ECON 100 Lecture 12 Wednesday, March 12

Announcements MIDTERM #1 is on Saturday March 22, at 10 A.M. Only material covered in lectures will be on the midterm. Send me an email if you will need a make up exam (must have a valid excuse!) Answers to PS #4 are posted on webpage. PS#5 is on its way. Sample exam(s) will be posted on webpage (later this week). I will have extended office hours next week on Thursday and Friday.

Elasticity and Its Applications 5 Elasticity and Its Applications

“As the price of a good rises, the quantity demanded falls “As the price of a good rises, the quantity demanded falls. ” But how much does it fall? A little or a lot?

How responsive is quantity demanded to changes in the price?

The price elasticity of demand Price elasticity of demand is a “measure” of how responsive the quantity demanded is to a change in price.

More generally… Elasticity is a measure of the responsiveness of the quantity demanded or the quantity supplied to a change in one of their determinants.

In today’s lecture we will focus on the price elasticity of demand.

…has no effect on the quantity demanded. Case 1 Price Demand $5.00 $4.00 The increase in price… 100 Quantity …has no effect on the quantity demanded.

Case 2 Demand 50 100 $4.25 $4 a small increase in price… 50 100 Quantity leads to a large decrease in quantity demanded.

Case 1: “Demand is inelastic” Case 2: “Demand is elastic .”

What makes the demand more elastic? Demand tends to be more elastic if, … there are close substitutes. the market is more narrowly defined (food versus milk). more time is allowed after the price change. the good is a luxury. (Necessities have inelastic demand.)

Substitutes? The patent expires on a brand-name drug and five generic drugs come on the market. As a result, the demand for the original drug becomes… more price elastic less price elastic The demand for the original drug becomes more price elastic.

Demand for fresh fruit v. demand for green apples The more broad (general) the classification, the fewer substitutes there are and this makes demand less elastic (inelastic) The price elasticity of demand is higher for “lettuce” than for “food.” vs. Instructor Notes:

Time is on our side… Less time to adjust means lower elasticity Over time consumers can adjust their behavior by finding substitutes (making demand more elastic). Instructor Notes:

Luxuries vs. necessities Demand for necessities is less price elastic. Demand for luxuries is more price elastic. Instructor Notes:

The Price Elasticity of Demand, EP The degree of responsiveness of quantity demanded to a change in price is quantified in a single number EP EP is computed as follows: The percentage change in quantity demanded divided by the percentage change in price.

Computing the Price Elasticity of Demand The formula: When the price of ice cream is ₺2, quantity demanded is 10 units (cones of ice-cream). When the price of ice-cream is ₺2.20, quantity demanded is 8 units. Please compute the price elasticity of demand at P = ₺2!

How to calculate a percentage change Step 1: Calculate the change (the new value minus the old value), Step 2: Divide that change by the old value (you will get a decimal number), Step 3: Multiply by 100 and add the "%" sign. Note: if new value > old value, it is a percentage increase, otherwise it is a decrease.

Computing the EP When P = ₺2.00,  QD = 10 When P = ₺2.20,  QD = 8 Change in QD (ΔQD) is (8 – 10) = –2. % change in QD is –(2/10)x100 = –20%. Change in price (ΔP) is (2.20 – 2.00) = +0.20 % change in price is (0.20/2)x100 = +10% EP = {% change in QD}/{% change in P} EP = –20/10 = –2.

Learning activity

When P = ₺5, you buy 20 units. When P = ₺4, you buy 23 units When P = ₺5, you buy 20 units. When P = ₺4, you buy 23 units. Please compute the price elasticity of demand at P = ₺5.

When P = ₺5, you buy 20 units. When P = ₺4, you buy 23 units. Change in QD: (23 – 20) = 3. % change in QD is (‒3)/20x100 = 15%. Change in price: (4.00 – 5.00) = ‒1.00 % change in price: (1.00/5.00)x100 = ‒20% EP = {% change in QD}/{% change in P} EP = 15/(‒20) = –3/4.

What does the EP number mean? Suppose the price elasticity of demand for gasoline is -0.2. This means: When the price of gasoline rises by 1%, the quantity demanded falls by 0.2% Gasoline demand is not very price sensitive. Some examples.

What does the EP number mean? Suppose the price elasticity of demand for gold jewelry is -2.5. This means: When the price of gold jewelry rises by 5%, the quantity demanded falls by 12.5%. Jewelry demand is price sensitive. Some examples.

Please note that Because price and quantity are negatively related (price↑, QD↓, and price ↓, QD↑), the price elasticity EP is always negative. We will refer to the price elasticity of demand EP by its absolute value (we will ignore the negative sign).

Elastic vs. inelastic demand When the price elasticity EP is between 0 and 1 in absolute value, we say that demand is inelastic. Inelastic demand means that the quantity demanded is not very responsive to the price. When the price elasticity EP is greater than 1 in absolute value, we say that demand is elastic. Elastic demand means that the quantity demanded is responsive to the price.

One more time Unit elastic: Price elasticity │EP│ = 1 1 2 3 4 5 6 Unit elastic ??? Inelastic Elastic │EP│ Unit elastic: Price elasticity │EP│ = 1 Inelastic: Price elasticity │EP│ < 1 Elastic: Price elasticity │EP│ > 1

Some real price elasticity numbers On average, in the United States, a 10% increase in the price of water can be expected to diminish demand in the urban residential sector by about 3 to 4 %. This is equivalent to saying that U.S. residential water price elasticity is in the range of –0.3 to –0.4. ….

Price Elasticity Estimates in New England

Oil price demand elasticity: on More recent numbers collected from scientific studies by the Bank of England (6/2008) Price elasticity is close to zero in short term. It increases with time, but remains low. www.theoildrum.com/node/4397

More computations! Learning activity #1

The table shows the prices of good X and good Y, the annual income of the consumer, and the quantities of good X consumed during a six year period. Year PX QX PY Income 2007 100 80 50 20,000 2008 110 90 40 18,000 2009 2010 2011 2012 25,000 Which pair of years will you use to calculate the price elasticity of demand for good X? Why? What is the price elasticity of demand for X?

Solution In 2008 : P = 110, Q = 90 In 2009 : P = 90, Q = 100 The percentage change in Q is about +10% (100–90)/90 The percentage change in P is about –20% (90–110)/110 EP = % change in Q divided by % change in P EP = –1/2 (inelastic)

Price elasticity and the linear demand curve The price elasticity EP varies (= EP is NOT constant) along a linear demand curve. This will be shown on the next few slides.

A Linear Demand Curve A B 7 6 5 4 3 2 1 2 4 6 8 10 12 14 Price 2 4 6 8 10 12 14 Quantity

The correct question: What is the price elasticity of demand at price Po? (Po is a specific price for example ₺28/kg –for beef)

A Linear Demand Curve Is this demand curve elastic or inelastic? A B Price 7 A B Is this demand curve elastic or inelastic? Is this demand curve elastic or inelastic at P = 6? Is this demand curve elastic or inelastic at P = 2? 6 5 4 3 2 1 2 4 6 8 10 12 14 Quantity

A little bit of mathematics Take the formula and rearrange it and rearrange it one more time

What is this ? (It is related to the slope of the demand curve.) Price decreases from P1 to P2. ΔP = (P2–P1) = the change in price. (ΔP < 0) Quantity demanded increases from Q1 to Q2. ΔQ = (Q2–Q1) = the change in quantity demanded. slope = ΔP/ΔQ ΔQ/ΔP = 1/slope Elasticity EP = (1/slope)x(P/Q) Price Quantity Demand P1 P2 DP Q1 Q2 DQ

A Linear Demand Curve Price 7 Elasticity is larger than 1. 6 5 4 Elasticity is smaller than 1. 3 2 1 2 4 6 8 10 12 14 Quantity

which we also write as EP = [1/slope]x(P/Q) Slope = ‒½ 1/slope = ‒2 EP at P = 6 is ‒2x(6/2) = ‒6 EP at P = 3.5 is ‒2x(3.5/7) = ‒1 EP at P = 1 is ‒2x(1/12) = ‒1/6

The “midpoint formula” for price elasticity of demand I need to teach them this formula. Sorry.

A Linear Demand Curve A B Price 7 A B Midpoint formula means computing EP at point C 6 5 4 3 2 1 2 4 6 8 10 12 14 Quantity

Revenue and price elasticity

Elasticity of Demand and Total Revenue A firm’s revenues are equal to price per unit times quantity sold. Revenue = Price x Quantity The elasticity of demand directly influences revenues when the price of the good changes. Instructor Notes:

Total Revenue and the Price Elasticity of Demand Total revenue is the amount paid by the buyers and received by the sellers of a good. Computed as the price times quantity sold. TR = P x Q

Total Revenue Price Demand $4.00 P x Q = $400 (revenue) 100 Quantity

Elasticity and Total Revenue If demand is elastic at P = Po, a small increase in price will lead to a decrease in total revenue. Raise P by 10%  QD will decline by 20%  TR = PxQ will decline. If demand is inelastic at P = Po, a small increase in price will lead to an increase in total revenue. Raise P by 10%  QD will decline by 5%  TR = PxQ will rise.

Relationship Between Elasticity and Total Revenue Price Rise Price Decline Elastic (EP > 1) TR decreases TR increases Unit Elastic (EP = 1) TR constant Inelastic (EP < 1) 7-50 50

Bridge Toll Example Current toll for the George Washington Bridge is $2.00/trip. Suppose the quantity demanded is 100,000 trips/hour. If the price elasticity of demand for bridge trips is EP = -- 0.5, what is the effect of a 10% toll increase on revenues? Your example. As of 2013, the George Washington Bridge carries approximately 102 million vehicles per year. It is the world's busiest motor vehicle bridge.

FSM and Boğaziçi Price AKS ARALIĞI 3.20 m’DEN KÜÇÜK İKİ AKSLI ARAÇLAR otomobiller, motosiklet Aks aralığı 3.20 m.’den küçük kamyon, kamyonet, ve minibüsler dahil TL4.25! Quantity … Aralık ayında (2011), Boğaziçi ve Fatih Sultan Mehmet köprülerinden 13.3 milyon araç geçiş yaparken,…

Bridge Toll increase with EP = -0.5 inelastic demand Price elasticity of demand = 0.5 Toll increase of 10% implies a 5% decline in the quantity demanded. Trips fall to 95,000/hour. Total revenue rises to $209,000/hour (= 95,000 x $2.20). ditto

Learning activity #2

Demand curve A and demand curve B are parallel Demand curve A and demand curve B are parallel. At price P = P0 a 1% increase in the price leaves the total revenue unchanged for demand curve A. How will a 1% increase in the price effect total revenue for demand curve B at P = P0?

There are a few additional slides on price elasticity of supply, income elasticity of demand etc., and three slides on computing the slope of a line. End of the lecture

Other Demand Elasticities Income elasticity of demand The percentage change in the quantity demanded divided by the percentage change in income. Income elasticity of demand is +2 means that when my income increases by 1% quantity demanded increases by 2%. Cross-Price elasticity of demand The percentage change in the quantity demanded divided by the percentage change in the price of the second (substitute or complement) good.

Price Elasticity Of Supply Price elasticity of supply is a measure of how much the quantity supplied of a good responds to a change in its price. It is computed as the percentage change in quantity supplied divided by the percent change in the price.

The Price Elasticity of Supply and Its Determinants Ability of sellers to change the amount of the good they produce. Beach-front land is inelastic. Books, cars, or manufactured goods are elastic. Time period. Supply is more elastic in the long run.

The other elasticities explained in more detail

Other Demand Elasticities Income elasticity of demand measures how much the quantity demanded of a good responds to a change in consumers’ income. It is computed as the percentage change in the quantity demanded divided by the percentage change in income.

Other Demand Elasticities Types of Goods Normal Goods have positive income elasticity Inferior Goods have negative income elasticity Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods.

Other Demand Elasticities Goods consumers regard as necessities tend to be income inelastic Examples include food, fuel, clothing, utilities, and medical services. Goods consumers regard as luxuries tend to be income elastic. Examples include sports cars, furs, and expensive foods.

Other Demand Elasticities Cross-Price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of another good. It is computed as the percentage change in the quantity demanded divided by the percentage change in the price of the second good.

PRICE ELASTICITY OF SUPPLY Price elasticity of supply is a measure of how much the quantity supplied of a good responds to a change in the price of that good. Price elasticity of supply is the percentage change in quantity supplied given a percent change in the price.

The Price Elasticity of Supply and Its Determinants Ability of sellers to change the amount of the good they produce. Beach-front land is inelastic. Books, cars, or manufactured goods are elastic. Time period. Supply is more elastic in the long run.

Computing the Price Elasticity of Supply The price elasticity of supply is computed as the percentage change in the quantity supplied divided by the percentage change in price.

Computing the Price Elasticity of Supply Suppose an increase in the price of milk from $2 to $2.20 a litre raises the amount that dairy farmers produce from 10000 to 12 000 litre (per month). The price elasticity of supply at P = 2 is calculated as follows The percent change in price is (2.20 - 2.00)/2.00x100 = 10% The percent change in quantity supplied is (12 000 - 10000) / 10 000 x 100 = 20% 20% = 2.0 Price elasticity of supply = 10%

Perfectly Inelastic Supply Price E = 0 Supply $5.00 100 $4.00 1. An increase in price… Quantity 2. …leaves the quantity supplied unchanged.

Inelastic Supply E < 0 Supply 100 110 $5.00 $4.00 Price Quantity 1. A 25% increase in price… 100 110 Quantity 2. …leads to a 10% increase in quantity supplied.

Unit Elastic Supply E = 1 Supply 100 125 $5.00 $4.00 Price Quantity 1. A 25% increase in price… 100 125 Quantity 2. …leads to a 25% increase in quantity supplied.

Elastic Supply E > 1 Supply 100 200 $5.00 $4.00 Price Quantity 1. A 25% increase in price… 100 200 Quantity 2. …leads to a 100% increase in quantity supplied.

Perfectly Elastic Supply Price E =  1. At any price above $4, quantity supplied is infinite. $4.00 Supply 2. At exactly $4, producers will supply any quantity. 3. At any price below $4, quantity supplied is zero. Quantity

How the price elasticity of supply can vary $15 525 Elasticity is less than 1 $12 500 Elasticity is greater than 1 $4 200 $3 100 Quantity

Summary Price elasticity of demand measures how much the quantity demanded responds to changes in the price. Price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price. If a demand curve is elastic, total revenue falls when the price rises. If it is inelastic, total revenue rises as the price rises.

Summary The income elasticity of demand measures how much the quantity demanded responds to changes in consumers’ income. The cross-price elasticity of demand measures how much the quantity demanded of one good responds to the price of another good. The price elasticity of supply measures how much the quantity supplied responds to changes in the price.

Appendix

Graphing: a brief review Slope of a line Ratio of the vertical distance covered To the horizontal distance covered As we move along the line Δ (delta) = change in a variable The “rise” (change in y) divided by the “run” (change in x).

Graphing: a brief review Slope of a line Fairly flat upward-sloping line Slope = small positive number Steep upward-sloping line Slope = large positive number Downward sloping line Slope = negative number Horizontal line Slope = zero Vertical line Infinite slope

Calculating the slope of a line Price of Novels 1 2 3 4 5 6 7 8 9 10 $11 Demand, D1 (21, $6) (13, $8) 6-8=-2 13 21-13=8 21 Quantity of novels purchased 5 15 10 25 20 30 To calculate the slope of the demand curve, we can look at the changes in the x- and y-coordinates as we move from the point (21 novels, $6) to the point (13 novels, $8). The slope of the line is the ratio of the change in the y-coordinate (–2) to the change in the x-coordinate (+8), which equals –1⁄4.