Elasticity slide 1

ELASTICITY

Elasticity is the concept economists use to describe the steepness or flatness of curves or functions.

In general, elasticity measures the responsiveness of one variable to changes in another variable.

Elasticity slide 2

PRICE ELASTICITY OF DEMAND

Measures the responsiveness of quantity demanded to changes in a good’s own price.

The price elasticity of demand is the percent change in quantity demanded divided by the percent change in price that caused the change in quantity demanded.

Elasticity slide 3

FACTS ABOUT ELASTICITYIt’s always a ratio of percentage changes.

That means it is a pure number -- there are no units of measurement on elasticity.

Price elasticity of demand is computed along a demand curve.

Elasticity is not the same as slope.

Elasticity slide 4

LOTS OF ELASTICITIES!

THERE ARE LOTS OF WAYS TO COMPUTE ELASTICITIES. SO BEWARE! THE DEVIL IS IN THE DETAILS.

MOST OF THE AMBIGUITY IS DUE TO THE MANY WAYS YOU CAN COMPUTE A PERCENTAGE CHANGE. BE ALERT HERE. IT’S NOT DIFFICULT, BUT CARE IS NEEDED.

Elasticity slide 5

What’s the percent increase in price here because of the shift in supply?

pE = $2

QE

S

D

Q

price

S'

pE = $2.50

CIGARETTE MARKET

Elasticity slide 6

IS IT:

A) [.5/2.00] times 100?

B) [.5/2.50] times 100?

C) [.5/2.25] times 100?

D) Something else?

Elasticity slide 7

From time to time economists have used ALL of these measures of percentage change --

including the “Something else”!

Notice that the numerical values of the percentage change in price is different for each case:

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Elasticity slide 9

Economists usually use the “midpoint” formula (option C), above) to compute elasticity in cases like this in order to eliminate the ambiguity that arises if we don’t know whether price increased or decreased.

Elasticity slide 10

Using the Midpoint Formula

Elasticity =

% change in p = times 100.

% change in p =

For the prices $2 and $2.50, the % change in p is approx. 22.22 percent.

Pin change %

Q in change %

Paverage

Pin change

100 )P

P(

MEAN

Elasticity slide 11

What’s the percent change in Q due to the shift in supply?

pE = $2

QE = 10

S

D

Q (millions)

price

S'

pE’ = $2.50

CIGARETTE MARKET

QE’ = 7

Elasticity slide 12

Use the midpoint formula again.

Elasticity =

% change in Q =

% change in Q =

For the quantities of 10 and 7, the % change in Q is approx. -35.3 percent. (3/8.5 times 100)

Pin change %

Q in change %

Q average

Q in change

100 )Q

Q (

MEAN

Elasticity slide 13

NOW COMPUTE ELASTICITY

% change in p = 22.22 percent

% change in Q = -35.3 percent

E = -35.3 / 22.22 = -1.6 (approx.)

Elasticity slide 14

But you can do the other options as well:

A) If you use the low price, and its corresponding quantity, as the base values, then elasticity = 1.2

B) If you use the high price, and its corresponding quantity, as the base values, then elasticity = 2.1 (approx.)

C) And the midpoint formula gave 1.6 (approx.)

SAME PROBLEM...DIFFERENT ANSWERS!!!SAME PROBLEM...DIFFERENT ANSWERS!!!

Elasticity slide 15

MORE ELASTICITY COMPUTATIONS

Q

PQUANTITY PRICE0 101 92 83 74 65 56 47 38 29 1

10 0

0

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0 2 4 6 8 10 12 14

Compute elasticity between prices of $9 and $8.

Compute elasticity between prices of $9 and $8.

Elasticity slide 16

The % change in Q =

The % change in P =

Therefore elasticity =

USE THE MIDPOINT FORMULA.

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Elasticity slide 19

Now we try different prices

Q

P

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 110 0

0

2

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6

8

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0 2 4 6 8 10 12 14

Compute elasticity between prices of $3 and $2.

Compute elasticity between prices of $3 and $2.

Elasticity slide 20

The % change in Q =

The % change in P =

Therefore elasticity =

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Elasticity slide 23

ELASTICITY IS NOT SLOPE!

Q

P Note that elasticity is differentat the two points even thoughthe slope is the same. (Slope = -1)

Note that elasticity is differentat the two points even thoughthe slope is the same. (Slope = -1)

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 110 0

0

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E = -5.67

E = -.33

Elasticity slide 24

TERMS TO LEARN

Demand is ELASTIC when the numerical value of elasticity is greater than 1.

Demand is INELASTIC when the numerical value of elasticity is less than 1.

Demand is UNIT ELASTIC when the numerical value of elasticity equals 1.

NOTE: Numerical value here means “absolute value.”

Elasticity slide 25

LIKE THIS!

Q

PQUANTITY PRICE0 101 92 83 74 65 56 47 38 29 110 0

0

2

4

6

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10

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14

0 2 4 6 8 10 12 14

Demand is elastic here.Demand is elastic here.

Demand is inelastic here.Demand is inelastic here.

Elasticity slide 26

A FINAL ELASTICITY MEASURE

POINT ELASTICITY OF DEMAND

If you know or can see the demand curve for a good (you don’t know just two points), you can compute “point elasticity of demand” at a single point on the demand curve.

Here’s the idea:

Elasticity slide 27

The % change in price can be written as:

P)/Pbase times 100

The % change in quantity can be written as:

Q)/Qbase times 100

So elasticity is: (Q)/ (P)) ( Pbase / Qbase)

Elasticity slide 28

So elasticity is Q)/ (P) multiplied by the ratio of base price to base quantity.

Point elasticity uses this formula to compute the elasticity of demand AT A POINT on a demand curve.

Elasticity slide 29

EXAMPLEEXAMPLE

D

$3

10

P

Q

6

18

Elasticity at a price of $3is .90.

Elasticity slide 30

There is an important relationship between what happens to consumers’ spending on a good and elasticity when there is a change in price.

Spending on a good = P Q.

Because demand curves are negatively sloped, a reduction in P causes Q to rise and the net effect on PQ is uncertain, and depends on the elasticity of demand.

Elasticity slide 31

Q

P

At P = $9, spending is $9 (= 1 times $9).At P = $8, spending is $16 ( = 2 times $8).

When price fell from $9 to $8, spending rose. Q must haveincreased by a larger percent than P decreased. So...

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 110 0

0

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Demand is elastic here.Demand is elastic here.

Elasticity slide 32

Q

P

At P = $3, spending is $21 (= 7 times $3).At P = $2, spending is $16 ( = 8 times $2).

When price fell from $3 to $2, spending fell. Q must haveincreased by a smaller percent than P decreased. So...QUANTITY PRICE

0 101 92 83 74 65 56 47 38 29 110 0

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Demand is inelastic here.Demand is inelastic here.

Elasticity slide 33

There is an easy way to tell whether demand is elastic or inelastic between any two prices.

If, when price falls, total spending increases, demand is elastic.

If, when price falls, total spending decreases, demand is inelastic.

Elasticity slide 34

But total spending is easy to see using a demand curve graph:

Q

P

The shaded area is P times Qor total spending when P = $9.

The shaded area is P times Qor total spending when P = $9.

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 1

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Elasticity slide 35

Q

P

The shaded area is P times Qor total spending when P = $8.The shaded area is P times Qor total spending when P = $8.

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 110 0

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Elasticity slide 36

Q

P

Total spending is higher at the price of $8 than it was at the price of $9.

Total spending is higher at the price of $8 than it was at the price of $9.

= loss in TR due to fall in P

= gain in TR due to rise in Q

QUANTITYPRICE0 101 92 83 74 65 56 47 38 29 110 0

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Elasticity slide 37

Q

P

The shaded area is total spending (total revenue ofsellers) when P = $3.

The shaded area is total spending (total revenue ofsellers) when P = $3.

QUANTITY PRICE0 101 92 83 74 65 56 47 38 29 1

10 0

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0 2 4 6 8 10 12 14

Elasticity slide 38

Q

P

Total revenue of sellers (total spending by buyers) falls when price falls from $3 to $2.

Total revenue of sellers (total spending by buyers) falls when price falls from $3 to $2.

QUANTITYPRICE0 101 92 83 74 65 56 47 38 29 110 0

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Elasticity slide 39

Here’s a convenient way to think of the relative elasticity of demand curves.

p

Q

p*

Q*

relatively more inelasticat p*relatively more inelasticat p*

relatively more elasticat p*relatively more elasticat p*

Elasticity slide 40

Examples of elasticityDoctors through the AMA restrict the supply of

physicians. How does this affect the incomes of doctors as a group?

A labor union negotiates a higher wage. How does this affect the incomes of affected workers as a group?

MSU decides to raise the price of football tickets. How is income from the sale of tickets affected?

Airlines propose to raise fares by 10%. Will the boost increase revenues?

Elasticity slide 41

MORE ...

MSU is considering raising tuition by 7%. Will the increase in tuition raise revenues of MSU?

CATA recently raised bus fares in the Lansing area. Will this increase CATA’s total receipts?

Elasticity slide 42

The answers to all of these questions depend on the elasticity of demand for the good in question. Be sure you understand how and why!

Elasticity slide 43

DETERMINANTS OF DEMAND ELASTICITY

The more substitutes there are available for a good, the more elastic the demand for it will tend to be. [Related to the idea of necessities and luxuries. Necessities tend to have few substitutes.]

The longer the time period involved, the more elastic the demand will tend to be.

The higher the fraction of income spent on the good, the more elastic the demand will tend to be.

Elasticity slide 44

OTHER ELASTICITY MEASURES

In principle, you can compute the elasticity between any two variables.Income elasticity of demand

Cross price elasticity of demand

Elasticity of supply

Elasticity slide 45

Each of these concepts has the expected definition. For example, income elasticity of demand is the percent change in quantity demand divided by a percent change income:

EINCOME =

Income elasticity of demand will be positive for normal goods, negative for inferior ones.

I in change %

Q in change %