CHAPTER 4 Elasticity

The Responsiveness of the Quantity Demanded to Price  When price rises, quantity demanded decreases.  The question is how much quantity will decrease in response to a given price increase.  We want a measure that is units free and can be compared across different commodities.

The Responsiveness of Quantity Demanded to Price The measure we will study that meets the criteria we want is the price elasticity of demand.

Price Elasticity of Demand  Price elasticity of demand is a measure of the responsiveness of the quantity demanded of a good to a change in its price (ceteris paribus).  Elastic Demand - means demand is sensitive to price  Inelastic Demand - means demand is insensitive to price

Elasticity: A Units-Free Measure Price elasticity of demand = Percentage change in quantity demanded Percentage change in price

Calculating Elasticity  Negative sign is ignored for convenience.  The changes in price and quantity are expressed as percentages of the average price and average quantity between the two prices and quantities being compared. –Avoids having two values for the price elasticity of demand

Calculating Elasticity Price elasticity of demand = Percentage change in quantity demanded Percentage change in price

Calculating Elasticity Price elasticity of demand = Percentage change in quantity demanded Percentage change in price

Calculating Elasticity Price elasticity of demand = Percentage change in quantity demanded Percentage change in price (Q2 - Q1)/Q ave (P2 - P1)/P ave =

Calculating the Elasticity of Demand - Example  P 1 = 410  P 2 = 390  Q 1 = 36  Q 2 = 44

Calculating the Elasticity of Demand Quantity (millions of chips per year) Price (dollars per chip) DaDa Original point (P1, Q1)

Quantity (millions of chips per year) Price (dollars per chip) DaDa Original point (P1, Q1) New point (P2, Q2) Calculating the Elasticity of Demand

Quantity (millions of chips per year) Price (dollars per chip) DaDa = 8 Original point (P1, Q1) New point (P2, Q2) Calculating the Elasticity of Demand ` =$20

Quantity (millions of chips per year) Price (dollars per chip) DaDa Original point (P1, Q1) New point (P2, Q2) P ave = $400 = $20 = 8 Calculating the Elasticity of Demand

Quantity (millions of chips per year) Price (dollars per chip) DaDa Original point (P1, Q1) New point (P1, Q1) P ave = $400 Q ave = 40 = $20 = 8 Calculating the Elasticity of Demand

Calculating Elasticity Price elasticity of demand = Percentage change in quantity demanded Percentage change in price (Q2 - Q1)/Q ave (P2 - P1)/P ave =

Calculating Elasticity Price elasticity of demand = Percentage change in quantity demanded Percentage change in price (Q2 - Q1)/Q ave (P2 - P1)/P ave = = 4

Elasticity Using Different Bases  Use P 1 and Q 1 as base –E = ((44 – 36)/36)/((390 – 410)/410) – = (8/36)/(-20/410) =.222/.0488 = 4.55  Use P 2 and Q 2 as base –E = ((44 – 36)/44)/((390 – 410)/390) – = (8/44)/(-20/390) =.182/.051 = 3.57  Note that average of these two elasticities is about 4, which is the elasticity obtained using the average Ps and Qs  P 1 = 410, Q 1 = 36; P 2 = 390, Q 2 = 44

Inelastic and Elastic Demand  Five demand curves that cover the entire range of possible elasticities of demand: –Perfectly inelastic (Elasticity=0) –Inelastic (0<Elasticity<1) –Unit elastic (Elasticity=1) –Elastic (1<Elasticity< ) –Perfectly elastic (Elasticity= )

Inelastic and Elastic Demand 6 12 Price Quantity D1D1 Elasticity = 0 Perfectly Inelastic

Inelastic and Elastic Demand  Perfectly inelastic demand –Implies that quantity demanded remains constant when price changes occur. –Price elasticity of demand = 0

Inelastic and Elastic Demand 6 12 Price Quantity D2D2 0<Elasticity<1 Inelastic

Inelastic and Elastic Demand  Inelastic demand –Implies the percentage change in quantity demanded is less than the percentage change in price. –Price elasticity of demand > 0 and < 1

Inelastic and Elastic Demand 6 12 Price Quantity D3D Elasticity = 1 Unit Elasticity

Inelastic and Elastic Demand  Unit elastic demand –Implies that the percentage change in quantity demanded equals the percentage change in price. –Price elasticity of demand = 1

Inelastic and Elastic Demand 6 12 Price Quantity D4D4 1<Elasticity< ∞ Elastic

Inelastic and Elastic Demand  Elastic demand –Implies the percentage change in quantity demanded is greater than the percentage change in price. –Price elasticity of demand > 1 and <

Inelastic and Elastic Demand 6 12 Price Quantity D5D5 Elasticity = Perfectly Elastic

Inelastic and Elastic Demand  Perfectly elastic demand –Implies that if price changes by any percentage quantity demanded will fall to 0. –Price elasticity of demand =

Examples of Elasticity Calculation (1)  Q 1 = 10, P 1 = 50, Q 2 = 8, P 2 = 60  Elasticity = ((8-10)/9)/(60-50)/55)  = (-2/9)/(10/55)=-1.22  Therefore demand over this range is elastic

Examples of Elasticity Calculation (2)  Q 1 = 30, P 1 = 20, Q 2 = 28, P 2 = 26  Elasticity = ((28-30)/29)/(26-20)/23) =  (-2/29)/(6/23)=-.264  Therefore demand over this range is inelastic

Examples of Elasticity Calculation (3)  Q 1 = 55, P 1 = 9, Q 2 = 45, P 2 = 11  Elasticity = ((45-55)/50)/(11-9)/10)  = (-10/50)/(2/10)=-1.00  Therefore demand over this range is unitary elastic

The Factors that Influence the Elasticity of Demand  The closer the substitutes for a good, the more elastic is demand.  The higher the proportion of income spent on a good, the more elastic is demand.  The greater the time elapsed since a price change, the more elastic is demand.

Total Revenue Test  The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue that results from a price change (all other things remaining the same).

Unitary Elastic Demand and Total Revenue  If demand is unitary elastic, an increase in price results in an equal percentage decrease in the quantity demanded and total revenue remains constant.

Elastic Demand and Total Revenue  If demand is elastic, an increase in price results in a larger percentage decrease in the quantity demanded and total revenue decreases.

Inelastic Demand and Total Revenue  If demand is inelastic, an increase in price results in a smaller percentage decrease in the quantity demanded and total revenue increases.

Example of Total Revenue Test Elasticity Calculation (1)  Q 1 = 10, P 1 = 50, Q 2 = 8, P 2 = 60  Elasticity = ((8-10)/9)/(60-50)/55)  = (-2/9)/(10/55)=-1.22 (elastic)  TR 1 = P 1 xQ 1 = 50x10 = 500  TR 2 = P 2 xQ 2 = 60x8 = 480  TR falls as P increases  Therefore demand is elastic

Example of Total Revenue Test Elasticity Calculation (2)  Q 1 = 30, P 1 = 20, Q 2 = 28, P 2 = 26  Elasticity = ((28-30)/29)/(26-20)/23)  = (-2/29)/(6/23)=-.264 (inelastic)  TR 1 = P 1 xQ 1 = 20x30 = 600  TR 2 = P 2 xQ 2 = 26x28 = 728  TR rises as P increases  Therefore demand is inelastic

Example of Total Revenue Test Elasticity Calculation (3)  Q 1 = 55, P 1 = 9, Q 2 = 45, P 2 = 11  Elasticity = ((45-55)/50)/(11-9)/10)  = (-10/50)/(2/10)=-1.00 (unitary elastic)  TR 1 = P 1 xQ 1 = 9x55 = 495  TR 2 = P 2 xQ 2 = 11x45 = 495  TR doesn’t change as P increases  Therefore demand is unitary elastic

Elasticity Along a Straight- Line Demand Curve  Elasticity is not the same as slope, but the two are related.  As the price increases, demand becomes more elastic.  Elasticity will equal 1.0 at the midpoint of any linear demand curve.

Other Commonly Used Elasticities  Income Elasticity of Demand  Cross Price Elasticity of Demand  Price Elasticity of Supply