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Chapter 6 Elasticity

The Elasticity Concept

Own Price Elasticity of Demand

The Midpoint Method

Elasticity and Total Revenue

Elasticity and Marginal Revenue

Cross-Price Elasticity

Income Elasticity

The Price Elasticity of Supply

Elasticity Applications

Controversy: Gambling

Summary

Review Questions

BA 210 Lesson I.7 Elasticity

The Elasticity Concept

- How responsive is variable “G = f(S) ” to a change in variable “S”?

(There, %D reads “percent change”.)

- One good property: Percentages do not depend on units of measure: $1 to $2 is a 100% increase in price, and 100 cents to 200 cents is also a 100% increase.
- The sign of elasticity indicates a relationship:
- If EG,S > 0, then S and G are positively (or directly) related.
- If EG,S < 0, then S and G are negatively (or inversely) related.
- If EG,S = 0, then S and G are unrelated.

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

Own Price Elasticity of Demand

- Negative according to the “law” of demand.
- Elastic:
- Inelastic:
- Unit elastic:

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

Some Estimated Price Elasticities of Demand

Good Price elasticity

Inelastic demand

- Eggs -0.1
- Beef -0.4
- Stationery -0.5
- Gasoline -0.5

Elastic demand

- Housing -1.2
- Restaurant meals -2.3
- Airline travel -2.4
- Foreign travel -4.1

|Price elasticity of demand| < 1

|Price elasticity of demand| > 1

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

- Predicting Revenue Change from One Product
- Suppose that a firm sells only one good. If the price of X changes, then total revenue will change by:
- In that equation, the term %DPX is the fractional percent change in price (for example, 1% = .01).
- For example:
- Suppose you only sell burgers.
- Suppose revenue RX from burgers is $100.
- Suppose the own price elasticity were zero.
- What is the effect on revenue of increasing burger price 10%?
- DR = ($100(1+0)) x (0.10) = $10.

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

- Aggregation
- Goods can sometimes be aggregated, like “cars”
- Goods can always be disaggregated, like “Honda cars” and “Toyota cars”
- Goods can only be aggregated when disaggregation makes perfect substitutes for consumers, like “Honda cars” and “Toyota cars”.

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

Perfectly Elastic (Price Taking) and Perfectly Inelastic Demand --- Is Farmer John sausage perfectly elastic? Is medical care perfectly inelastic?

Price

Price

D

D

Quantity

Quantity

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

Substitution and Income Effects of a Price Increase

- The substitution effect is decreased quantity demanded because the good is not as good of a deal. --- Examples?
- The income effect is decreased purchasing power (assuming you do not work for a company making the good), and so decreased quantity demanded if the good is normal. --- Significant Examples? Housing? Salt?
- The gross effect is the substitution plus income effect.

BA 210 Lesson I.7 Elasticity

Own Price Elasticity of Demand

Factors Affecting Own Price Elasticity

- Available Substitutes
- The more substitutes available for a good, the bigger the substitution effect and the more elastic the demand. --- Medical care?
- Time
- Demand becomes more elastic over time as consumers find and use available substitutes. --- Examples? Gasoline? Alternatives?
- Expenditure Share
- Among normal goods, because of the income effect, the larger the expenditure on a good, the larger the income effect the more elastic the demand. --- Housing?

BA 210 Lesson I.7 Elasticity

Using the midpoint method

- The midpoint method is a more accurate technique for calculating any percent change.
- In this technique, calculate changes in a variable compared with the average, or midpoint, of the starting and final values.

BA 210 Lesson I.7 Elasticity

Price of crossing

Total Revenue by Area

$0.90

Total revenue = price x quantity = $990

D

0

1,100

Quantity of crossings (per day)

BA 210 Lesson I.7 Elasticity

Elasticity and Total Revenue

- When a seller raises the price of a good, there are two countervailing effects on total revenue (except in the rare case of a good with perfectly elastic or perfectly inelastic demand):
- A price effect: After a price increase, each unit sold sells at a higher price, which tends to raise revenue.
- A quantity effect: After a price increase, fewer units are sold, which tends to lower revenue.
- The gross effect on revenue will depend on elasticity

BA 210 Lesson I.7 Elasticity

Price of crossing

Effect of a Price Increase on Total Revenue

Price effect of price increase: higher price for each unit sold

Quantity effect of price increase: fewer units sold

$1.10

C

0.90

B

A

D

0

900

1,100

Quantity of crossings (per day)

BA 210 Lesson I.7 Elasticity

Own-Price Elasticity and Total Revenue

- Elastic
- E < -1, so 1+E < 0, so %DP > 0 implies DR < 0.
- Increased price implies decreased total revenue.
- Lower price to increase revenue, but profits may decrease because supply costs increase.

BA 210 Lesson I.7 Elasticity

Own-Price Elasticity and Total Revenue

- Inelastic
- E > -1, so 1+E > 0, so %DP > 0 implies DR > 0.
- Increased price implies increased total revenue.
- Increase price to increase profit (increase revenue and decrease supply cost).
- It is most profitable to have inelastic (rather than elastic) demand, so distinguish your product. --- Examples? --- How can you distinguish gasoline? (Chevron with Techron.)

BA 210 Lesson I.7 Elasticity

Own-Price Elasticity and Total Revenue

- Unit Elastic
- Total revenue is maximized (unaffected by small price changes) at the point where demand is unit elastic.

BA 210 Lesson I.7 Elasticity

Elasticity, Total Revenue and Linear Demand

P

TR

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80

800

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Q

Q

0

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20

BA 210 Lesson I.7 Elasticity

Elasticity, Total Revenue and Linear Demand

P

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1200

60

800

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Q

Q

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BA 210 Lesson I.7 Elasticity

Elasticity, Total Revenue and Linear Demand

P

TR

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80

1200

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Q

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BA 210 Lesson I.7 Elasticity

Elasticity, Total Revenue and Linear Demand

P

TR

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80

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60

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800

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Q

Q

0

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BA 210 Lesson I.7 Elasticity

Where quantity is less than 25, a price decrease causes a quantity increase and an increase in revenue. So demand is elastic since price and revenue are negatively related.

P

TR

100

Elastic

80

1200

60

40

800

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Q

Q

0

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Elastic

BA 210 Lesson I.7 Elasticity

Where quantity is greater than 25, a price decrease causes a quantity increase and a decrease in revenue. So demand is inelastic since price and revenue are positively related.

P

TR

100

Elastic

80

1200

60

Inelastic

40

800

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Q

Q

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Elastic

Inelastic

BA 210 Lesson I.7 Elasticity

Unit elasticity divides elasticity from inelasticity.

P

TR

100

Unit elastic

Elastic

Unit elastic

80

1200

60

Inelastic

40

800

20

30

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50

Q

Q

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Elastic

Inelastic

BA 210 Lesson I.7 Elasticity

Elasticity and Marginal Revenue

Marginal Revenue is the extra revenue from increasing output. It is positive when output is less than 25 and demand is elastic, and is negative when output is greater than 25 and demand is inelastic.

P

TR

100

Unit elastic

Elastic

Unit elastic

80

1200

60

Inelastic

40

800

20

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50

Q

Q

0

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Elastic

Inelastic

BA 210 Lesson I.7 Elasticity

Elasticity and Marginal Revenue

For a linear demand curve, the marginal revenue curve has the same intercept on the price axis but twice the slope. So

- MR > 0, where demand is elastic
- MR = 0, where demand is unit elastic
- MR < 0, where demand is inelastic

P

100

Elastic

Unit elastic

80

60

Inelastic

40

20

Q

40

50

0

10

20

MR

BA 210 Lesson I.7 Elasticity

Summary

- Elastic
- Increased price implies decreased total revenue.
- Decreased price implies increased total revenue.
- Given the law of demand, increased quantity (decreased price) implies increased total revenue.
- Marginal revenue is positive.
- Inelastic
- Increased price implies increased total revenue.
- Decreased price implies decreased total revenue.
- Given the law of demand, increased quantity (decreased price) implies decreased total revenue.
- Marginal revenue is negative.
- Unit elastic is neither elastic nor inelastic so MR = 0.

BA 210 Lesson I.7 Elasticity

- Cross Price Elasticity of Demand
- If EQX,PY > 0, then X and Y are gross substitutes because as the price of good Y increases, the demand for good X increases. This can happen from either of two effects.
- Good X substitutes for Good Y. For example, as the price of Y = apples increases, the demand for X = oranges increases because consumers substitute oranges for apples.
- Good X is needed because it is affordable. For example, as the price of Y = Pepperdine University education increases, Pepperdine students must economize and consume more affordable goods, like X = Ramain Noodles.
- Since there are two effects, their sum is called the gross effect.

BA 210 Lesson I.7 Elasticity

- Cross Price Elasticity of Demand
- If EQX,PY< 0, then X and Yare gross complements because as the price of good Y increases, the demand for good X decreases. This can happen from either of two effects.
- Good Y complements Good X. For example, as the price of Y = bread increases, the demand for X = butter decreases because consumers need less butter when there is less bread.
- Good X is not wanted because it is unaffordable. For example, as the price of Y = Pepperdine University education increases, Pepperdine students must economize and consume fewer unaffordable goods, like X = Filet Mignon.
- Since there are two effects, their sum is called the gross effect.

BA 210 Lesson I.7 Elasticity

Income ElasticityIf EQX,M> 0, then X is a normal good. Higher income M implies higher demand.If EQX,M < 0, then X is a inferior good. Higher income M implies lower demand.

BA 210 Lesson I.7 Elasticity

The Price Elasticity of Supply

The Price Elasticity of Supply is the percent change in supply divided by the percent change in price. It is always positive.BA 210 Lesson I.7 Elasticity

Business Applications of Elasticity

- Pricing and managing cash flows.
- Effect of changes in competitors’ prices.

BA 210 Lesson I.7 Elasticity

Example 1: Pricing and Cash Flows

- According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64.
- AT&T needs to boost revenues in order to meet it’s marketing goals.
- To accomplish this goal, should AT&T raise or lower it’s price?

BA 210 Lesson I.7 Elasticity

Answer: Lower price.

- Since demand is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T.

BA 210 Lesson I.7 Elasticity

Example 2: Quantifying the Change

- If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

BA 210 Lesson I.7 Elasticity

Example 3: Effect of a change in a competitor’s price

- According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06.
- If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

BA 210 Lesson I.7 Elasticity

- Answer
- AT&T’s demand would fall by 36.24 percent.

BA 210 Lesson I.7 Elasticity

A lottery is a form of gambling which involves the drawing of lots for a prize. Some governments outlaw it, while others endorse it to the extent of organizing a national or state lottery. At the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in many countries, including the U.S.A. and most of Europe. This remained so until after World War II. In the 1960s casinos and lotteries began to appear throughout the world as a means to raise revenue in addition to taxes.

BA 210 Lesson I.7 Elasticity

Lotteries and gambling are an effective way to raise revenue because there are few substitutes. As the government taxes any good, it raises the price, and so consumers lower demand, which lowers tax revenue. But with few substitutes, the demand for gambling is very inelastic, and so consumers’ demand is only slightly lower, which means tax revenue is only slightly lower.

Lotteries and gambling are controversial, however, if you believe most gamblers are irrational. If irrational, a gambler could hurt themselves by saying yes to gambling when they should have said no.

BA 210 Lesson I.7 Elasticity

Summary

- Elasticityis a general measure of responsiveness that can be used to answer various questions.
- The price elasticity of demand — the percent change in the quantity demanded divided by the percent change in the price (dropping the minus sign) — is a measure of the responsiveness of the quantity demanded to changes in the price.

BA 210 Lesson I.7 Elasticity

Summary

- The responsiveness of the quantity demanded to price can range from perfectly inelastic demand, where the quantity demanded is unaffected by the price, to perfectly elastic demand, where there is a unique price at which consumers will buy as much or as little as they are offered. When demand is perfectly inelastic, the demand curve is vertical; when it is perfectly elastic, the demand curve is horizontal.
- The price elasticity of demand is classified according to whether it is more or less than 1. If it is greater than 1, demand is elastic; if it is exactly 1, demand is unit-elastic; if it is less than 1, demand is inelastic. This classification determines how total revenue, the total value of sales, changes when the price changes.

BA 210 Lesson I.7 Elasticity

Summary

- The price elasticity of demand depends on whether there are close substitutes for the good, whether the good is a necessity or a luxury, the share of income spent on the good, and the length of time that has elapsed since the price change.
- The cross-price elasticity of demand measures the effect of a change in one good’s price on the quantity of another good demanded.
- The income elasticity of demand is the percent change in the quantity of a good demanded when a consumer’s income changes divided by the percent change in income. If the income elasticity is greater than 1, a good is income elastic; if it is positive and less than 1, the good is income-inelastic.

BA 210 Lesson I.7 Elasticity

Summary

- The price elasticity of supply is the percent change in the quantity of a good supplied divided by the percent change in the price. If the quantity supplied does not change at all, we have an instance of perfectly inelastic supply; the supply curve is a vertical line. If the quantity supplied is zero below some price but infinite above that price, we have an instance of perfectly elastic supply; the supply curve is a horizontal line.
- The price elasticity of supply depends on the availability of resources to expand production and on time. It is higher when inputs are available at relatively low cost and the longer the time elapsed since the price change.

BA 210 Lesson I.7 Elasticity

- Review Questions
- You should try to answer some of the following questions before the next class.
- You will not turn in your answers, but students may request to discuss their answers to begin the next class.
- Your upcoming Exam 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.

BA 210 Lesson I.7 Elasticity

- Follow the link
- http://faculty.pepperdine.edu/jburke2/ba210/PowerP1/Set6Answers.pdf
- for review questions for Lesson I.7 that practices these skills:
- Use the midpoint method for calculating percent change.
- Compute price elasticity of demand.
- Identify elastic and inelastic demand according to the price elasticity of demand.
- For elastic demand, apply the negative relation between price and revenue.
- For inelastic demand, apply the positive relation between price and revenue.
- Remember demand is more elastic when there are more substitutes or closer substitutes.
- Compute the price elasticity of supply.
- Compute cross-price elasticities of demand.
- Relate cross-price elasticities of demand to gross substitutes and gross complements.
- Identify elastic and inelastic portions of a linear demand curve.
- Compute income elasticity of demand.

BA 210 Lesson I.7 Elasticity

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