Elasticity

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Objectives

• To outline the importance of demand sensitivity analysis to the behavior of the organization

• To consider the factors that affect the price elasticity of demand

• To consider the relationship between price, demand, marginal and total revenue

• To develop the concepts of supply elasticity, advertising, cross-price, and income elasticity to the behavior of the organization

• To understand the direction of economic impact of government policy

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Elasticity of demand – the degree of responsiveness of quantity demanded to a change in price.

Percentage change in the Qty.

Ed = demanded of Good x Percentage change in the price

of Good x = % Qdx % Px

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Q1 = Qd before PQ2 = Qd after PP1 = P before P

P2 = P after P

= (Q2 – Q1 / Q1)

(P2 – P1 / P1)

Illustration – Q1=2,000, Q2=2,500

P1= 10, P2= 9 then

2500 – 2000 / 2000 = - 2.5 9–10 / 10

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The use of proportion

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The use of proportionate or % measures

• It allows comparison of changes in two qualitatively different things measured in two different types of units.

• It avoids the problem of what size units to use• It is the only sensible way of deciding how big a

change in price or quantity is.The sign (+ or -)

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Point elasticity

the measurement of elasticity at a point on a curve

E = Q . P P QIn terms of calculus

e = dq . P dp qdq/dp is the reciprocal of the slope of demand curve i.e. dp/dq which is constant therefore Ed depend on P/Q

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Arc elasticity the measurement of elasticity between two points on a curve

E = Q . (P1 + P2) P (Q1 + Q2)

Relative responsiveness of quantity demanded to a discrete change in price, and its intention is to provide a measure of the elasticity of demand over a range of prices.

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Exercise

If P1=5, P2=4, Q1=200, Q2=260 then measure point elasticity and arc elasticity.

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Types/degrees of price elasticity

• Perfectly elastic• Perfectly inelastic• Unity elastic• Relatively elastic• Relatively inelastic

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E = -1 At midpoint on demand curve

Qdx = A + BPx

if Q = 0 then P = - A/B

or if P = 0 then Q = A

Slope of linear demand curve = P Q B Is reciprocal of the slope of demand curveQdx = A + Qdx . Px

Px As E = Qdx . Px

Px Qx

ThenQdx = A + E.Qx

Dividing both sides by Qx

1 = A + E QxSolving for E

E = (Qx – A) / Qx 11

Mid point on D is at A/2, substituting this in above equation gives E = -1

Q < A/2 E > -1Q > A/2 E < -1

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QA

E = -

P

O

- > E > -1

E = -1

-1 > E > 0

E = 0

-A / B

A / 2

Total revenue and elasticity (QdX = 80 – 2Px)

Price of Software

(Px)

Quantity of Software Sold (Qx)

Own Price Elasticity

(EQxPx)

Total Revenue

(PXQX)

A 0 80 0.00 0

B 5 70 -0.14 350

C 10 60 -0.33 600

D 15 50 -0.60 750

E 20 40 -1.00 800

F 25 30 -1.66 750

G 30 20 -3.00 600

H 35 10 -7.00 350

I 40 0 - 013

Elasticity and revenue

Total revenue test – if demand is elastic, an increase (decrease) in price will lead to a decrease (increase) in tr. If demand is inelastic, an increase (decrease) in price will lead to a increase (decrease) in total revenue. Finally, tr is maximized at the point where demand is unitary elastic.

Various types of revenuesTR, AR, MR, incremental revenue

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Demand, elasticity and total revenue

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QA

E = -

P

O

- > E > -1

E = -1

-1 > E > 0

E = 0

-A / B

A / 2

Q

TR

0

TR

Relationship between ed, MR and TR– when ed>1, MR is positive and TR rises as price

falls– when ed=1, MR=0, TR=max– when ed<1, MR is negative and TR falls as price

fallsRelationship between ed and TR

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elasticity price increases

price decreases

e > 1 TR falls TR rises

e = 1 TR constant TR constant

e < 1 TR rises TR falls

Using price elasticity of demand: Application to Phillip Morris

• In 1993, Phillip Morris cut cigarette prices by 18%, Others including R J Raynolds matched it

• In 1994, demand increased by 12.5% but profit declined by 25% due to bad pricing strategy

• All this happened because price was cut when demand was inelastic (-0.694)

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Exercise‘Cut price and make it up in volume’E = -1.7 e = % QPrice cut = 5% % P

Will sale increase enough to increase TR due to price cut?

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G Gasoline price and consumer response in US

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5558,70015.71.311981

6389,30014.50.861979

25% 6809,60014.10.621977

6859,40013.70.571975

736 7%9,80013.3$ 0.401973

Avg. Fuel consumption

(gallons)

Avg. Miles driven per vehicle per

Year

Avg. Miles per

gallon

Avg. Price of

gasoline

Year

Estimates of price elasticity (US – 1975)

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Good or service Estimated price elasticity

Electricity -0.13 SR

Electricity -1.89 LR

Water -0.14 LR

Motion pictures -3.69 LR

Gasoline -0.15 SR

Gasoline -0.78 LR

Foreign travel -4.10 LR

Determinants of price elasticity ?

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Determinants of price elasticity

• Nature of the commodity (less elastic for broadly defined products)• Range of substitutes• Proportion of income spent• Time period• Durability of a commodity• Extent of use• Income level• Urgency of demand

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Income elasticity of demand – the responsiveness of demand to a change in consumer’s incomePoint Ey = %Q = Q . Y % Y Y QArc Ey = Q2-Q1 - Y2 + Y1

Y2-Y1 Q2+Q1

ExampleDemand for auto = f(per capita Y)Q=50,000+5(Y)Y1=10,000 then Q1=100,000, Y2=11,000 then Q2=105,000Ey(Arc)= 105,000-100,000 11,000+10,000 = =0.512 11,000-10,000 105,000+100,00Ey(Point) = 5. 10,000 = 0.5 (dq = 5)

100,000 dy

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Income elasticity and decision making Inferior goods(Ey<0), normal goods(1>Ey>0),

superior goods(Ey>1) In different stages of business cycle International tradeEngel’s law and the plight of the farmer(1940 US farmer to feed 11 people, now he feeds

80 people)

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Income elasticity of demand, selected commodities, global

Good Elasticity Good Elasticity

Grain(China) -0.12 to 0.15 Cream (US) 1.72

Potatoes(UK)

-0.32 Eggs (UK) -0.21

Potatoes(US)

0.15 Eggs (US) 0.57

Oranges (US)

0.83 Break (UK) -0.17

Apples (US) 1.32 Other cereal products (UK)

0.18

Lettuce (US) 0.88 Domestic cars (US)

1.62

Meat (China)

0.1 to1.2 European cars (US)

1.93

Milk (UK) 0.05 Asian cars (US) 1.65

Milk (US) 0.5029

Income elasticity of selected commodities in India 1960 -76

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Commodity Rural Urban

Minor cereals -0.83 -1.32

Major cereals 0.55 0.12

Handloom cloth -0.12 0.21

Mill made cloth 0.66 0.70

Bidi tobacco 0.64 -0.19

Cigarette tobacco 1.51 1.17

NCAER, 1964

NSSO Survey 2011

1999-2009 Rural Urban

Food 70% 78%Education 378% 345%Overall expenditure

8% 20%

Medical care 152% 136%

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ToI 25 July 2011

Cross-price elasticity of demand The responsiveness of demand for one good to a change in the price of another. Cross elasticity provides a measure of substitution and complementarities between two products

Exy = %Qx %Py Exy = Qx . Py

Py QxQx = 100+0.5Py , at Py = 20 and Qx = 110 Exy = 0.5 . 20/110 = 0.09

ARC Exy = Qx2- Qx1 . Py1 + Py2

Py2 - Py1 Qx1 + Qx2

= 150-125 . 100+50 = 0.27100-50 150+125

Exy >0 for substitutes and Exy<0 for complementary productsExy may not be symmetrical

Usefulness – pricing strategy, boundaries between industries 32

Trade elasticities in India 1960-91

CountryForeign Ey for India’s Exports

India’s Ey for imports

Exy for India’s exports

Exy for India’s imports

ROW 0.49 1.02 -0.94 -0.26

Australia 0.53 1.21 - -0.11

Belgium 1.53 3.91 - -0.83

Canada 0.18 0.43 -0.34 -0.37

France 1.76 2.08 - -

Germany 1.42 1.08 -0.18 -1.0133

Trade elasticities in India 1960-91 cont.

CountryForeign Ey for India’s Exports

India’s Ey for imports

Exy for India’s exports

Exy for India’s imports

Italy 0.76 1.70 -1.78 -0.53

Japan 0.49 2.00 -0.05 -1.88

Netherlands

1.24 1.35 -0.28 -0.64

Switzerland

1.52 2.32 - -0.01

UK 0.55 1.68 -0.09 -1.79

USA 1.13 0.39 - -0.46

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Reference - Gupta G S and Keshava H, 1994, Income and Price Elasticities in India’s Trade, Vikalpa, Vol. 19, No. 2, pp 13-19.

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Why advertise?

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Advertisement and its effect on demand

1. Shift DD to right 2. Make it less price elasticElasticity of advertisement – responsiveness of sales to changes in advertising expenditures

EA = %Q sales%adv.exp.

= Qx . Ax Ax Qx

ARC EA = Qx2- Qx1 . Ax1 + Ax2

Ax2 - Ax1 Qx1 + Qx2

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The objectives of an advertising Create awareness Inform customers Create the desired perception Create a preference Persuade customer to purchase! Advertisement response curve ! Factors determining ea Type of commodity Market share Rival’s reactions State of economy

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Price elasticity of supply The responsiveness of supply to a change in the price

ES = % QS

% P

Determinants of ES

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Determinants of ES

-Es>1 when less additional cost -spare capacity -easy supply of raw material- ready transformation- time period

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Degrees of elasticity of supply

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Perfectly elastic- Es = infinity

Perfectly inelastic- Es = 0

Unity elastic- Es = 1

Relatively elastic- Es > 1

Relatively inelastic- Es < 1

Unit elastic supply curve

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6

5

4

3

1

2

0 1 2 3 4 5 6

b

c

S1

a

f

S2

S3

e

d gP

Q

Elasticity of supply for self-consumption of own product

Hicks in Value and Capital explained that supply becomes backward bending due to self consumption

(Ref.: Kothari, V N, 1999, Elasticity of demand for self-consumption of own product, Indian Economic Journal, 46(2), pp 140-142)

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