Elasticity... …is a concept that relates the responsiveness

(or sensitivity) of one variable to a change in another variable.

• Elasticity of A with respect to B = % change in A / % change in B

• Elasticity answers the question of how much one variable will change when another one changes.

With elasticity we will be able to answer the question:

If the price of a good increases by a certain amount, then how much will the quantity demanded decrease by because of this.

Why is elasticity important?

Importance of elasticity• Many business and economic decisions are not

based on if something will happen, but buy how much will it change by:

Example: How much should business firms raise or lower their prices and by?

Will total revenue (this affects profit) go up or down when price increases? By how much?

• The effects of public policy will be different depending on the elasticity of the good in question…

…for example: How much will the price of a good increase if a tax is placed on it?

Price Elasticity of Demand... ...measures the responsiveness of quantity demanded (QD)

of a good to the change in the price of the good (P). • Price elasticity of demand = %

change in QD / % change in P.• It is a number(unit free measurement) that represents

the % change in QD for a 1% change in price.• Example: Suppose the price of a good rises by 5%. We

observe that the quantity demanded declines by 10%.

The price elasticity of demand is -10% / 5% = - 2. • This means for every 1% change in price, the quantity

demanded of this good will change by - 2%.

Calculating elasticitySometimes we must first find the % change in a variable from

some absolute numbers to calculate elasticity

• Example: Suppose the price of a Fore Golf car is $10,000 and Fore sells 500,000 of them.

• Fore then raises it’s price to $11,000. The next year they find they have sold 465,000 Golf cars

• What is the price elasticity of demand for Fore Golf cars?

• Price elasticity of demand = % change in QD / % change in P

• We can use what is called the mid-point formula to calculate the % change in QD and P...

…the mid point formula uses the average of the beginning and ending values to calculate the % change

Calculating elasticityPrice elasticity of demand = % change in QD / % change in P.

% change in QD = change in QD / average of the 2 quantities

% change in QD = Q2 - Q1 / {(Q2 + Q1)/2} x 100%% change in QD = 465,000 - 500,000 / {(465,000 + 500,000)/2} x 100%

% change in QD = -35,000 / 482,500 x 100%

% change in QD = - 7.25%% change in QD = - 7.25%

% change in P = change in P/ average of the 2 prices

% change in P = P2 - P1 / {(P2 + P1)/2} x 100%% change in P = $11,000 - $10,000 / {($11,000 + $10,000) / 2} x 100%

% change in P = 1,000 / 10,500 x 100%

% change in P = 9.52%% change in P = 9.52%Price elasticity of demand = - 7.25 / 9.52 = - 0.76Interpretation: A 1% increase in Fore Golf Cars will reduce

their quantity demanded by 0.76%

$11,000 +$10,000465,000 - 500,000

This calculation can be reduced to a more manageable formula:

Price elasticity of Demand =

Q2 - Q1

Q2 + Q1x

P2 + P1

P2 - P1=

465,000 + 500,000x

$11,000 -$10,000

=- 35,000

965,000x $21,000

$1,000

=- 0.0363 x

= - 0.76• Importance: Given any 4 of the above variables you can always

find the 5th.• Suppose Fore Golf want sell 550,000 (instead of 500,000) cars and

know the elasticity is -0.76. If the original price was $10,000 you can find the price they must charge to sell 550,000 cars!

• Once a firm estimates it’s price elasticity it can estimate changes in sales from a price change; or to reach a sales target, estimate how much to cut prices.

21

Price

Quantity

P1

P2

Q1 Q2

Given any two points on a demand curve wecan calculate it’s elasticity between the two points

=Q2 - Q1

Q2 + Q1x

P2 + P1

P2 - P1

Price elasticity of Demand (Pd)

• Since elasticity is unit free it is better than using the slope of a line for measuring the responsiveness of variables.

• Still, the price elasticity of demand will affect the way we draw the demand curve.

Types of Elasticity's• Economists group the numbers that are

calculated into different types of elasticity depending on which percentage change is greater: price or quantity

• Depending on the number that is calculated we put that number into 1 of 5 different types

• We ignore the minus sign (use absolute value) when doing so.

Price Price

Quantity Quantity

P1 P1

Q1 Q1

P2 P2

Q2 Q2

Elastic Demand: 1< Pd < 8

the % change in QD is greater than the % change in P that caused it. Indicates that consumers are very responsive or sensitive to price changes and there can be large large changes in QD.changes in QD.

Inelastic Demand: 0 < Pd < 1

the % change in QD is less than the % change in P that caused it.Indicates that consumers are not very responsive or sensitive to price changes and there will be small small changes in QDchanges in QD.

D

D

Price Price Price

Quantity Quantity Quantity

the % change in QD is the same as the % change in Pthat caused it.

Unit Elastic demand Pd = 1

Perfectly Inelastic demand Pd = 0

Quantity demanded doesnot change at all no matterhow much price changes

Example: Prescription drugsthat are needed to live

…no substitutes available

Perfectly Elastic demand Pd = 8

Any change is price willcause QD to go to zeroPractical application:A firm facing this demandcurve can sell all that itwants at this predeterminedprice, but no higher…infinite perfect substitutes

Total Revenue and Elasticity

• Total Revenue (TR) = Price (P) x Quantity (Q)• If a business firm raises the price it charges will total

revenue go up?

• It depends, because when price increases, quantity decreases

• While the price increase will raise revenue per unit, the firm will sell less units.

• The elasticity of demand will determine whether total revenue goes up or down when price goes up or down.

Price

Quantity

P1

Q1

D

Total Revenue = Price x Quantity This is shown by the Light Blue shaded area on the graph

P2

Q2

• When price increases, the firm gains the green area in revenue...

TR = P x Q

Let’s draw an inelastic demand curve and compare the areas gained and lost.

...but will lose the red area because of the decline in sales.

Price

Quantity

P1

Q1

D

Total Revenue = Price x Quantity

Inelastic Demand: P increase > Q decreaseP2

Q2

• The % increase in P is greater than the % decrease in QD

TR = P x Q

The revenue gained from the P increase > revenue lost from the QD decrease.The green area is greater than the red area

Total revenue increases when price rises for an inelastic good!

Price

Quantity

P1

Q1

D

Total Revenue = Price x Quantity

Elastic Demand: P increase < Q decreaseP2

Q2

• The % increase in P is less than the % decrease in QD

TR = P x Q

The revenue gained from the P increase < revenue lost from the QD decrease.The green area is less than the red area

Total revenue decreases when price rises for an elastic good!

Total revenue does not change

Total revenue does not change

Same percentage change in quantity and price

Equal to 1.0Unitary elastic

Total revenue decreases

Total revenue increases

Smaller percentage change in quantity

Less than 1.0Inelastic

Total revenue increases

Total revenue decreases

Larger percentage change in quantity

Greater than 1.0

Elastic

Effect of a decrease in price on total revenue

Effect of an increase in price on total revenue

Change in quantity versus change in priceValue of Ed

Type of demand

Elasticity and Total Revenue: Summary

• When demand is inelastic, price and total revenues are directly related. Price increases generate higher revenues.

• When demand is elastic, price and total revenues are indirectly related. Price increases generate lower revenues.

What determines price elasticity of demand ? • Most important is the number of substitute goods. More substitutes = higher elasticity. Why? Consumers can easily switch from one good to another. If there are few or no substitutes then switching is

impossible……consumers will find it hard to reduce purchases of the good

when price increases

• How important is the item in a consumers budget?

The price elasticity of salt will be very low because it is insignificant in a consumers budget

Housing, car payments are a much higher proportion of a budget and will have a higher elasticity

• Time is also important, because more substitute goods appear and the consumer can change his behavior.

Some calculated price elasticity of demand. Item Short-run elasticity Long run elasticity

Gasoline - 0.4 -1.5

Housing - 0.3 -1.88

Tobacco products - 0.46 -1.89

Automobiles -1.87 -2.24

Movies -0.87 -3.67

Furniture -1.26

Books, Magazines, Newspapers -0.32

Other measures of Elasticity.• 1. Income Elasticity of Demand..... measures the

responsiveness of consumer purchases to changes in consumer income.

• Income elasticity = % change in consumer demand / % change in income

• Why is it important?• Determines if a good is a normal good (a positive

number) or an inferior good (a negative number).• Goods with positive numbers greater than 1

(income elastic) are sometimes referred to as “luxuries”; goods with positive numbers less than 1 (income inelastic) are referred to as “necessities”

Other measures of Elasticity

Firms that produce income elastic goods do very well in prosperous times...

....but very bad during recessions.

For “necessities” the opposite is true.

• With this knowledge, firms can plan production according to expectations of consumers income.

Some calculated income elasticity of demand.

Item Short-run elasticity Long run elasticity Potatoes -0.81 Pork 0.27 0.18 Beef 0.51 0.45 Autos 5.50 1.07 Jewelry 1.00 1.60 Foreign travel 0.24 3.09 Physician Services 0.28 1.15 Movies 3.41 Restaurant meals 1.61 Clothing 0.51Telephone 0.32

Cross elasticity of demand... ...measures the responsiveness of buyers to the

purchase of one good in response to changes in the price of another good (substitute or complementary)

• Cross elasticity= % change in quantity of good X % change in price of good Y

• Positive number = goods are substitutes

• Negative number = goods are complements

• Zero = goods are unrelated

Price elasticity of Supply... …measures the responsiveness of quantity quantity

suppliedsupplied (QS) by business firms to changes in the price of a goodprice of a good (P).

• Price elasticity of supply = % change in QS / % change in P

• This is always a positive number.

Elastic supply...greater than 1 but less than infinity

Inelastic supply...greater than 0 but less than 1

Price Price

Quantity Quantity

P2 P2

Q1 Q1

P1 P1

Q2 Q2

Elastic Supply: 1< Ps < 8

the % change in QS is greater than the % change in P that caused it.Indicates that Firms are very responsive or sensitive to price changes and are willing and able to make a lot more of the product available with small price increases.

Inelastic Supply: 0 < Ps < 1

the % change in QS is less than the % change in P that caused it.Indicates that Firms are not very responsive or sensitive to price changes and are either not able or willing to make more of this product available without a large price increase.

S

Price Elasticity of Supply

S

Price Price Price

Quantity Quantity Quantity

the % change in QS is the same as the % change in Pthat caused it.

Unit Elastic Supply PS = 1

Perfectly Inelastic Supply Ps = 0

Quantity supplied doesnot change at all no matterhow much price changes

Example: Fixed seating at a theater or arena.

Perfectly Elastic Supply Ps= 8

Any change is price willcause QS to go to zeroPractical application:A firm is willing to make as much of this product available at a constant price(Could happen if costs donot change)

Factors influencing the Price elasticity of supply

1. How much does the cost per unit of output rise as quantity supplied increases?

The more it (costs /output) increases the more inelastic supply will be.

If costs don’t rise at all as QS increases then supply is perfectly elastic.

2. Time is a factor in costs per unit.

Usually, as time increases, costs per unit do not rise as much and supply is more elastic.

Firms find better and faster ways of production

Application using Elasticity • Tax Burden (Who pays an excise tax?)

The government places an excise tax on the suppliers of a good such as tobacco, liquor, and gasoline.

Do business firms simply pass the entire tax to consumers in the form of higher prices? (This is called tax shifting)

It depends on the elasticity of demand and supply. • Knowing both elasticity allows economists to

determine who pays the greater amount of an excise tax on sellers of a good.

Price

Quantity of gasoline

$3.00

Q1Suppose the government then decides to put a $0.50 cent tax per

gallon on gasoline……an excise tax will raise the cost of a gallon of gasoline by the

amount of the tax: $0.50, which will cause the supply curve to shift upward {decrease in supply} by $0.50.

S1

D

This graph initially shows a good without the excise tax...S2

$0.50

$3.50 S2 is $0.50 cents greaterthan S1, reflecting the tax

$3.25

Q2

But the equilibrium price($3.25) occurs where the new supply curve intersects the demand curve. (Surplus at $3.50)

By comparing the price consumers pay and firms receive after the tax (compared to the before tax price) we can determine how much of the tax has been paid by consumers and firms.

}

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2

$3.25

Q2

$2.75

By comparing the price consumers pay and firms receive after the tax (compared to the before tax price) we can determine how much of the tax has been paid by consumers and firms.

Firms receive $3.25 per gallon from the consumer

Out of that $3.25 they must pay $0.50 to the governmentFirms only receive $2.75$2.75 out of every gallon of gas sold

Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

•Consumers pay $0.25 of the tax and firms pay $0.25 of the tax•The Green area represents consumers share, the Light Blue area represents firms share of the tax

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2

$3.40

Q2

$2.90

Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

Consumers pay $0.40 of the tax and firms pay $0.10 of the tax

What if Demand for gas isinelastic while Supply is thesame as before (unit elastic)}$0.50

Why do consumers pay more of the tax when demand is inelastic?

Since consumers don’t respond very much to price changes firms are able to pass on most of the tax in the form of higher prices without a large reduction in sales

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2

$3.10

Q2

$2.60

Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

Consumers pay $0.10 of the tax and firms pay $0.40 of the tax

What if while Demand for gas is elastic Supply is thesame as before (unit elastic)}$0.50

Why do Firms pay more of the tax when demand is elastic?

Since consumers respond very much to price changes firms are unable to pass on very much of the tax in the form of higher prices due to the large loss in sales.

Tax incidence and elasticity• Government gets more revenue from taxing

goods and services that are inelastic...

…quantity sold does not go down as much

• Rule of Thumb: The more inelastic side of the market will pay the GREATER PROPORTION of the tax.

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2$3.50

Q2

Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

}$0.50

If Supply is perfectly elastic, Consumers pay all the tax.

Example Tax Burden: Extreme Case

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2

$3.50

Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

}

If Demand is perfectly inelastic, Consumers pay all the tax.

Example Tax Burden: Extreme Case

$0.50

Price

Quantity of gasoline

$3.00

Q1

S1

D

S2

$3.03 Tax paid by consumer

Tax paid by firms

Total tax paid to Gov’t

}

If Supply is almost perfectly inelastic, Firms pay virtually all of the tax.

Example Tax Burden: Extreme Case

$0.50

$2.53

Q2