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## Lecture 7 Elasticities

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Lecture 7Elasticities

- Elasticities are measures of responsiveness
- The response of one variable to changes in another
- Can be positive or negative
- If “close” to zero, relative unresponsive
- If “far” from zero, relatively responsive
- Calculated as the ratio of two percentage changes:
- (%∆Y)/(%∆X)
- Is said to be “the elasticity of Y with respect to X”

An exampleConsider this hypothetical relationship

- The elasticity of grades with respect

to time spent studying

- Likely positive
- η=(%∆G)/(%∆S)>0
- If η>1, we say “elastic”

(relatively responsive)

- If η<1, we say “inelastic”

(relatively unresponsive)

- Special case: η=1 “unit elastic”

Study Time

Grade

Another exampleAgain, a purely hypothetical example (you hope!)

- The elasticity of grades with

respect to wine consumption

- Likely negative (?)
- ε = (%∆G)/(%∆W) < 0
- If |ε|>1, we say “elastic”

(relatively responsive)

- If |ε| < 1, we say “inelastic”

(relatively unresponsive)

- Special case: |ε| = 1

“unit elastic”

Wine Consumption

0

Grades

The (own) Price Elasticity of DemandProbably the most important elasticity we’ll encounter

- Measures the responsiveness of quantity demanded to changes in their (own) price of a good
- Defined thus:
- ε = [(%∆in quantity demanded)/(%∆ in price)]
- Or ε = [(%∆Qd)/(%∆P)]
- Note that εmust be negative (Law of Demand)
- Sometimes convenient to refer to the absolute value, |ε|

Examples of demand elasticities

Suppose a 10% rise in the price of a good causes a 20% reduction in the quantity demanded

ε = -20%/+10% = -2

Suppose a 15% decline in the price of a good causes a 10% increase quantity demanded

ε = +10%/-15% = -0.67

Categories of demand elasticities“Elastic” demand

- Elastic demand
- |ε| > 1
- Qd relatively responsive to price
- Price change leads to spending

change in opposite direction

- Thus,
- Higher price → lower spending
- Lower price → higher spending

P

D

Q

Demand elasticity (con’t)“Inelastic” demand

- Inelastic demand
- |ε| < 1
- Qd relatively unresponsive to price
- Price change leads to spending

change in same direction

- Thus,
- Higher price → higher spending
- Lower price → lower spending

P

D

Q

Demand elasticities (con’t)“Unit elastic” demand

- Unit elastic demand
- |ε| = 1
- The knife-edge case
- Spending on the good is

independent of its price

- Whether price rises or falls, spending remains constant

P

Q

Why would you care?Some uses of demand elasticities

- Avoid mistakes
- A higher price is no guarantee of higher revenue
- Interpreting data
- Use of upc scanner to aid in pricing products
- Solve puzzles
- Property crime and the price of heroin
- The simple path to higher wealth:
- If revenue rises when price, ask yourself:

Why isn’t price even higher ?

Real World ElasticitiesCollected by Assorted Economists Over Time

Estimated Elasticity

Product or Service Short Run Long Run

Lamb 2.65 --

Bread 0.15 --

Tires 0.8 1.2

Auto Repairs 1.4 2.4

Radio & TV Repairs 0.5 3.8

Theatre & Opera 0.2 0.31

Movies 0.87 3.7

Foreign Travel by U.S. Residents 0.1 1.8

Public Transportation 0.6 1.2

Electricity 0.1 1.8

Jewelry & Watches 0.4 0.6

The Linear Demand CurveIllustrating that elasticity is not a slope

- Top portion is elastic
- Bottom portion is

inelastic

- The point in the middle

is unit elastic

ε = [(%∆Qd)/(%∆P)]

P

Elastic portion

>1

Unit elastic =1

Inelastic portion <1

Q

Total Revenue and Elasticity

Key to a firm is knowing if total revenue will rise or fall if product prices are increased or decreased.

Price/Software Q Software Sold Own Price Elas. T.R.

$ 0 80 0.00 $ 0

5 70 - 0.14 350

10 60 - 0.33 600

15 50 - 0.60 750

20 40 - 1.00 800

25 30 - 1.67 750

30 20 - 3.00 600

35 10 - 7.00 350

40 0 - 0

Total Revenue and Elasticity

We see if demand is elastic, an increase (decrease) in price will lead to a decrease (increase) in total revenue. If demand is inelastic, just the opposite. Total Revenue is maximized when elasticity is one.

Total

Revenue

Price

Elastic

$800

Unit Elasticity

$20

Inelastic

40

Quantity

40

Quantity

Marginal Revenue

Other demand-related elasticities

- Cross-price elasticity of demand
- Measure of responsiveness of demand to changes in prices of substitutes and complements:

(%∆ Dx)/(%∆ Py)

- If positive, goods are substitutes, by definition
- If negative, goods are complements, by definition
- Income elasticity of demand
- Measure of responsiveness of demand to changes in income:

(%∆ Dx)/(%∆ l)

- If positive, good is normal, by definition (>1, superior)
- If negative, good is inferior, by definition

Estimates of Cross Elasticities

- These are estimates of cross elasticities between various goods (goods that are substitutes) in the U.S.:

Electricity and natural gas 0.20 (weak substitutes)

Beef and Pork 0.20

Natural gas and fuel oil 0.44

Margarine and butter 0.81 (strong substitutes)

Estimates of Income Elasticities

- These are estimates of income elasticities from different studies in the U.S.:

Flour -0.36 (inferior good)

Margarine -0.20 (inferior good)

Milk and cream 0.07 (little change)

Dental Services 1.41 (highly responsive to

Restaurant meals 1.48 income increases)

Elasticity of SupplyLikely second most important elasticity

- Measures the responsiveness of quantity supplied to changes in the (own) price of a good
- Defined thus:

η = [(%∆ in quantity supplied)/(%∆ in price)]

Or η = [(%∆Qs)/(%∆P)]

- Note that η is positive, because supply curves are positively sloped

An example

- Suppose the supply of unskilled labor in some geographic region is known to be 0.8
- Suppose wage rises by 20% due to an increase in demand
- What will be impact on employment of unskilled workers in region?
- η = (%∆Qs)/(%∆P)
- We know η and %∆P, and seek %∆Qs
- Rearranging, %∆Qs = (+0.8)(+20) = +16%
- Thus, employment will rise 16%

Questions About Elasticity

- In the past 40 years, the percentage of income Americans spend on food has fallen while incomes have risen.
- What does this tell us about the income elasticity of demand for food?

Elasticity Questions

Story in newspaper said: “Detroit bus system is losing money. It wants to raise fares but not cut its schedule.”

Two questions:

- For revenue to rise as a result of fare hike, what must be true about demand elasticity?
- If fare is raised, what will happen to schedule?

Elasticities

- A marketing study estimated the elasticity of demand for all products of a wide range of companies to be

-0.985.

What does that mean?

Elasticity

- A study of gasoline sales found that price elasticity for regular gasoline was -6 and for premium gasoline was -3.

What does that mean?

Changing Elasticity

- For many years, Kodak film completely dominated the U.S. market and had a large majority of the world market.
- What happened to price elasticity when Fuji became a major competitor and 3-M entered the store-brand market?

Is the Demand for Prescription Drugs Infinite?

- It is often asserted that prescription drugs can be sold for any price because they are patented (protected against copying) and people need them to live. What would you suspect the elasticity for drugs is? What are the substitutes for drugs?

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