Elasticity*

Objectives

To outline the importance of demand sensitivity analysis to the behavior of the organizationTo consider the factors that affect the price elasticity of demandTo consider the relationship between price, demand, marginal and total revenueTo develop the concepts of supply elasticity, advertising, cross-price, and income elasticity to the behavior of the organizationTo understand the direction of economic impact of government policy*

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 priceof Good x = % Qdx % Px

*Q1 = Qd before PQ2 = Qd after PP1 = P before PP2 = P after P

= (Q2 Q1 / Q1) (P2 P1 / P1)

Illustration Q1=2,000, Q2=2,500 P1= 10, P2= 9 then

2500 2000 / 2000 = - 2.5 910 / 10

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The use of proportionate or % measuresIt 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 useIt 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 curveE = 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*

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

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Types of price elasticityPerfectly elasticPerfectly inelasticUnity elasticRelatively elasticRelatively inelastic*

E = -1 At midpoint on demand curve

Qdx = A + BPxif Q = 0 then P = - A/Bor 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 QxThenQdx = A + E.QxDividing both sides by Qx1 = A + E QxSolving for EE = (Qx A) / Qx*

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

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

Price of Software (Px)Quantity of Software Sold (Qx)Own Price Elasticity (EQxPx)Total Revenue (PXQX)A0800.000B570-0.14350C1060-0.33600D1550-0.60750E2040-1.00800F2530-1.66750G3020-3.00600H3510-7.00350I400- 0

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*

*QTR0TR

Relationship between ed, MR and TRwhen ed>1, MR is positive and TR rises as price fallswhen ed=1, MR=0, TR=maxwhen ed 1TR fallsTR risese = 1TR constantTR constante < 1TR risesTR falls

TR, MR, AR AND EMR = d(TR) = d(PQ) = P + Q dP dQ dQ dQMR = P (1 + Q dP ) P dQSince Q . dP = 1 P dQ E MR = P (1 + 1 ) EMR = f (E), If E = -1 ThenMR = P (1 + 1 ) = 0 -1

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Using price elasticity of demand: Application to Phillip MorrisIn 1993, Phillip Morris cut cigarette prices by 18%, Others including R J Raynolds matched itIn 1994, demand increased by 12.5% but profit declined by 25% due to bad pricing strategyAll this happened because price was cut when demand was inelastic (-0.694)*

ExerciseCut price and make it up in volumeE = -1.7e = % QPrice cut = 5% % P

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

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ExerciseGiven: the demand equation is P = 81 9Q1. What is the equation for MR2. At what output is MR = 03. At what output TR is maximum4. Determine the price elasticity of demand at the output where TR is maximum.*

Gasoline price and consumer response in US

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Estimates of price elasticity (US 1975)

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Good or serviceEstimated price elasticityElectricity-0.13SRElectricity-1.89LRWater-0.14LRMotion pictures-3.69LRGasoline-0.15SRGasoline-0.78LRForeign travel-4.10LR

Income expenditure tree and elasticity *

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 consumers income

Point 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(EyEy>0), superior goods(Ey>1)In different stages of business cycleInternational tradeEngels law and the plight of the farmer(1940 US farmer to feed 11 people, now he feeds 80 people)*

Income elasticity of demand, selected commodities, global*

GoodElasticityGoodElasticityGrain(China)-0.12 to 0.15Cream (US)1.72Potatoes(UK)-0.32Eggs (UK)-0.21Potatoes(US)0.15Eggs (US)0.57Oranges (US)0.83Break (UK)-0.17Apples (US)1.32Other cereal products (UK)0.18Lettuce (US)0.88Domestic cars (US)1.62Meat (China)0.1 to1.2European cars (US)1.93Milk (UK)0.05Asian cars (US)1.65Milk (US)0.50

Income elasticity of selected commodities in India 1960 -76

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CommodityRuralUrbanMinor cereals-0.83-1.32Major cereals0.550.12Handloom cloth-0.120.21Mill made cloth0.660.70Bidi tobacco0.64-0.19Cigarette tobacco1.511.17NCAER, 1964

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 productsExy = %Qx %Py Exy = Qx . Py Py QxQx = 100+0.5Py , at Py = 20 and Qx = 110 Exy = 0.5 . 20/110 = 0.09ARC Exy = Qx2- Qx1 . Py1 + Py2 Py2 - Py1 Qx1 + Qx2 = 150-125 . 100+50 = 0.27100-50 150+125Exy >0 for substitutes and Exy

Trade elasticities in India 1960-91*

CountryForeign Ey for Indias ExportsIndias Ey for importsExy for Indias exportsExy for Indias importsROW0.491.02-0.94-0.26Australia0.531.21--0.11Belgium1.533.91--0.83Canada0.180.43-0.34-0.37France1.762.08--Germany1.421.08-0.18-1.01

Trade elasticities in India 1960-91 cont.*

CountryForeign Ey for Indias ExportsIndias Ey for importsExy for Indias exportsExy for Indias importsItaly0.761.70-1.78-0.53Japan0.492.00-0.05-1.88Netherlands1.241.35-0.28-0.64Switzerland1.522.32--0.01UK0.551.68-0.09-1.79USA1.130.39--0.46

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

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 QxARC EA = Qx2- Qx1 . Ax1 + Ax2 Ax2 - Ax1 Qx1 + Qx2

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The objectives of an advertisingCreate awarenessInform customersCreate the desired perceptionCreate a preferencePersuade customer to purchaseAdvertisement response curve Factors determining eaType of commodityMarket shareRivals reactionsState of economy

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Price elasticity of supply The responsiveness of supply to a change in the priceES = % QS % PDeterminants of ES Es>1 when less additional cost, spare capacity, easy supply of raw material, ready transformation Time period*

Degrees of elasticity of supply

*Perfectly elastic- Es = infinityPerfectly inelastic- Es = 0Unity elastic- Es = 1Relatively elastic- Es > 1Relatively inelastic- Es < 1

Unit elastic supply curve*

Elasticity of supply for self-consumption of own productHicks 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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ExerciseAfter a careful statistical analysis, Raynolds company concludes that the demand function for its product isQ = 500-3P+2Po+0.1IWhere Q is the quantity demanded for its product, Po is the price of its rivals product, and I is per capita disposable income($). At present, P=$10, Po= $20, and I= $6,000.Calculate price,income, and cross elasticity of demand. What is the implicit assumption regarding the population in the market?*

Elasticity in managerial decisions

Point and arc elasticity Identification problem of other factors Quick and easy method Bridge the gap of pricing in theory and pricing in practice Plays role in organizations ability to discriminate between markets Incidence of tax*

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