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Chapter 4: Elasticity Elasticity of Demand: It measures the responsiveness of quantity demanded (or demand) with respect to changes in its own price (or income or the price of some other commodity). Why is Elasticity Important? How does a firm go about determining the price at which they should sell their product in order to maximize total revenue? Total Revenue = Price Quantity You are a marketing manager for Intel A new computer chip has been developed Decision to Be Made Do you sell the new chip at a high price ($400)? Do you sell the new chip at a low price ($200)? Price (dollars per chip) Demand and Total Revenue 400 300 200 Da 100 40 80 120 Quantity (millions of chips per year) Price (dollars per chip) Demand and Total Revenue 400 300 200 100 Db 40 60 80 120 Quantity (millions of chips per year) Price (dollars per chip) Price (dollars per chip) Demand and Total Revenue Da Db Quantity (millions of chips per year) Quantity (millions of chips per year) Slope Depends on Units of Measurement In these two examples, we can compare the slopes of the demand curves We cannot do so if we are dealing with different goods and services. Effect of a change of unit of measurement on Slope 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Slope Depends on Units of Measurement In these two examples, we can compare the slopes of the demand curves We cannot do so if we are dealing with different goods and services. Elasticity is independent of the units of measurement. Price elasticity of demand A measure of the responsiveness of the quantity demanded of a good to a change in its own price (ceteris paribus). Elasticity: A Units-Free Measure Percentage Change in Quantity Demanded εd Percentage Change in Price Price Elasticity of Demand Q d %Δ Q d Q avg P %Δ P Pavg Calculating Elasticity The changes in price and quantity are expressed as percentages of the average price and average quantity. This way we avoid having two values for the price elasticity of demand for the same range of the demand curve Example: Suppose, quantity demanded changes from 150 to 100 when Price increases from 5 to 10 dollars. Find out the price elasticity of demand for this specific range of the demand curve. εd Q 50 2 Q avg 125 2 1.5 3 5 .6 P 5 1 5 1 5 Pavg 7.5 1.5 Price (dollars per chip) Calculating the Elasticity of Demand Original point 410 390 Da 36 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point 410 New point 390 Da 36 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point 410 P = -$20 New point 390 Da 36 Q = 8 44 Quantity (millions of chips per year) Price (dollars per chip) Original point 410 P= -$20 400 Pave = $400 New point 390 Da 36 Q = 8 44 Quantity (millions of chips per year) Price (dollars per chip) Calculating the Elasticity of Demand Original point 410 P= 400 -$20 Pave =$400 New point Qave = 40 390 Da 36 Q = 8 40 44 Quantity (millions of chips per year) Calculating Elasticity Percentage Change in Quantity Demanded εd Percentage Change in Price Q %Δ Q d %Δ P Q avg 8 / 40 P 20 / 400 = - 4 Pavg Inelastic and Elastic Demand Three demand curves that cover the entire range of possible elasticities of demand: Perfectly inelastic Unit elastic Perfectly elastic Q d Q avg εd P Pavg Perfectly inelastic demand Implies that quantity demanded remains constant when price changes occur. Price elasticity of demand =0 Price D Elasticity = 0 12 Perfectly Inelastic 6 0 1 Quantity Q d Q avg εd P Pavg Unit elastic demand Implies that the percentage change in quantity demanded equals the percentage change in price. Price elasticity of demand = -1 Pric e Unit Elastic Demand Elasticity = -1 12 Unit Elasticity 6 D 1 2 3 Quantity Q d Q avg εd P Pavg Perfectly elastic demand Implies that if price increases by any percentage, quantity demanded will fall to 0 and if price decreases by any percentage, quantity will rise to infinity. Price elasticity of demand = Price Perfectly Elastic Demand Elasticity = 12 D3 6 Perfectly Elastic Quantity Inelastic and Elastic Demand Q d Q avg εd P Pavg Inelastic demand Implies the percentage change in quantity demanded is less than the percentage change in price. In absolute sense, price elasticity of demand > 0 and < 1 Elastic demand Implies the percentage change in quantity demanded is greater than the percentage change in price. In absolute sense, price elasticity of demand > 1 Price (dollars per chip) Elasticity Along a Straight-Line Demand Curve 500 400 300 250 200 100 0 40 80 100 120 160 200 Quantity (millions of chips per year) Price (dollars per chip) Elasticity Along a Straight-Line Demand Curve Elasticity = -4 500 Elastic 400 Lowering the price from $500 to $300 results in a price elasticity of demand of -4. 300 250 200 100 0 40 80 100 120 160 200 Quantity (millions of chips per year) Price (dollars per chip) Elasticity Along a Straight-Line Demand Curve 500 Lowering the price from $200 to $0 results in a price elasticity of demand of -1/ 4. 400 Inelastic 300 250 200 Elasticity = -1/4 100 0 40 80 100 120 160 200 Quantity (millions of chips per year) Price (dollars per chip) Elasticity Along a Straight-Line Demand Curve 500 |Elasticity| > 1 400 Lowering the price from $500 to $0 results in a price elasticity of demand of -1. |Elasticity| = 1 300 250 200 |Elasticity| < 1 100 0 40 80 100 120 160 200 Quantity (millions of chips per year) TR = P x Q Elasticity, Total Revenue and Expenditure Q d Q avg εd P Pavg Elastic demand — a 1 percent decrease in price will result in a greater than 1 percent increase in quantity demanded. Total revenue will increase Unit elastic demand — a 1 percent decrease in price will result in a 1 percent increase in quantity demanded Total revenue will not change Elasticity, Total Revenue and Expenditure Q d Q avg εd P Pavg Inelastic demand — a 1 percent decrease in price will result in a less than 1 percent increase in quantity demanded. Total revenue will decrease Elasticity, Total Revenue and Expenditure Total Revenue Test Price elasticity of demand can be estimated by observing the change in total revenue that results from a price change (ceteris paribus). Elasticity, Total Revenue and Expenditure Total Revenue Test Price cut and total revenue increases demand is elastic. Price cut and total revenue decreases demand is inelastic Price cut and total revenue does not change Price (dollars per chip) 500 400 300 250 200 100 0 D 100 TR = P x Q 200 Price (dollars per chip) 500 400 300 250 200 Total Revenue (billions of dollars) 100 0 25 D 100 200 20 15 10 TR 5 0 100 200 Quantity (millions of chips per year) Price (dollars per chip) 500 Elastic demand 400 Unit elastic 300 250 200 Inelastic demand When demand is elastic, price cut increases total revenue Total Revenue (billions of dollars) 100 0 25 100 200 Maximum total revenue 20 15 When demand is inelastic, price cut decreases total revenue 10 5 0 100 200 Quantity (millions of chips per year) More Elasticities of Demand Cross elasticity of demand Measures the responsiveness of the demand for a good to a change in the price of a substitute or complement good. Cross elasticity = of demand Percentage change Demand Percentage change in price of a substitute or complement Price of Walkmans Cross Elasticity of Demand D0 Quantity of Walkmans Price of Walkmans Cross Elasticity of Demand Price of a CD player, a substitute, rises. Positive cross elasticity D0 Quantity of Walkmans D1 Price of Walkmans Cross Elasticity of Demand D0 Quantity of Walkmans Price of Walkmans Cross Elasticity of Demand Price of a tape, a complement, rises. Negative cross elasticity D2 D0 Quantity of Walkmans Income Elasticity of Demand Income elasticity Measures the responsiveness of the demand to a change in income. Income elasticity = of demand Percentage change in quantity demanded Percentage change in income Income Elasticity of Demand Income elasticity can be: 1 ) Greater than 1 (normal good, income elastic) luxury goods - ocean cruises, jewelry 2 ) Between zero and 1 (normal good, income inelastic) necessities - food, clothing 3 ) Less than zero (inferior good) potatoes, rice Unit Tax and Tax Burden: 10 S2 9 8 7 6 5 $2 S1 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Unit Tax and Tax Burden: 10 $2 S2 Consumers’ part 9 8 7 6 5 S1 4 3 2 1 Suppliers’ part 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Elasticity and Tax Burden: Perfectly Inelastic Demand 10 $2 S2 Consumers’ part 9 8 7 6 5 S1 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Elasticity and Tax Burden: Perfectly Elastic Demand 10 9 8 7 6 5 $2 S2 Producers’ part S1 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Elasticity and Tax Burden: Perfectly Elastic Supply 10 $2 Consumers’ part 9 8 7 6 5 S2 S1 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity Elasticity and Tax Burden: Perfectly inelastic Supply S1 10 9 8 7 6 5 $2 Producers’ part 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 Quantity