------------------------(iii)

In ∆DPT AND ∆TQL <4=<9(RIGHT ANGLES) <7=<8(vertically opposite

angles) PT= TQ(when AR and MR slope

downward from left to right in a straight line,the slope of MR will be the double of the slope of AR).

Hence,∆s are congruent(≈)PT=TQ, DP=QL,DT=TL

---------------------------(iv)

Putting the value of DP in equation(iii) from equation(iv) we get,

epx=QM/QL Epx=QM/QM-LM Epx= AR/AR-MR e= A/A-M (AR=A, MR=M, Epx=e) e(A-M)=A eA- eM =A eA- A=eM A(e-1)=eM M=A (e-1)/e A=eM/e-1= M(e/e-1)

SNIDER BILAS FORMULA.Epx=±[∆Q/∆P X Pm/Qm). H.H.Leibhafsky Formula. Epx=1-∆E/∆P.X Income Elasticity Of Demand ( Eix or Eyx)Income elasticity is the ratio of % or

proportionate change in the Q(D)x to the % or proportionate change in the income of the consumer.

In the words of Prof.R.G.Lipsey, “ The responsiveness of demand to change in income is termed as income elasticity of demand.”

According to Prof. D.S.Watson, “ Income elasticity of demand to change in income is termed as income elasticity of demand.”

Degrees(Types) of Eyx :PositiveEyx:- Y D

D 0 X

ZERO INCOME ELASTICITY OF DEMAND. y

p Q1Price of X

P1 Q

0 M Quantity Demanded of X x

NEGATIVE INCOME ELASTICITY OF DEMAND. Y

D y1y y D

0 M M1 X Q(D)X

METHOD OF MEASUREMENT.

y D2 negative Eyx D1 Eyx=0 D positive Eyx y

0 Q(D)x x

% 0R PROPORTIONATE METHOD

This method was propounded by Dr. Alfred Marshall and finally developed and used by Prof. Flux and Mrs. Joan Robinson. Therefore, this method is also known as Flux Method. According to this method, other things being remaining the same, Eyx is the ratio of % or proportionate

change in the Q(D)x to the % or proportionate change in the income of the consumer.

Eix or Eyx=(%or proportionate change in Q(D)x/% or proportionate change in the income of the consumer).

Eix or Eyx=(∆Q/Q X100/∆Y/Y X100)

Eix or Eyx=(∆Q/Q/∆Y/Y)

Eix or Eyx=∆Q/Q/∆Y/Y

Eyx = ∆Q/∆Y X Y/Q

DEGREE OF CROSS ELASTICITY OF DEMAND.

Positive Cross Elasticity of Demand Y D

P1 Price of y (Coffee) P

D

0 M M1 Quantity Demanded of X(tea) X

ZER0 CROSS ELASTICITY OF DEMAND. y

P1 Q1

P Q Price of shoes

P2 Q2

0 M X Quantity of Demanded of X(cars)

MEASUREMENT OF EPX

Y D

Ecx is negative ( complementary goods)

Py (Cars)

D

Q(D)x(petrol) 0

X

Y

D Ecx is Positive(SubstituteGoods)

Py(Coffee)

D

0 Q(D)x (Tea) X

% OR PROPORTIONATE METHOD.

The method was propounded by Dr. Marshall later on it was developed and used by Mrs. Joan Robinson and Dr. Flux. That is why it is also known Flux Method;

According to this Method: Ecx=% or proportionate change in

Q(D)x(tea)/% or proportionate change in Py(coffee).

Ecx=(change in Q(D)x/Initial Q(D)x x100)/(change in Py/Initial Py x100)

Ecx=(∆Qx/Qx X ∆Py/Py)Ecx= (∆Qx/Qx x Py/∆Py).Ecx=∆Qx/∆Py X Py/ Qx.