# Measurement And Interpretation Of Elasticities

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MeasurementandInterpretationof ElasticitiesChapter 2 What Are Elasticities? Measure of the relationship between twovariablesPercentage change in yElasticity Percentage change in x Elastic vs. inelastic Arc vs. pointAlfred Marshall Popularized concepts– Changed the name andface of economics Quirks Elasticities1

Elasticities of Demand Own-price elasticity of demand– responsiveness of changes in quantity associatedwith a change in the goods own price Income elasticity of demand– responsiveness of changes in quantity associatedwith a change in income Cross-price elasticity of demand– responsiveness of changes in quantity associatedwith a change in price of another goodOwn-Price Elasticity of DemandOwn-priceElasticity Percentage change in quantityPercentage change in own price(QA- QB)/[(QA QB)/2]Own-price elasticity (PA- PB)/[(PA PB)/2]ΔQΔQ PQ ΔPΔP QP Interpretation -- 1% increase in price leadsto a x% change in quantity purchased overthis arcOwn-Price Elasticity 12A11B109Price876Consumer bundle B to AChange in quantity 2 to 1Change in price 9 to 10What is the own-price elasticityof demand at this arc?5432100123456789101112Quantity2

Math Details Recall change in quantity 2 to 1 and price 9 to 10% change in quantity(1- 2)/[(1 2)/2]- 0.667 -6.33% change in own price (10 - 9) /[(10 9) / 2] 0.105 orΔQ P (1- 2) (10 9) / 2 -1 9.5 -6.33ΔP Q (10 - 9) (1 2) / 2 1 1.5 Interpretation -- 1% increase in price leads to a 6.33%decrease in quantity purchased over this arcOwn-Price Elasticity Bundles C to D% change in quantity(5 - 6)/[5 6)/2] % change in own price (6 - 5) /[(6 5) / 2]- 0.18 -1.000.18DUnitary Elasticity -- 1%Cincrease in price leads to a1% decrease in quantitypurchased over this n-Price ElasticityInterpretation -- 1%increase in price leadsto a 0.29% decreasein quantity purchased1211109 Bundles E to FPrice8765F4E3% change in quantity% change in price(8 - 9)/[8 9)/2] (3 - 2) /[(3 2) / 2]- 0.117 -0.2940.402100123456789101112Quantity3

Own-Price Elasticity Cont.ΔQ P ΔP Q Generally elasticities vary over the curve Negative – law of demand Linear demand curve - specificPriceElastic where % Q % PUnitary Elastic where % Q % PInelastic where % Q % PQuantityOwn-Price ElasticityIf value of theelasticitycoefficient isLess than -1.0Demand issaid to be% in quantity isElasticGreater than % inpriceEqual to -1.0UnitaryelasticInelasticSame as % in priceGreater than -1.0Less than % inpriceUse - example What is arc elasticity for corn between theprices of 15 (6 corn) and 20 (5 corn) /dozen?Pricedollar per dozen ears̀Demand Curve for Corn6050403020100024568Quantitydozen ears of corn4

Use Cont. Calculation of arc elasticity––– Elastic or inelastic– % change in Price (20-15)/[(20 15)/2] 0.28% change in Q (5-6)/[(5 6)/2] -0.18Own-price elasticity -0.18/(0.28) -0.63Why?Goal is to increase revenues. The currentprice is 17.50 / dozen, should you increase ordecrease price?Revenue Implications - KnowOwn-priceelasticity isCutting theprice willIncreasingthe price asticNo change in No change venueUse Cont. Necessary information from earlier calculations––– Price increase from 15 to 20Quantity decreases from 6 to 5Own-price elasticity -0.18/(0.28) -0.63Current price 17.50 with Q 5.5Goal is to increase revenues–––Current TR 17.5 x 5.5 96.25Incr retation?% change in quantity steak % change in corn price(2.75 - 2.5)/[(2.75 2.5)/2] 0.1 -0.33(15 - 20) /[(15 20) / 2]- 0.2811

Interpreting the Cross PriceElasticity of Demand - KnowIf the cross priceelasticity isThe goods areclassified ndentStimulus Bill Example 2009 Stimulus Bill– Included a up to a 1500 tax credit for insulation andenergy efficient windows, doors, HVAC units What is a tax credit? Why pass the bill and potential economiceffects? - nonpoliticalStimulus Bill Insulation Assume you have calculated the followingelasticities for insulation––––– Income elasticity of demand 1.2Own-price elasticity -0.4Cross price elasticity with lumber -0.02Cross price elasticity with energy 0.09Assume tax credit decreases insulation price by30%What is the effect of the stimulus bill giventhese elasticities? Recession has decreasedincomes by 10%12

Stimulus Bill Insulation Decrease in insulation sales – recession– – -30% x -0.4 12% - increase in insulation salesChange in lumber sales – stimulus bill– -10% x 1.2 -12% - decrease in insulation salesIncrease in insulation sales – stimulus bill-30% x -0.02 0.6% - increase in lumber salesChange in energy use – stimulus bill–-30% x 0.09 -2.7% - decrease in energy useCosts of the Bill Decrease in tax revenues – insulation tax creditIncrease in tax revenues – increase in insulationsalesIncrease in tax revenues – increase in lumbersalesDecrease in tax revenues – decrease in energyuseEnvironmental / otherOverall ?Price Flexibility of Demand Price flexibility is the reciprocal of own priceelasticity–Price flexibility 1/(own price elasticity)PriceFlexibility of Demand Percentage change in pricePercentage change in quantityRearrange% Δ price price flexibility x % Δ quantity13

Price Flexibility Use Example If the calculated elasticity is -0.25, then theprice flexibility 1/(-0.25) - 4.0Useful concept to producers to help form priceexpectationsExample USDA projects an additional 2% ofsupply will come on the market, what happensto price.If supply increases% Price price flexibility x % Quantity - 4.0 x ( 2%) - 8%by 2%, price wouldfall by 8%!Revenue Implications – DemandElasticity and Changes in SupplyOwn-priceelasticity isIncrease insupply willDecrease insupply asticNo change in No change venueCharacteristic of agricultureSummary - Know Know how to interpret all three elasticities Know how to interpret a price flexibility Understand revenue implications for producers ifprices are cut (raised) Understand the welfare implications forconsumers if prices are cut (raised)14

Cross-price elasticity of demand –responsiveness of changes in quantity associated with a change in price of another good Elasticities of Demand Interpretation -- 1% increase in price leads to a x% change in quantity purchased over this arc Own-Price Elasticity of Demand Own-price Elasticity Percentage change in quantity

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