ECON 100 Lecture 13 Monday, March 18

Announcements MIDTERM #1 is next week Tuesday March 26, at 6 30 P.M. Answers to PS #4 is posted on web page. Please start studying. A sample exam will be posted on webpage (this afternoon). I will have extended office hours next week. Monday (1 30 P.M. to 4 30 P.M.) Tuesday (10 A.M. to 12 00 and (1 30 P.M. to 4 30 P.M.).

Elasticity and Its Applications 5 Elasticity and Its Applications

Think about this: As the price of a good rises, the quantity demanded falls. How much does it fall? A little or a lot? How responsive is demand 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.

What makes the demand more elastic? Demand will be more elastic, if there are close substitutes.

Computing the Price Elasticity of Demand, EP The measure of responsiveness of quantity demanded to a change in price in a given situation is quantified by a single number EP that is computed as… The percentage change in quantity demanded divided by the percentage change in price.

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

Computing the EP Price = ₺2.00, QD = 10 Price = ₺2.20, QD = 8 Change in price (ΔP) is (2.20 – 2.00) = 0.20 % change in price is (0.20/2)x100 = 10 Change in QD (ΔQD) is (8 – 10) = –2. % change in QD is –(2/10)x100 = –20. EP is % change in QD divided by % change in P EP = –20/10 = –2.

One more time … When the price of good X ₺5, you buy 20 units. When the price is ₺4, you buy 23 units. Compute the price elasticity of demand at P = ₺5. Solution Change in price: (4.00 – 5.00) = -1.00 % change in price: (1.00/5.00)x100 = -20 Change in QD: (23 – 20) = 3. % change in QD is –(3/20)x100 = 15. EP is % change in QD divided by % change in P EP = 15/-20 = –3/4.

Examples: price elasticity of demand, 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. Suppose the price elasticity of demand for gold jewelry is -2.6. When the price of gold jewelry rises by 1%, the quantity demanded falls by 2.6%. Jewelry demand is price sensitive. Some examples.

More examples Remember that elasticity is a measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants. So there is also a price elasticity of supply. I am trying to give supply and demand about equal billing here. My text does elasticities before the detailed demand and supply discussions.

So, we can say things like… Price elasticity of supply for beef (dana eti) is 5. What we mean by this is that when the price of beef increases by 1%, the quantity supplied increases by 5%. So, beef supply is price sensitive.

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

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) PO = Current price of good X QO = Quantity demanded at that price ΔP = a small change in the current price ΔQ = the resulting change in quantity demanded

A little bit of mathematics Take the formula Rearrange the formula

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 1/slope = ΔQ/ΔP 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 Suppose we have the following information At P = PA quantity demanded is QA At P = PB quantity demanded is QB. Assume the demand curve is linear around PA and PB. Compute the price elasticity of demand at P = (PA+PB)/2 and (QA +QB)/2. This is what is called “the midpoint formula” for price elasticity of demand, which we will never ever use in Econ100. 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

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 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 sensitive to the price. When an 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 sensitive 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

Revenue and price elasticity

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

Pricing and revenue management, scenario I According to your marketing research department the price elasticity of demand for your product is -2. You need to increase revenues by 10% to meet your marketing goals. Your current price is 10 and you are selling 200 units per week. To achieve your goal, what should be your new price?

solution Current revenue is 10x200 = 2000, we want revenues to be 2200 (10% increase) EP = -2, if we lower the price by 1% quantity demanded will increase by 2% and as a result revenues will go up. Attempt #1: Lower P to 9, this is a 10% decline, Q will increase by 20% to 240. Revenue is 9x240 = 2160 ANSWER: P = 9 will increase revenue by (approximately) 10%.

Pricing and revenue management, scenario II According to your marketing research department the price elasticity of demand for your product is -1/2. You need to increase revenues by 10% to meet your marketing goals. Your current price is 10 and you are selling 200 units per week. To achieve your goal, what should be your new price?

solution Current revenue is 10x200 = 2000, we want revenues to be 2200 (10% increase) EP = -1/2, if we raise the price by 1% quantity demanded will decrease by 0.5%, and as a result revenues will go up. Attempt #1: Raise P to 11, this is a 10% increase, Q will decrease by 5% to 190. Revenue is 11x190 = 2090. Attempt #2: Raise P to 12, this is a 20% increase, Q will decrease by 10% to 180. Revenue is 12x180 = 2160. ANSWER: P = 12 will increase revenue by (approximately) 10%.

How Total Revenue Changes When Prices Changes: Inelastic Demand $3.00 P x Q = $240 (revenue) $1.00 P x Q = $100 (revenue) 80 100 Quantity

How Total Revenue Changes When Prices Changes: Elastic Demand $5.00 $4.00 Revenue = $200 Revenue = $100 20 50 Quantity

Elasticity and Total Revenue If demand is elastic at P = Po, a small increase in price leads to a decrease in total revenue. This is so because a 1% increase in price leads to a more than 1% decrease in quantity demanded. If demand is inelastic at P = Po, a small increase in price leads to an increase in total revenue. This is so because a 1% increase in price leads to a less than 1% decrease in quantity demanded.

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) 7-36 36

Mathematical proof (boring) TRo = PxQ Raise price by ΔP, Q declines by ΔP New revenue is TR1 = (P+ΔP)x(Q-ΔQ) = PQ + ΔPxQ -PxΔQ - ΔQxΔP The difference TR1 – TRo is ΔPxQ - PxΔQ - ΔQxΔP Ignore ΔQxΔP Ask : is ΔPxQ - PxΔQ > 0 (Can we raise TR by charging a higher price?) ΔPxQ - PxΔQ > 0  > 1 – (ΔQ/ΔP)(P/Q) > 0  1 – EP > 0  EP < 1.

A difficult question

What Limits to Using Money Prices to Buy and Sell? Gary Becker What Limits to Using Money Prices to Buy and Sell?

Gary Becker (1930) is a professor of economics and sociology at the University of Chicago. He won the Nobel Prize in Economics in 1992. He was one of the first economists to go into research questions that were traditionally considered topics belonging to sociology, including racial discrimination, crime, family organization, and drug addiction (see Rational addiction). According to the Beckerian view, many different types of human behavior can be seen as rational and utility maximizing, even altruistic behavior.

What is you view on this? Buy and sell human organs (kidneys)? Paying (or getting paid) for military service?

Other elasticities

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.

Summary In most markets, supply is more elastic in the long run than in the short run. The price elasticity of supply is calculated as the percentage change in quantity supplied divided by the percentage change in price.