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Elasticity

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Elasticity measures What are they?

– Responsiveness measures

Why introduce them?– Demand and supply responsiveness clearly matters

for lots of market analyses.

Why not just look at slope?– Want to compare across markets: inter market – Want to compare within markets: intra market– slope can be misleading– want a unit free measure

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Why Economists Use Elasticity

An elasticity is a unit-free measure. By comparing markets using elasticities

it does not matter how we measure the price or the quantity in the two markets.

Elasticities allow economists to quantify the differences among markets without standardizing the units of measurement.

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What is an Elasticity?

Measurement of the percentage change in one variable that results from a 1% change in another variable.

Can come up with many elasticities. We will introduce four.

– three from the demand function– one from the supply function

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2 VIP Elasticities

Price elasticity of demand: how sensitive is the quantity demanded to a change in the price of the good.

Price elasticity of supply: how sensitive is the quantity supplied to a change in the price of the good.

Often referred to as “own” price elasticities.

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Examples of Own Price Demand Elasticities

When the price of gasoline rises by 1% the quantity demanded falls by 0.2%, so gasoline demand is not very price sensitive.– Price elasticity of demand is -0.2 .

When the price of gold jewelry rises by 1% the quantity demanded falls by 2.6%, so jewelry demand is very price sensitive.– Price elasticity of demand is -2.6 .

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Examples of Own PriceSupply Elasticities

When the price of DaVinci paintings increases by 1% the quantity supplied doesn’t change at all, so the quantity supplied of DaVinci paintings is completely insensitive to the price.– Price elasticity of supply is 0.

When the price of beef increases by 1% the quantity supplied increases by 5%, so beef supply is very price sensitive.– Price elasticity of supply is 5.

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Examples of Unit-free Comparisons

Gasoline and jewelry – It doesn’t matter that gas is sold by the gallon

for about $1.09 and gold is sold by the ounce for about $290.

– We compare the demand elasticities of -0.2 (gas) and -2.6 (gold jewelry).

– Gold jewelry demand is more price sensitive.

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Examples of Unit-free Comparisons

Paintings and meat – It doesn’t matter that classical paintings

are sold by the canvas for millions of dollars each while beef is sold by the pound for about $1.50.

– We compare the supply elasticities of 0 (classical paintings) and 5 (beef).

– Beef supply is more price sensitive.

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Inelastic Economic Relations

When an elasticity is small (between 0 and 1 in absolute value), we call the relation that it describes inelastic.– Inelastic demand means that the quantity

demanded is not very sensitive to the price.

– Inelastic supply means that the quantity supplied is not very sensitive to the price.

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Elastic Economic Relations

When an elasticity is large (greater than 1 in absolute value), we call the relation that it describes elastic.– Elastic demand means that the quantity

demanded is sensitive to the price.– Elastic supply means that the quantity

supplied is sensitive to the price.

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Size of Price Elasticities

Unit elastic: own price elasticity equal to 1

0 1 2 3 4 5 6

Unit elastic

Inelastic Elastic

Elastic: own price elasticity greater than 1

Inelastic: own price elasticity less than 1

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General Formula for own price elasticity of demand

P = Current price of good X XD = Quantity demanded at that price P = Small change in the current price XD= Resulting change in quantity demanded

Pricein Change Percentage

DemandedQuantity in Change PercentageElasticity

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Note:

The own price elasticity of demand is always negative.

Economists usually refer to the own price elasticity of demand by its absolute value (ignore the negative sign).

So, even though the formula says that the own price elasticity of demand is negative, we would say the elasticity of demand is 1.5 in the first example and 0.67 in the second.

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Arc Formula for Elasticity - General

Although the exact formula for calculating an elasticity is useful for theory, in practice economists usually calculate an approximation called the arc elasticity.

You are really approximating the elasticity between two points.

Need two points to perform the calculation.

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Arc Formula for Own Price Elasticity of Demand

Get two points of the demand curve: Points A and B.

Consider PA and XA and PB and XB from the demand relationship.

Note: we’ll take absolute value

PavgPP

XavgXXelasticity

BA

BA

/)(

/)(

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Point Formula for Own Price Elasticity of Demand

The exact formula for calculating an elasticity at the point A on the demand curve.

Note: we’ll take absolute value

atAP

X

X

Pelasticity

D

A

A

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Slope of the Demand Curve P is the

change in price. (P<0)

Price

Quantity

Demand

X X + X

X

P

P+ PP

X is the change in quantity.

slope = P/ X

X

P

slope

1/slope = X/ P

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Slope Compared to Elasticity

The slope measures the rate of change of one variable (P, say) in terms of another (X, say).

The elasticity measures the percentage change of one variable (X, say) in terms of another (P, say).

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Example: Elasticity Calculation at “A” Slope =

(40-32)/(10-14)=-2 1/slope = -1/2 P/X = 36/12 = 3 at

point A P/X x 1/slope

= -1.5 Elasticity of

demand = -1.5 Absolute value of

the elasticity = 1.5

Linear Demand Curve

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40

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10 11 12 13 14

Quantity

Pri

ce A

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Exercise -- Linear Demand

Compute the elasticity at the point indicated in red on the table (X=18,P=24).

Slope = -2 1/Slope = -1/2 P/X = 24/18 = 4/3 Elasticity = -2/3

Quantity Price10 4011 3812 3613 3414 3215 3016 2817 2618 2419 2220 20

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Elasticities and Linear Demand

The elasticity varies along a linear demand (or supply) curve. This is illustrated in the linear demand curve table above.

Note: Usually we would report last column as absolute value

Linear Demand

Quantity Price Slope 1/SlopeExact

Elasticity10 4011 38 -2 -0.5 -1.727312 36 -2 -0.5 -1.500013 34 -2 -0.5 -1.307714 32 -2 -0.5 -1.142915 30 -2 -0.5 -1.000016 28 -2 -0.5 -0.875017 26 -2 -0.5 -0.764718 24 -2 -0.5 -0.666719 22 -2 -0.5 -0.578920 20

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Supply Elasticities

The price elasticity of supply is always positive.

Economists refer to the price elasticity of supply by its actual value.

Exactly the same type of point and arc formulas are used to compute and estimate supply elasticities as for demand elasticities.

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Some Technical Definitions For Extreme Elasticity Values

Economists use the terms “perfectly elastic” and “perfectly inelastic” to describe extreme values of price elasticities.

Perfectly elastic means the quantity (demanded or supplied) is as price sensitive as possible.

Perfectly inelastic means that the quantity (demanded or supplied) has no price sensitivity at all.

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Perfectly Elastic Demand We say that

demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded.

Price

Quantity

Perfectly Elastic Demand (elasticity = )

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Perfectly Inelastic Demand We say that

demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded.

Price

Quantity

Perfectly Inelastic Demand (elasticity = 0)

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Perfectly Elastic Supply We say that

supply is perfectly elastic when a 1% change in the price would result in an infinite change in quantity supplied.

Price

Quantity

Perfectly Elastic Supply (elasticity = )

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Perfectly Inelastic Supply We say that

supply is perfectly inelastic when a 1% change in the price would result in no change in quantity supplied.

Price

Quantity

Perfectly Inelastic Supply (elasticity = 0)

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Determinants of elasticity

What is a major determinant of the own price elasticity of demand? – Availability of substitutes in consumption.

What is a major determinant of the own price elasticity of supply? – Availability of alternatives in production.

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Reminders

Value of own price elasticity usually changes along a demand curve– there are many interesting intra elasticity

applications Can also compare elasticities across

markets– there are interesting inter elasticity

questions

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Using Demand Elasticity: Total Expenditures

Do the total expenditures on a product go up or down when the price increases?

The price increase means more spent for each unit.

But, quantity demanded declines as price rises.

So, we must measure the measure the price elasticity of demand to answer the question.

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Bridge Toll Example

Current toll for the George Washington Bridge is $2.00/trip.

Suppose the quantity demanded at $2.00/trip is 100,000 trips/hour.

If the price elasticity of demand for bridge trips is 2.0, what is the effect of a 10% toll increase?

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Bridge Toll: Elastic Demand

Price elasticity of demand = 2.0 Toll increase of 10% implies a 20%

decline in the quantity demanded. Trips fall to 80,000/hour. Total expenditure falls to $176,000/hour

(= 80,000 x $2.20). $176,000 < $200,000, the revenue from

a $2.00 toll.

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Bridge Toll Example, Part 2

Now suppose the elasticity of demand for bridge trips is 0.5.

How would the number of trips and the expenditure on tolls be affected by a 10% increase in the toll?

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Bridge Toll: Inelastic Demand

Price elasticity of demand = 0.5 Toll increase of 10% implies a 5%

decline in the quantity demanded. Trips fall to 95,000/hour. Total expenditure rises to $209,000/hour

(= 95,000 x $2.20). $209,000 > $200,000, the revenue from

a $2.00 toll.

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Elasticity and Total Expenditures

A price increase will increase total expenditures if, and only if, the price elasticity of demand is less than 1 in absolute value (between -1 and zero)– Inelastic demand

A price reduction will increase total expenditures if, and only if, the price elasticity of demand is greater than 1 in absolute value (less than -1).– Elastic demand

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Elasticity and Total Expenditure (Graph)

At the point M, the demand curve is unit elastic. M is the midpoint of this linear demand curve

Above M, demand is elastic, so total expenditure falls as the price rises

Below M, demand is inelastic. so total expenditure falls as price falls.

Total expenditure is maximized at the point M, where the elasticity = 1.

Price

Quantity

M

Elasticity = 1: Total expenditure is at a maximum

Elasticity > 1: Price reduction increases total expenditure; price increase reduces it.

Elasticity < 1: Price reduction reduces total expenditure; price increase increases it.

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Change in Expenditure Components

Old (price, quantity) is (P,Q).

New (price, quantity) is (P*,Q*).

Expenditures increase if G is bigger than E.

Since the point (P,Q) is above the midpoint of the linear demand curve, we know that total expenditures will increase at the lower price (P*,Q*). So, E must be smaller than G.

Price

Quantity

E

F G

P*

P

Q Q*

Demand

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Two real world examples

Gas taxes in Washington DC

Vanity plates in Virginia

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Other Price Elasticities: Cross- Price Elasticity of Demand

Elasticity of demand with respect to the price of a complementary good (cross-price elasticity)– This elasticity is negative because as the price of

a complementary good rises, the quantity demanded of the good itself falls.

– Example (from last week) software is complementary with computers. When the price of software rises the quantity demanded of computers falls.

– Cross-price elasticity quantifies this effect.

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Other Price Elasticities: Cross Price Elasticity of Demand

Elasticity of demand with respect to the price of a substitute good (also a cross-price elasticity)– This elasticity is positive because as the price of a

substitute good rises, the quantity demanded of the good itself rises.

– Example (from last week) hockey is substitute for basketball. When the price of hockey tickets rises the quantity demanded of basketball tickets rises.

– Cross-price elasticity quantifies this effect.

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Other Elasticities: Income Elasticity of Demand

The elasticity of demand with respect to a consumer’s income is called the income elasticity.– When the income elasticity of demand is positive (normal

good), consumers increase their purchases of the good as their incomes rise (e.g. automobiles, clothing).

– When the income elasticity of demand is greater than 1 (luxury good), consumers increase their purchases of the good more than proportionate to the income increase (e.g. ski vacations).

– When the income elasticity of demand is negative (inferior good), consumers reduce their purchases of the good as their incomes rise (e.g. potatoes).