Our Friend Elasticity Or, how I learned to love percentages

Measuring Responsiveness or Sensitivity Slope –Unit dependent Currency Quantities –No Starting Point Percentages –Unit free –Relational Slope –Unit dependent Currency Quantities –No Starting Point Percentages –Unit free –Relational

Computing Elasticity Price elasticity of demand = %change in quantity demanded/% change in price Income elasticity of demand = %change in demand/% change in income Cross-price elasticity of demand = %change in demand/% change in the price of a related good Price elasticity of demand = %change in quantity demanded/% change in price Income elasticity of demand = %change in demand/% change in income Cross-price elasticity of demand = %change in demand/% change in the price of a related good

An Intuitive Approach to Elasticity Since price elasticity is always zero (law of demand) we ignore the negative sign and take the absolute value of price elasticity. E p > 1 Responsive or elastic –%ΔQ d > %ΔP a small %ΔP creates a large %ΔQ d E p < 1 Not responsive or inelastic –%ΔQ d < %ΔP a large %ΔP creates a small %ΔQ d E p = 1 unit elastic –%ΔQ d = %ΔP a given %ΔP creates an equal %ΔQ d Since price elasticity is always zero (law of demand) we ignore the negative sign and take the absolute value of price elasticity. E p > 1 Responsive or elastic –%ΔQ d > %ΔP a small %ΔP creates a large %ΔQ d E p < 1 Not responsive or inelastic –%ΔQ d < %ΔP a large %ΔP creates a small %ΔQ d E p = 1 unit elastic –%ΔQ d = %ΔP a given %ΔP creates an equal %ΔQ d

So???? Price and Total Revenue TR= P X Q E p > 1 Responsive or elastic –%ΔQ d > %ΔP if P goes down (up) total revenue goes up (down) E p < 1 Not responsive or inelastic –%ΔQ d < %ΔP if P goes down (up) total revenue goes down (up) E p = 1 unit elastic –%ΔQ d = %ΔP if P goes down (up) total revenue stays the same E p > 1 Responsive or elastic –%ΔQ d > %ΔP if P goes down (up) total revenue goes up (down) E p < 1 Not responsive or inelastic –%ΔQ d < %ΔP if P goes down (up) total revenue goes down (up) E p = 1 unit elastic –%ΔQ d = %ΔP if P goes down (up) total revenue stays the same

Figure 2 Total Revenue Copyright©2003 Southwestern/Thomson Learning Demand Quantity Q P 0 Price P × Q = $400 (revenue) $4 100

Determinants of Price Elasticity Availability of close substitutes Necessity versus luxury Definition of the market Time horizon Percentage of consumer budget Availability of close substitutes Necessity versus luxury Definition of the market Time horizon Percentage of consumer budget

Price Elasticity – Using Numbers E p = %ΔQ d / %ΔP = (Q 2 - Q 1 )/[(Q 2 + Q 1 )/2] (P 2 - P 1 )/[(P 2 + P 1 )/2] E p = %ΔQ d / %ΔP = (Q 2 - Q 1 )/[(Q 2 + Q 1 )/2] (P 2 - P 1 )/[(P 2 + P 1 )/2]

Calculating Price Elasticitymputing the Price Elasticity of Demand Demand is price elastic $5 4 Demand Quantity Price

Linear Demand Curve:Elasticity

Elasticity of Other Demand Curves Perfectly Elastic Perfectly Inelastic Unit Elastic Perfectly Elastic Perfectly Inelastic Unit Elastic

Figure 1 The Price Elasticity of Demand (e) Perfectly Elastic Demand: Elasticity Equals Infinity Quantity 0 Price $4 Demand 2. At exactly $4, consumers will buy any quantity. 1. At any price above $4, quantity demanded is zero. 3. At a price below $4, quantity demanded is infinite.

Figure 1 The Price Elasticity of Demand Copyright©2003 Southwestern/Thomson Learning (a) Perfectly Inelastic Demand: Elasticity Equals 0 $5 4 Quantity Demand An increase in price leaves the quantity demanded unchanged. Price

Figure 6 The Price Elasticity of Supply Copyright©2003 Southwestern/Thomson Learning (e) Perfectly Elastic Supply: Elasticity Equals Infinity Quantity 0 Price $4 Supply 3. At a price below $4, quantity supplied is zero. 2. At exactly $4, producers will supply any quantity. 1. At any price above $4, quantity supplied is infinite.

Elasticity of Supply Price elasticity of supply = %change in quantity supplied/% change in price E s = %ΔQ s / %ΔP = (Q 2 - Q 1 )/[(Q 2 + Q 1 )/2] (P 2 - P 1 )/[(P 2 + P 1 )/2] Perfectly elastic and inelastic supply Relatively elastic, relatively inelastic and unit elastic (crossing the Q or P axis or the origin) Supply curves where elasticity varies Price elasticity of supply = %change in quantity supplied/% change in price E s = %ΔQ s / %ΔP = (Q 2 - Q 1 )/[(Q 2 + Q 1 )/2] (P 2 - P 1 )/[(P 2 + P 1 )/2] Perfectly elastic and inelastic supply Relatively elastic, relatively inelastic and unit elastic (crossing the Q or P axis or the origin) Supply curves where elasticity varies

Figure 6 The Price Elasticity of Supply Copyright©2003 Southwestern/Thomson Learning (a) Perfectly Inelastic Supply: Elasticity Equals 0 $5 4 Supply Quantity An increase in price leaves the quantity supplied unchanged. Price

Figure 6 The Price Elasticity of Supply Copyright©2003 Southwestern/Thomson Learning (b) Inelastic Supply: Elasticity Is Less Than $ Quantity 0 1. A 22% increase in price... Price leads to a 10% increase in quantity supplied. Supply

Figure 6 The Price Elasticity of Supply Copyright©2003 Southwestern/Thomson Learning (d) Elastic Supply: Elasticity Is Greater Than 1 Quantity 0 Price 1. A 22% increase in price leads to a 67% increase in quantity supplied $5 200 Supply

Figure 6 The Price Elasticity of Supply Copyright©2003 Southwestern/Thomson Learning (c) Unit Elastic Supply: Elasticity Equals $ Quantity 0 Price leads to a 22% increase in quantity supplied. 1. A 22% increase in price... Supply

Determinants of elasticity of supply –Ability to increase or decrease production (e.g Ellensburg agates, farm crops, automobiles) –Time period Determinants of elasticity of supply –Ability to increase or decrease production (e.g Ellensburg agates, farm crops, automobiles) –Time period

Applications of Elasticity Farmers : fallacy of composition and good crop/bad revenue years The economics of addictive drugs Pricing decisions and your future business Farmers : fallacy of composition and good crop/bad revenue years The economics of addictive drugs Pricing decisions and your future business

Figure 8 An Increase in Supply in the Market for Wheat Copyright©2003 Southwestern/Thomson Learning Quantity of Wheat 0 Price of Wheat and a proportionately smaller increase in quantity sold. As a result, revenue falls from $300 to $220. Demand S1S1 S2S leads to a large fall in price When demand is inelastic, an increase in supply $3 100

Government and Markets Price Controls –Price Ceilings (e.g. rent control) –Price Floors (e.g. water) Taxes –Who appears to pay the tax? Buyers “pay” tax Sellers “pay” tax –Who really pays the tax? Tax incidence and burden Price Controls –Price Ceilings (e.g. rent control) –Price Floors (e.g. water) Taxes –Who appears to pay the tax? Buyers “pay” tax Sellers “pay” tax –Who really pays the tax? Tax incidence and burden

Case study – The payroll tax: Federal Insurance Contribution Act (FICA) for Social Security and Medicare

Elasticity and Tax Incidence Intuitive approach: –If the buyers can respond relatively more to price changes more than suppliers, suppliers pay more of the tax. –If the suppliers can respond relatively more than the buyers, then the buyers pay more of the tax. Intuitive approach: –If the buyers can respond relatively more to price changes more than suppliers, suppliers pay more of the tax. –If the suppliers can respond relatively more than the buyers, then the buyers pay more of the tax.

Extreme examples: –Perfectly elastic demand –Perfectly elastic supply –Perfectly inelastic demand –Perfectly inelastic supply Less extreme examples (e.g. the luxury tax) Extreme examples: –Perfectly elastic demand –Perfectly elastic supply –Perfectly inelastic demand –Perfectly inelastic supply Less extreme examples (e.g. the luxury tax)