CH 7: Elasticity
What is Elasticity? Elasticity: shows how sensitive a change in quantity is to a change in price There are 4 types: 1. Elasticity of Demand 2. Elasticity of Supply 3. Cross-Price Elasticity (Substitutes or Complements) 4. Income Elasticity (Normal or Inferior goods)
Elasticity of Demand
Price Elasticity of Demand: Elastic Demand It is a measurement of consumers responsiveness to a change in price What will happen if price increases? How much will it affect quantity demanded? Price elasticity of demand is always expressed as a positive number (E>1)
Price Elasticity of Demand: Elastic Demand Example: The price of apples increases by 50% per pound How much will quantity demanded change?
Price Elasticity of Demand: Elastic Demand Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price (independent of units) E D =% change in Quantity Demanded % change in Price
Price Elasticity of Demand: Elastic Demand Demand is elastic if the percentage change in quantity is greater than the percentage change in price Elastic demand =E D > 1
Characteristics of Elastic Goods Many substitutes Luxuries Large portion of income Plenty of time to decide Elasticity coefficient greater than 1
When is demand elastic? Substitutes: The price of Coke goes up 25% so consumers substitute Pepsi Luxury item: The price of a yacht increases 50% Large portion of income: The cost of a new refrigerator Plenty of time to decide: Buying a new set of tires for your car
Draw the Graph: Relatively Elastic Demand P D Q
Perfectly Elastic Demand This curve is perfectly elastic, meaning that Q responds enormously to changes in price, E D = P D Q
Price Elasticity of Demand: Inelastic Demand When demand is inelastic, quantity demanded is insensitive to a change in price meaning there will be little change If price increases, quantity demanded will fall a little If price decreases, quantity demanded will increase a little In other words, people will continue to buy it
Price Elasticity of Demand: Inelastic Demand Demand is inelastic if the percentage change in quantity is less than the percentage change in price Inelastic demand= E D < 1
Characteristics of Inelastic Goods Few substitutes Necessities Small portion of income Required now, rather than later Elasticity coefficient less than 1
When is a good inelastic? Few substitutes: Gasoline Necessity: Water and food Small portion of income: Pencils, pens, and paper
Draw the Graph: Inelastic Demand P D Q
Perfectly Inelastic Demand This curve is perfectly inelastic, meaning that Q does not respond at all to changes in price, E D = 0. Q is insensitive to changes in P. P D Q
Elasticity Along a Demand Curve P E D = Perfectly elastic (where intersects P) E D > 1 Elastic E D = 1 Unit elastic (at midpoint) Elasticity declines along this straight-line demand curve as we move towards the Q axis E D < 1 Inelastic Elastic Inelastic Q E D = 0 Perfectly inelastic (where intersects Q)
Calculating Elasticity: Using the Midpoint Formula One way to calculate elasticity is to use the midpoint formula E D = %ΔQ %ΔP = Q2 Q1 ½(Q2+Q1) P2 P1 ½(P2+P1) When given price and quantity for two points on a line, we can use the above formula (this is the way the textbook teaches it)
Calculating Elasticity: Using the Midpoint Formula P What is the price elasticity of demand between A and B? $20 $16 $12 B 20 C 22 24 Midpoint A D E D = = Q %ΔQ %ΔP 24 20 ½(24+20) 12 20 ½(12+20) = Q2 Q1 ½(Q2+Q1) P2 P1 ½(P2+P1) -.36 = = 0.36.50 Relatively inelastic
Calculating Elasticity: Using the Midpoint Formula Figure out the midpoint (sum the two numbers and divide by two): %ΔQ midpoint / %ΔP midpoint 4 / -8 22 16 = 0.36
Calculating Elasticity: Using the % Δ Formula Another way to calculate elasticity (when given two sets of points) is to use the percent change formula: Q2 Q1 Q1 (New) Q 2 minus (old) Q 1 divided by (old) Q 1 P2 P1 P1 (New) P 2 minus (old) P 1, divided by (old) P 2
Calculating Elasticity: Using the % Δ Formula Example: Price is $20, quantity is 20. Then, it changes to $12 and quantity of 24. %ΔQ %ΔP 24-20 20 12-20 20 4 20-8 20
Calculating Elasticity: Using the % Δ Formula Example: Price is $20, quantity is 20. Then, it changes to $12 and quantity of 24. = 4 20-8 20 = 4 20 X 20-8 4-8 1 0.5-2 Demand is relatively inelastic This would one way to show your work if asked by the College Board
Calculating Elasticity: Total Revenue Test You can also use the total revenue test to show how changes in price will affect total revenue (TR) Total Revenue = Price x Quantity
Calculating Elasticity: Total Revenue Test Elastic Demand: If E D > 1 Price increase causes TR to decrease Price decrease causes TR to increase Inelastic Demand: If E D < 1 Price increase causes TR to increase Price decrease causes TR to decrease Unit Elastic: If E D = 1 A change in price changes leaves TR unchanged
Calculating Elasticity: Total Revenue Test Let s use the same example: Price is $20, quantity is 20. Then, it changes to $12 and quantity of 24. Total Revenue = Price x Quantity $20 (20)= $400 (old P and Q) $12 (24) =$288 (new P and Q) As price decreased, so did TR. Demand is relatively inelastic.
Figuring Out Elasticity You can use the midpoint formula, the percent change formula, or the total revenue test to figure out elasticity of demand Know all three ways If asked to show your work on an FRQ, set-up the math and go from there using one of the methods Remember, the math on the AP exam must be doable without a calculator
More on Elasticity Price discrimination occurs when a firm separates the people with less elastic demand from those with more elastic demand Firms that price discriminate charge more to the individuals with inelastic demand and less to individuals with elastic demand Examples of price discrimination Last minute purchase of airfare New cars
Elasticity and Substitution Substitution makes demand (or supply) more or less elastic A general rule is: The more substitutes a good has, the more elastic its supply or demand If a good has substitutes, a rise in the price of the good will cause the consumer to shift consumption to substitute goods
Income Elasticity of Demand Income elasticity of demand measures the responsiveness of demand to changes in income E Income = % change in Demand % change in Income
Income Elasticity of Demand Normal goods: consumers buy more of these goods when income increases Normal goods: E income > 0 Necessity: 0 < E income < 1 (greater than 0 and less than 1) Luxury: E Income > 1
Income Elasticity of Demand Inferior goods: consumers buy fewer of these goods when income increases E Income < 0 (negative number)
Cross Price Elasticity of Demand Cross price elasticity of demand measures the responsiveness of demand to changes in prices of other goods E cross-price = % change in Demand % change in P of related good
Cross Price Elasticity of Demand Cross-price elasticity tells us if goods are substitutes or complements Here, positive and negative matters Substitutes: E cross-price > 0 (positive number) Complements: E cross-price < 0 (negative number)
Elasticity of Supply
Price Elasticity of Supply: Elastic Supply Elasticity of supply shows how sensitive producers are to a change in price Elasticity of supply is based on time limitations Producers need time to produce more goods
Price Elasticity of Supply: Elastic Supply Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price E S = % change in Quantity Supplied % change in Price This tells us exactly how quantity supplied responds to a change in price (elasticity is independent of units)
Elasticity of Supply Supply is elastic if the percentage change in quantity is greater than the percentage change in price Elastic supply=e S > 1 Supply is inelastic if the percentage change in quantity is less than the percentage change in price Inelastic supply =E S < 1
Drawing the Graph: Relatively Elastic Supply P S Q
Drawing the Graph: Inelastic Supply P S Q
Elasticity Along a Supply Curve At the point on the supply curve that intercepts the price axis, supply is perfectly elastic E s = Points become less elastic as you move out along the supply curve At the point on the supply curve that intercepts the quantity axis, supply is perfectly inelastic E s = 0 Points become more elastic as you move along the supply curve Supply is unit elastic if it intercepts the origin
Elasticity Along a Supply Curve P $10 $8 $6 E s = (perfectly elastic) $4 $2 E s = 1 Unit elastic (intercepts origin) E s = 0 Perfectly inelastic 2 4 6 8 10 Q
Calculating Elasticity: Midpoint Formula P What is the price elasticity of supply between A and B? $5.00 $4.75 $4.50 Midpoint A C B S E S = = %ΔQ %ΔP = 485 476 ½(485+476) 5 4.50 ½(5+4.50) Q2 Q1 ½(Q2+Q1) P2 P1 ½(P2+P1) 0.0187 = = 0.18 0.105 476 480.5 485 Q
Calculating Elasticity: Using the Midpoint Formula %ΔQ midpoint / %ΔP midpoint 9 /.50 480.5 4.75 = 0.18
Chapter Summary Elasticity is percentage change in quantity divided by percentage change in some variable that affects demand (supply). The most common elasticity is price. E D = E S = % change in Quantity Demanded % change in Price % change in Quantity Supplied % change in Price
Chapter Summary Five price elasticity of demand or supply terms are: Elastic E>1 Inelastic E<1 Unit elastic E=1 Perfectly inelastic E=0 Perfectly elastic E= Demand becomes less elastic as we move down along a demand curve The most important factor affecting the number of substitutes in supply is time. The longer the time interval, the more elastic is supply
Chapter Summary Factors affecting the number of substitutes in demand are: Time period Degree to which the good is a luxury Market definition Importance of the good in one s budget The more substitutes a good has, the greater its elasticity
Chapter Summary When a supplier raises price: If demand is inelastic, total revenue increases If demand is elastic, total revenue decreases If demand is unit elastic, total revenue remains constant Other important elasticities are: Income elasticity is the percentage change in demand divided by the percentage change in income Cross-price elasticity is the percentage change in demand divided by the percentage change in the price of a related good