ElasticityECON1E: Principles of MicroeconomicsUniversity of St. La Salle3

ElasticityA general concept used to quantify the response in one variable when another variable changes.Elasticity measures the responsiveness of one variable to a certain change of another variable.

ElasticityThe basic formula to determine elasticity is:Elasticity = percentage change in variable x percentage change in variable yUsing mathematical symbols, = %x/%y

Types of ElasticityElasticThe percentage change in variable x is greater than the percentage change in variable y. It is said to be elastic whenever the elasticity coefficient is greater than 1 ( > 1).InelasticThe percentage change in variable x is less than the percentage change in variable y. The elasticity coefficient is less than 1 ( < 1).

Types of ElasticityUnitary ElasticThe percentage change in variable x is equal to the percentage change in variable y. The elasticity coefficient is equal to 1 ( = 1).Perfectly ElasticAny change in variable y will have an infinite effect on variable x ( = infinity).

Types of ElasticityPerfectly InelasticAny change in variable y will have no effect on variable x ( = 0).

Price ElasticityPrice elasticity measures the percentage change in quantity with respect to percentage change in price. Categories of price elasticity include price elasticity of demand and price elasticity of supply.

Price Elasticity of DemandPrice elasticity of demand measures the responsiveness of the quantity demanded with respect to its price. The basic formula used to calculate the coefficient of price elasticity of demand (D) is:D = %Qd / %P

Price Elasticity of DemandMathematically, the point elasticity of demand (in absolute value):D = %Qd = Q2 Q1 or Q2 Q1 P1 % PQ1 P2 P1 Q1 P2 P1 P1x

Price Elasticity of DemandMathematically, the arc elasticity of demand (in absolute value):ARC = Q2 Q1 (P1 + P2) / 2 P2 P1 (Q1 + Q2) / 2x

Hypothetical Data of Point and Arc Elasticity

PointsPrice of Good X (Px)Quantity Demanded of Good X (Qdx)A4700B5475C9430D12400E15393F20344G26310H30300I39150

Price Elasticity of DemandPoint elasticity of demandFrom Points A to ED = Q2 Q1 = 393 700 = 0.44

Q1 700 2.75

P2 P1 15 4 = |-0.16|

P1 4 inelastic

Price Elasticity of DemandArc elasticity of demandFrom Points E to IARC = Q2 Q1 (P1 + P2) / 2 P2 P1 (Q1 + Q2) / 2 = 150 393 (15+39) / 2 39 15 (393 + 150) / 2 = |-1.01| elasticxx

Price Elasticity of DemandClassificationsElastic DemandA small change in price results to greater change in quantity demanded. This means that consumers are very sensitive to the price of goods.

Price Elasticity of DemandClassificationsInelastic DemandA percentage change in quantity demanded is less than the percentage change in price. Consumers are not sensitive to any change in price. Any change in price has little significance.

Price Elasticity of DemandClassificationsUnitary Elastic DemandA change in price is equal to a change in quantity demanded. The change in price exactly matches the change in quantity demanded.

Price Elasticity of DemandClassificationsPerfectly Elastic DemandWithout change in price, infinite change occurs in quantity demanded.

Price Elasticity of DemandClassificationsPerfectly Inelastic DemandAny change in price creates no change in quantity demanded.

Income Elasticity of DemandIncome elasticity of demand measures the percentage change in demand over a percentage change in income.The basic formula is:Y = %Qd / %Y

Income Elasticity of DemandMathematically:Y = Q2 Q1orQ2 Q1 Y1 Q1 Y2 Y1 Q1 Y2 Y1 Y1

x

Income Elasticity of Demand

Type of GoodsIncome Elasticity CoefficientInferior goodNegative elasticity ( < 0)Normal, luxury goodPositive elasticity greater than one ( > 1)Normal, necessity goodPositive elasticity less than one (0 1)

YQd% Qd%YYType of Good40020------------50035(35-20)/20 = .75(500-400)/400 = .253Normal, luxury60043(43-35)/35 = .23(600-500)/500 = .201.15Normal, luxury

70047(47-43)/43 = .09(700-600)/600 = .17.53Normal, necessity80050(50-47)/47 = .06(800-700)/700 = .14.43Normal, necessity90048(48-50)/50 = -.04(900-800)/800 = 1.25-.32inferior100047(47-48)/48 = -.02(1000-900)/900 = .11-.18inferior

Cross Elasticity of DemandCross elasticity of demand measures the responsiveness of quantity demanded of a good to a change in the price of another goodThe basic formula is:xy = %Qdx / %Py

Cross Elasticity of DemandMathematically:

xy = Qx2 Qx1

Qx1

Py2 Py1

Py1

Cross Elasticity of Demand

Type of GoodsIncome Elasticity CoefficientComplementary goodsNegative elasticitySubstitute goodsPositive elasticityUnrelated goodsZero

Cross Elasticity of Demand

GoodBeforeAfterPriceQuantityPriceQuantity(x) Playstation1000901000100(y)Xbox9004595080

Cross Elasticity of Demandxy = Qx2 Qx1 = 100 90

Qx1 90

Py2 Py1 950 900

Py1 900

= 0.11 = 1.83 0.06 substitute goods

Cross Elasticity of Demand

GoodBeforeAfterPriceQuantityPriceQuantity(y) Computer70015009001200(x)CD-ROM2565025600

Cross Elasticity of Demandxy = Qx2 Qx1 = 600 650

Qx1 650

Py2 Py1 900 700

Py1 700

= 0.08 = 0.28 0.29 complementary goods

****Source: http://www.sparknotes.com/economics/micro/elasticity/section1.rhtml*Source: prenhall.com*Source: http://www.sanandres.esc.edu.ar/secondary/economics%20packs/microeconomics_sl/images/pic094.gif*Source: https://upload.wikimedia.org/wikipedia/commons/d/da/Perfectly_Inelastic_Demand.GIF*