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THE ELASTICITY OF DEMANDPrice Elasticity of Demand

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THE ELASTICITY OF DEMAND

Price Elasticity of Demand : a measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price.

Price Elasticity of Demand and it’s Determinants

Necessities versus Luxuries: Necessities tend to have inelastic demand whereas luxuries have elastic demands.

Ex. Inelastic - The demand for milk will change little even if the price increases since it is a necessity. Elastic - The demand for air travel will decrease considerably if the price goes up since it is considered to a luxury.

Availability of Close Substitutes: Goods with close substitutes tend to have more elastic demand because it is easier for consumers to switch from that good to others.

Ex. Inelastic – that demand for eggs changes little since there are little substitutes. Elastic – that demand for butter will go down if the price goes up because margarine is a close substitute.

Definition of the Market: narrowly defined markets tend to have more elastic demand then broadly defined markets because it is easier to find close substitutes for narrowly defined goods.

Ex. Food a broad category has a fairly inelastic demand. Cheesecake a narrower category has a more elastic demand because there are substitutes for deserts, such as ice-cream.

Time Horizon: Goods tend to have more elastic demand over a longer time horizons.

Ex. When the price of gasoline rises, there is little change in demand initially, however in the long run people made by smaller cars or find other transportation means.

How Is Price Elasticity of Demand Calculated

Price Elasticity of Demand (E

d

) = Percentage change in quantity demanded (Q

d

) Percentage change in price (P)

Example,

If a price increase of 10% in ice cream results in a 20% decrease in demand, then the price elasticity of ice cream is,

Price elasticity (ice cream) = 20% = 2 10%

An elasticity of two indicates that that change in the quantity demanded is proportionally twice as large as the change in the price. Note that the negative sign associated with the decrease in demand is ignored in the calculations. Elasticity is reported as absolute values.

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The midpoint method is a better way to calculate percentage changes and elasticity.

Ex. Point A: Price = $4 Quantity = 120

Point B: Price = $6 Quantity = 80

Note, the percentage change will be different if you’re going from point A to point B compared to going from point B to point A..

E

a-b =

(80-120)/120 = 33% = 0.66

(6-4)/4 50%

E

b-a =

(120-80)/80 = 50% = 1.5

(4-6)/6 33%

To avoid this, the midpoint between point A and B is used to calculate elasticity. You get the same answer no matter what direction you go.

Ex. The mid point between A and B, Price is $5 Quantity = 100

E= (80-120)/100 = 40% = 1.00

(6-4)/5 40%

or

E= (120-80)/100 = 40% = 1.00

(4-6)/6 40%

We can express the midpoint method with the following formula for the price elasticity of demand between two points (Q

1

, P

1

) and (Q

2

, P

2

).

(E

d

) = (Q

2 -

Q

1

)/[ (Q

2 +

Q

1

)/2]

(P

2 -

P

1

)/[ (P

2 +

P

1

)/2]

The Variety of Demand Curves and Elasticity

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Total Revenue And The Price Elasticity of Demand

Total Revenue: the amount paid by buyers and received by sellers of a good, computed as the price of the good multiplied by the quantity sold.

In the graph, below, the total amount paid by buyers, and received as revenue by sellers, equals the area of the box under the demand curve, P X Q, If the price is $4 and the quantity sold is 100 units, ten the total revenue is $4 X 100 = $400

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The following graph shows how total revenue changes when the price changes for an Inelastic Demand . Note that an increase in price leads to a decrease in quantity demanded that is proportionally smaller. Therefore, the overall effect is that total revenue increases. In this example, an increase in price from $1 to $3 causes quantity demanded to fall from 100 to 80, but note that the total revenue increases from $100 to $240

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The following graph shows how total revenue changes when the price changes for an Elastic Demand . Note that an increase in price leads to a decrease in quantity demanded that is proportionally larger. Therefore, the overall effect is that total revenue decreases. In this example, an increase in price from $4 to $5 causes quantity demanded to fall from 50 to 20, note that the total revenue decreases from $200 to $100

SUMMARY

When a demand curve is inelastic (a price elasticity less than 1), a price increase raises total revenue, and a price decrease reduces total revenue.

When a demand curve is elastic (a price elasticity greater than 1), a price increase reduces total revenue, and a price decrease raises total revenue.

If the price elasticity were equal to 1, a change in price does not affect total revenue.

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Elasticity And Total Revenue Along A Linear Demand Curve

Although some demand curves have an elasticity that is the same along the entire curve, this is not always the case. The simplest example of a demand curve along which the elasticity changes is that of a straight curve (line).

PRIC

E QUANTIT

Y TOTAL

REVENU E

% CHANGE

, PRICE

% CHANGE, QUANTIT

Y

ELASTICIT

Y DESCRIPTIO

N

$7 0 $0 15 200 13.0 Elastic

6 2 12 18 67 3.7 Elastic

5 4 20 22 40 1.8 Elastic

4 6 24 29 29 1.0 Unit Elastic

3 8 24 40 22 0.6 Inelastic

2 10 20 67 18 0.3 Inelastic

1 12 12 200 15 0.1 Inelastic

0 14 0

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Other Types of Demand Elasticities

Income Elasticity of Demand: is a measure of how much the quantity demanded of a good responds to a change in consumer’s income. It is calculated as follows,

Income Elasticity of Demand = % change in Quantity Demanded % change in Income

Note: normal goods will have a positive elasticity value, while inferior goods will have a negative elasticity value.

The Cross-Price Elasticity of Demand: measures how much the quantity demanded of one good responds to a change in the price of another good. It is calculated as follows,

Cross Price Elasticity of Demand = % change in Quantity Demanded of Good #1 % change in the Price of Good#2

Note: Substitute goods will have a positive elasticity value, while compliment goods will have a negative elasticity value.

THE ELASTICITY OF SUPPLY

Price Elasticity of Supply : a measure of how much the quantity supplied of a good responds to a change in the price of that good, computed as the percentage change in quantity supplied divided by the percentage change in price.

Price Elasticity of Supply (E

s

) = Percentage change in quantity supplied (Q

s

) Percentage change in price (P)

The Variety of Supply Curves and Elasticity

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Real World Scenario – Price Elasticity Varies Along the Supply Curve

Because most firms have maximum capacity for amounts produced, the elasticity of supply can be very high at low levels of production and very low at high levels of production. This is shown in the graph below.

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APPLICATIONS OF ELASTICITY

CASE 1 – OPEC AND WHY IT FAILED TO KEEP OIL PRICES HIGH

When the supply of oil falls the response depends on the time horizon. In the short run,

supply and demand are relatively inelastic as seen in the graph, part (a) below. Thus when

the supply curve shifts from S

1

to S

2

, the price rise is considerable. However, in the long

run people will decrease their dependency on oil by driving smaller cars, conservation,

finding alternative energy sources, etc. This results in a more elastic demand and supply as

seen in (b). The same size shift in the supply curve S

1

to S

2

results in a less significant price

increase.

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CASE 2 – THE WAR AGAINST DRUG USE

When the government spends money on more police to arrest drug pushers and suppliers, it reduces the supply of drugs from S

1

to S

2

, as seen in (a) below. If the demand for drugs is inelastic, then the total amount paid by drug users rises, even if the amount of drug use falls (more money for those pushers who don’t get arrested). By contrast, drug education

reduces the demand for drugs from D1 to D

2

, as seen in (b). Because both price and

quantity fall, the revenues to drug pushers drops. Maybe this is a better incentive to change their business savvy into more legal endeavours.

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References

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