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##### The Concept of Elasticity

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**Elasticity**What is the concept and why do we need it? Elasticity is used to measure the effects of changes in economic variables**The Most Important Elasticity**• Price elasticity of demand • A measure of the responsiveness of the quantity demanded of a good to a change in its price.**Demand: Gallons vs Litres**Price($/g) Quant(g) Price($/L) Quant(L) a 100 0 a' 25 0 b 50 25 b' 12.50 100 c 0 50 e' 0 200**Elasticity: A Units-Free Measure**Percentage change in quantity demanded Price elasticity of demand = Percentage change in price**Calculating Elasticity**= (Q/P)(Pave/Qave) Which is negative, but price elasticity of demand is given as a positive number**Calculating Elasticity**• Negative sign is ignored • The changes in price and quantity are expressed as percentages of the average price and average quantity.**Calculating the Elasticity of Demand**Original point 410 Price (dollars per chip) 400 New point 390 Da 36 40 44 Quantity (millions of chips per year)**= $20**= 8 Calculating the Elasticity of Demand Original point 410 Price (dollars per chip) 400 New point 390 Da 36 40 44 Quantity (millions of chips per year)**= $20**= 8 Original point 410 Price (dollars per chip) 400 Pave = $400 New point 390 Da 36 40 44 Quantity (millions of chips per year)**= $20**= 8 Calculating the Elasticity of Demand Original point 410 Price (dollars per chip) 400 Pave = $400 New point Qave = 40 390 Da 36 40 44 Quantity (millions of chips per year)**Calculating Elasticity**Price elasticity = 4 meaning, on average, each 1% price decrease Causes a 4% increase in quantity demanded**Some Interesting Characteristics**of Linear Demand Curves (It is a straight Line) Can be Deduced**Compute Elasticity for Gasoline (in Gallons) from Earlier**Example When: Price falls from $100/gal to $0/gal Price ($/unit) 100 |P/Q| = 100/50 = 2 Pavg = 100/2 (=50) Qavg = 50/2 (=25) Pavg/ Qavg = (100/2)/(50/2) = 2 Gallons: slope = -2 50 25 0 25 50 100 200 Quant. (G)**|P/Q| = 100/50 = 2**Pavg/ Qavg = (100/2)/(50/2)= 2 The ratio of midpoint Price and Quantity = The slope But for elasticity we want |Q/P|, the reciprocal of demand curve slope |Q/P| = 1/2 Elasticity = |Q/P| (Pavg/ Qavg) = (1/2)*2 =1**A Lesson: Elasticity on linear demand curves**Price ($/unit) 100 For any Price-Quantity combination Elasticity > 1 Elasticity = 1 50 Elasticity < 1 25 0 25 50 100 200 Quant. (G or L)**Three types of price elasticity of demand**• inelastic • Unit elastic • elastic**Inelastic Demand**• Inelastic demand • The percentage change in quantity is less than the percentage change in price. • Price elasticity of demand < 1**Extreme Case: Perfectly Inelastic Demand**D1 Elasticity = 0 WHY? Price 12 (Q/P)(Pave/Qave) = 6 (0/P)(Pave/Qave) = 0 Because Q = 0 Quantity**Elastic Demand**• Elastic demand • The percentage change in quantity is greater than the percentage change in price. • Price elasticity of demand > 1**Extreme Case:Perfectly Elastic Demand**Price Elasticity = 12 D3 (Q/P)(Pave/Qave) = 6 (Q/0)(Pave/Qave) = Because P = 0 Quantity**Unit Elastic Demand**• Unit elasticity • The percentage change in quantity equals the percentage change in price. • Price elasticity of demand = 1**Extreme Case:Unit Elastic Demand Everywhere**Price Elasticity = 1 12 Unit Elasticity 6 D2 Quantity 1 2 3**Factors That Influence Elasticity**• The Closeness of Substitutes. • The closer the substitutes, the more elastic the demand • more elastic means a higher price elasticity (but not necessarily > 1)**Elasticity and Closeness of Substitutes**Orange Roughy 10 Price (dollars per pound) 5 Close subs No close subs 1 2 3 4 7 Quantity (pounds per week)**Factors That Influence Elasticity**• Proportion of Income Spent on the Good • The greater the proportion of income spent on food, the more elastic the demand • Because of Income Effect of a price change**Factors That Influence Elasticity**• Time Elapsed Since Price Change • The longer the time, the more elastic the demand • Short-run demand • Long-run demand**Factors Affecting Price Elasticity of Demand**• Availability of substitutes • The better & more numerous the substitutes for a good, the more elastic is demand • Percentage of consumer’s budget • The greater the percentage of the consumer’s budget spent on the good, the more elastic is demand • Time period of adjustment • The longer the time period consumers have to adjust to price changes, the more elastic is demand**Income Elasticity**• Income elasticity (EM) measures the responsiveness of quantity demanded to changes in income, holding the price of the good & all other demand determinants constant • Positive for a normal good • Negative for an inferior good**Cross-Price Elasticity**• Cross-price elasticity (EXY) measures the responsiveness of quantity demanded of good X to changes in the price of related good Y, holding the price of good X & all other demand determinants for good X constant • Positive when the two goods are substitutes • Negative when the two goods are complements