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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 Percentage change in quantity demanded Price elasticity of demand = Percentage change in price %Q %P Calculating Elasticity Percentage change in quantity demanded Price elasticity of demand = Percentage change in price %Q %P Q / Qave P / Pave Calculating Elasticity Percentage change in quantity demanded Price elasticity of demand = Percentage change in price %Q %P = Q / Qave P / Pave (Q2 - Q1)/Qave (P2 - P1)/Pave Calculating the Elasticity of Demand - Example P1 = 410 P2 = 390 Q1 = 36 Q2 = 44 Price (dollars per chip) Calculating the Elasticity of Demand Original point (P1, Q1) 410 400 390 Da 36 40 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point (P1, Q1) 410 400 New point (P2, Q2) 390 Da 36 40 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point (P1, Q1) 410 P `=$20 400 New point (P2, Q2) 390 Da 36 Q = 8 40 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point (P1, Q1) 410 P= $20 400 Pave = $400 New point (P2, Q2) 390 Da 36 Q = 8 40 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point (P1, Q1) 410 P= $20 400 Pave = $400 New point (P1, Q1) Qave = 40 390 Da 36 Q = 8 40 44 Quantity (millions of chips per year) Calculating Elasticity Percentage change in quantity demanded Price elasticity of demand = Percentage change in price %Q %P = Q / Qave P / Pave (Q2 - Q1)/Qave 8 / 40 (P2 - P1)/Pave 20 / 400 Calculating Elasticity Percentage change in quantity demanded Price elasticity of demand = Percentage change in price %Q %P = Q / Qave P / Pave (Q2 - Q1)/Qave 8 / 40 = 4 (P2 - P1)/Pave 20 / 400 Elasticity Using Different Bases Use P1 and Q1 as base – E = ((44 – 36)/36)/((390 – 410)/410) – = (8/36)/(-20/410) = .222/.0488 = 4.55 Use P2 and Q2 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 P1 = 410, Q1 = 36; P2 = 390, Q2 = 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= ) Price Inelastic and Elastic Demand D 1 Elasticity = 0 12 Perfectly Inelastic 6 Quantity Inelastic and Elastic Demand Perfectly inelastic demand – Implies that quantity demanded remains constant when price changes occur. – Price elasticity of demand = 0 Price Inelastic and Elastic Demand D 2 0<Elasticity<1 12 Inelastic 6 Quantity 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 Price Inelastic and Elastic Demand D 3 Elasticity = 1 12 Unit Elasticity 6 1 2 3 Quantity 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 Price Inelastic and Elastic Demand 12 1<Elasticity< ∞ D4 Elastic 6 Quantity 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 < Price 12 6 Inelastic and Elastic Demand Elasticity = D5 Perfectly Elastic Quantity 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) Q1 = 10, P1 = 50, Q2 = 8, P2 = 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) Q1 = 30, P1 = 20, Q2 = 28, P2 = 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) Q1 = 55, P1 = 9, Q2 = 45, P2 = 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) Q1 = 10, P1 = 50, Q2 = 8, P2 = 60 Elasticity = ((8-10)/9)/(60-50)/55) = (-2/9)/(10/55)=-1.22 (elastic) TR1 = P1xQ1 = 50x10 = 500 TR2 = P2xQ2 = 60x8 = 480 TR falls as P increases Therefore demand is elastic Example of Total Revenue Test Elasticity Calculation (2) Q1 = 30, P1 = 20, Q2 = 28, P2 = 26 Elasticity = ((28-30)/29)/(26-20)/23) = (-2/29)/(6/23)=-.264 (inelastic) TR1 = P1xQ1 = 20x30 = 600 TR2 = P2xQ2 = 26x28 = 728 TR rises as P increases Therefore demand is inelastic Example of Total Revenue Test Elasticity Calculation (3) Q1 = 55, P1 = 9, Q2 = 45, P2 = 11 Elasticity = ((45-55)/50)/(11-9)/10) = (-10/50)/(2/10)=-1.00 (unitary elastic) TR1 = P1xQ1 = 9x55 = 495 TR2 = P2xQ2 = 11x45 = 495 TR doesn’t change as P increases Therefore demand is unitary elastic Elasticity Along a StraightLine 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