Download CHAPTER 5 ELASTICITY Elasticity The degree to which one

CHAPTER 5
ELASTICITY
Elasticity
The degree to which one variable, Y, responds to a change in another variable, X, is the elasticity of the response variable Y.
Elasticity is the ratio of the percent change in variable Y to the percent change in variable X.
Absolute change versus relative (percent) change
The absolute change is simply the difference between the new value of the variable and initial value. Using the symbol ∆
(delta) to denote “change” or “difference”, the absolute change in y is represented by:
∆y = y₁ − y₀
Relative or percent change in y is the absolute change relative to (divided by) the initial value:
∆y% =
y1  y 0 y

y0
y0
For example if y increases from y₀ = 10 to y₁ = 15, then the percent change in y is:
∆y% =
15  10 5
= 0.5 or 50%

10
10
Similarly, if the variable x changes from x₀ = 20 to x₁ = 25, then the percent change in x is:
∆x% =
E=
25  20 5
= 0.25 or 25%

20
20
y% 50%

2
x% 25%
Price elasticity of demand
The price elasticity of demand is the ratio of percent change in Q (quantity demanded) to the percent change in P (price).
Let’s apply this definition to the following demand function: Q = 1500 – 500P.
P₀ = $1.00
Q₀ = 1,000
P₁ = $0.80
Q₁ = 1,100
Absolute change in quantity:
Percent change:
∆Q = Q1 – Q0
∆Q% = ∆Q ∕ Q0
∆Q = 1100 − 1000 = 100
∆Q% = 100 ∕ 1000 = 0.1 (or 10%)
Absolute change in price:
Percent change:
∆P = P1 – P0
∆P% = ∆P ∕ P0
∆P = $0.80 − $1.00 = −$0.20
∆P% = $0.20 ∕ $1.00 = 0.20 (or 20%)
E = ∆Q% ∕ ∆P%
E = 10 ∕ 20 = 0.5
The coefficient of price elasticity of demand is 0.5. Note that we have ignored the “−“ algebraic sign. We already know that
price and quantity demanded change in the opposite directions. So the negative sign is redundant. The coefficient E = 0.5
means that for each 1% decrease in price, quantity demanded increases by 0.5%. Since percentage change in quantity
demanded is less than the percentage change in price, the demand is said to be inelastic.
Now consider a change in price and quantity in the other direction.
P₀ = $0.80
Q₀ = 1,100
1
P₁ = $1.00
Q₁ = 1,000
Absolute change in quantity:
Percent change:
∆Q = Q1 – Q0
∆Q% = ∆Q ∕ Q0
∆Q = 1000 − 1100 = −100
∆Q% = 100 ∕ 1100 = 0.091 (or 9.1%)
Absolute change in price:
Percent change:
∆P = P1 – P0
∆P% = ∆P ∕ P0
∆P = $1.00 − $0.80 = $0.20
∆P% = $0.20 ∕ $0.80 = 0.25 (or 25%)
E = ∆Q% ∕ ∆P%
E = 9.1 ∕ 25 = 0.364
Note that we get a different value for the coefficient E for a price increase compared to the E for a price decrease. We
don’t want this to happen. We want the same E for a price change in either direction.
Midpoint Formula for Coefficient of Price Elasticity of Demand
Using the “midpoint” formula, we obtain the same value for E regardless of the direction of price change.
P₀ = $1.00
Q₀ = 1,000
P₁ = $0.80
Q₁ = 1,100
Absolute change:
∆P = P1 – P0
∆P = $0.80 − $1.00 = −$0.20
Percent change:
∆P% = ∆P ∕ Average(P0, P1)
∆P% = $0.20 ∕ $0.90 = 0.222 (or 22.2%)
Average(P0, P1) = (P0 + P1) ∕ 2
Absolute change:
∆Q = Q1 – Q0
Percent change:
∆Q% = ∆Q ∕ Average(P0, P1)
Average(Q0, Q1) = (Q0 + Q1) ∕ 2
E = ∆Q% ∕ ∆P%
∆Q = 1100 − 1000 = 100
∆Q% = 100 ∕ 1050 = 0.095 (or 9.5%)
E = 9.5 ∕ 22.2 = 0.414
(Confirm that E = 0.414 when price increases from $0.80 to $1.00 and quantity demanded decreases from 1,100 to 1,000.)
The midpoint formula for E is:
Q1  Q0
(Q0  Q1 ) 2
E
p1  P0
(P0  P1 ) 2
How Elastic is Elastic?
Elasticity of demand basically depends upon the availability of substitutes. If there are close substitutes for good X, then
the demand for that good is price elastic.
A diabetic person’s demand for insulin is perfectly inelastic because for most diabetics there are no substitutes for insulin.
A diabetic needs to use a prescribed dosage of insulin per period, regardless of the price of that drug. The demand curve
for insulin is therefore a vertical line.
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D
Price
$40
$20
30
Quantity of Insulin per month
Demand for farmer Jones’ corn is perfectly (infinitely) elastic because farmer Smith’s corn is a perfect substitute. The
slightest increase in the price of famer Jones’ corn would cause the quantity demanded for Jones’ corn to fall to zero. Also,
the demand price for Jones’ corn remains unchanged regardless of quantity of Jones’ corn available for purchase. The
demand for Jones’ corn is horizontal. Note that the demand for corn in the overall corn market is not perfectly elastic.
Here we are talking about Jones’ corn versus smith’s or any other farmer’s corn. The demand for each individual farmer’s
corn is perfectly elastic.
Price
D
$4.00
20
40
Quantity of Jones' corn
Demand for cigarettes is inelastic because for a nicotine addict close substitutes are unavailable. If the price of cigarettes
rises the smoker may reduce his consumption but by not much. Or, among all smokers the rise in the cigarette price may
lead only a few people to quit smoking. In the diagram below, with a 40% increase in the price from $4 to $6 per pack
(using the midpoint formula), the quantity demand has decreased by only 13% from 320 to 280.
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Price
per
pack
$6.00
$4.00
D
280 320
Packs of cigaretts per day (1,000)
Demand for wild salmon is elastic because close substitutes are available. Also wild salmon is considered a luxury item.
Demand for luxury goods tend to be highly elastic. In the diagram below ∆P% = 18% decrease in price causes the quantity
demand to increase by 40%.
Price
per
pound
$30.00
$25.00
D
20,000 30,000
Quantity (pounds)
Unit elastic demand case is a special situation where the percent change in quantity demanded is equal to the percent
change in price. There is no specific example of a class of goods that have unit elastic demands. In fact demand for any
good becomes unit elastic at a specific price range along the demand curve for that good. In the case of the demand for
wild salmon, the demand at a relatively high price of $30 is elastic. At this relatively high price, compared to the price of
other fish, salmon is considered a luxury. But as the price falls and the price of wild salmon gets closer to the price of other
fish, demand for wild salmon becomes less elastic. At a certain price range then the percent change in quantity demanded
comes very close or becomes equal to the percent change in price. This is where demand becomes unit elastic. In the
diagram below, the price decreases by 20% from $22 to $18. In response, the quantity demand increases by 20% from
36,000 to 44,000 pounds. Thus, the demand is unit elastic at this price range.
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Price
per
pound
$22.00
$18.00
D
36,000
44,000
Quantity (pounds)
Total Revenue Test of Elasticity
Another approach to determine the elasticity of demand is to observe how much buyers spend on a given good before and
after the change in price. This involves comparing the total expenditure on the product (P × Q) at two different prices P₀
and P₁. Since what buyers spend becomes sellers revenue, this approach to test for elasticity is called the total revenue test.
Price Effect versus Quantity Effect
(1) The price effect and quantity effect of a price decrease
When the price of a good decreases, per law of demand quantity demanded increases. The decrease in price and increase
in quantity demanded (sold) impact the total revenue in two opposite directions. The decrease in price—the price effect—
has a negative impact on total revenue, but the increase in quantity sold—quantity effect—has a positive impact. The net
impact depends on the magnitude of the price effect and quantity effect. The question is which effect is dominant?
Demand is inelastic if the price effect of a price decrease dominates the quantity effect. Consider the demand in the
following diagram.
P
$1.00
$0.80
PE
QE
D
1000 1100
5
Q
At P₀ = $1.00, Q₀ = 1,000. Total revenue is TR₀ = P₀ × Q₀ = $1,000. When price is lowered to P₁ = $0.80 quantity demanded
increases to Q₁ = 1,100. Total revenue changes to TR₁ = P₁ × Q₁ = $880. Total revenue has decreased. The price and
quantity effects are computed as follows:
Price effect
Quantity effect
PE = (0.80 – 1.00)(1,000) = −$200
QE = (0.80)(1,100 – 1,000) = $100
Note that PE dominates QE. Revenue gain from increased sales does not compensate for the revenue loss from the lower
price. Total revenue decreases. Demand is inelastic.
TR0 = $1.00 × 1,000 = $1,000
TR1 = $0.80 × 1,100 = $880
∆TR = $880 − $1,000 = −$120
Demand is elastic if the quantity effect dominates the price effect of a price decrease. When price decreases, total
revenue increases. Consider the demand in the following diagram.
P
$1.00
PE
$0.80
D
QE
1000
1400
Q
The price and the quantity effects are as follows:
Price effect
Quantity effect
PE = ($0.80 – $1.00)(1000) = −$200
QE = ($0.90)(1,400 – 1000) = $360
QE dominates PE. Revenue gain from increased sales more than compensates for the revenue loss from the lower price.
Total revenue increases. Demand is elastic.
TR0 = $1.00 × 1000 = $1,000
TR1 = $0.80 × 1,400 = $1,120
∆TR = $1,120 − $1,000 = $120
(2) The price effect and quantity effect of a price increase.
The price effect of a price increase on total revenue is positive. Since fewer quantities are sold, the quantity effect of a
price increase on total revenue is negative.
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Demand is inelastic if the price effect of a price increase dominates the quantity effect. Consider the demand for
cigarettes discussed above.
Price
per
pack
$6.00
PE
$4.00
QE
D
280 320
Packs of cigaretts per day (1,000)
The price and quantity effects of the rise in price from $4.00 to $6.00 are as follows—
PE = ($6 − $4) × 280 = $560
QE = $4 × (−40) = −$240.
The price effect of the price increase dominates. Total revenue increases from TR₀ = $1,280 to TR₁ = $1,680.
Demand is elastic if the quantity effect dominates the price effect of a price increase. Consider the demand for wild
salmon again. This time the price increases from $25 to $30 per pound.
Price
per
pound
$30.00
PE
$25.00
QE
20,000 30,000
Quantity (pounds)
The price and quantity effects of the rise in price from $25 to $30 are as follows—
PE = ($30 − $25) × 20,000 = $100,000
QE = $25 × (20,000 − 30,000) = −$250,000.
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D
The quantity effect dominates the price effect of a price increase. Total revenue decreases from TR₀ = $750,000 to
TR₁ = $600,000. Demand for wild salmon is elastic.
In short:
Price decrease
Price increase
Price effect
Dominates
Quantity effect
TR decreases
TR increases
TR increases
TR decreases
Dominates
Dominates
Dominates
Demand is inelastic
Demand is elastic
Demand is inelastic
Demand is elastic
A simple way of remembering the total revenue test is this:
Demand is inelastic—P and TR change in the same direction: P ↑ → TR↑ and P ↓ → TR↓
Demand is elastic—P and TR change in the opposite directions: P ↑ → TR↓ and P ↓ → TR↑
Price elasticity along the demand curve
Price elasticity does not remain constant along the demand curve. Along a linear demand curve, the slope is constant, but
elasticity changes. In fact, demand becomes less elastic as we move down the demand curve, that is, as the price falls. The
diagram below shows the hypothetical demand curve for wild salmon. Using the total revenue test of elasticity, we can see
that the price effect of a price decrease becomes dominant as we move down the demand curve. At the mid section of the
demand curve the price effect and quantity effect balance each other out, making the demand unit elastic. At points above
the mid section demand is elastic and at point below the mid section demand is inelastic.
Price
$34
$30
$22
$18
$10
$6
D
12
20
36
44
60
68
Quantity (thousands of pounds)
The following diagram shows the relationship between the hypothetical demand function for wild salmon (Q = 80 – 2P) and
the total revenue. Note that at the price of $40 per pound quantity demanded and total revenue (shown in the lower
diagram as the product of price and quantity, P × Q) are both zero. As the price falls quantity demanded increases. Total
revenue also increases at first until price falls to $20, at which total revenue reaches the maximum TR = $20 × 40 = $800.
This mean that demand is elastic until the price falls to $20 and quantity increases to 40. After that, any decrease in price
will result in a lower total revenue. Demand, therefore, becomes inelastic at prices below $20.
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P
44
40
36
32
28
24
20
16
12
8
4
D
0
0
8
16
24
32
40
48
56
64
72
80
88
Quantity (thousands of pounds)
TR
800
768
768
672
672
512
512
288
288
0
0
8
16
24
32
40
48
56
64
72
80
88
Quantity (thousands of pounds)
Another way of looking at why demand elasticity decreases down the demand curve is to consider the percent changes.
Note that the coefficient of elasticity is determined as the ratio of percent change in quantity over percent change in price.
As the price goes down along the vertical axis percentage change in price increases, but as quantity demanded increases
along the horizontal axis, percent change in quantity decreases. Thus the coefficient of price elasticity of demand becomes
smaller and smaller.
Price decrease
From $34 to $30
From $22 to $18
From $10 to $6
∆P%
12.5%
20.0%
50.0%
Quantity increase
From 12 to 20
From 36 to 44
From 60 to 68
∆Q%
50.0%
20.0%
12.5%
E = ∆Q% ∕ ∆P%
4.00
1.00
0.25
Factors Determining the Price Elasticity of Demand


Availability of substitutes— The more substitutes are available, the more elastic the demand is. One can easily
switch from good A to good B if the price A goes up.
Luxury goods versus necessities— If the price of luxury good increases one can easily forgo or postpone the
consumption of that good. So demand for luxuries is price elastic. If a good is a necessity, such as medicine, one
cannot forgo or postpone its consumption if the price rises.
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

Share of income spent on the good— If the expenditure on a good accounts for a small share of a consumer’s
income the demand for that good is inelastic. After all doubling the price of good that costs 50¢ would barely
make a dent in ones budget. Note that demand for wild salmon is elastic because $35 per pound of this fish grabs
a big chunk of one’s weekly grocery budget of, say, $100. A 50% decrease in price constitutes a big saving.
Time— Demand for gasoline tends to be inelastic in the short-run. If the price of gasoline doubles overnight, one
has to continue to go to work or perform the other day-to-day car-dependent daily routine tasks. So the demand
for gasoline tends to be unresponsive to price changes in the short-run. But given time, one could adjust one’s
behavior by buying a smaller car or plan less trips and other efforts to rely less on cars.
Other Demand Elasticities
Cross price elasticity of demand
Cross price elasticity of demand measures the effect of the change in one good’s price on the quantity demanded of a
related good.
CPE =
Q A %
PB %
The two related goods can either be substitutes or complements.
A and B are substitute:
Coke and Pepsi are substitute goods. If the price of Coke increases (∆PC↑), demand for Pepsi will increase (∆QP↑).
Q P %
Therefore, CPE =
0
PC %
In cross price elasticity, therefore, the algebraic sign of coefficient of elasticity is important. Thus, if CPE > 0, the two goods
are substitutes
We also pay attention to the magnitude of the CPE coefficient. If the response to the rise in price of Coke is strong, that is,
if many people switch from Coke to Pepsi, then CPE > 1. This means that Coke and Pepsi are close substitutes. Otherwise, if
only a few people switch, then CPE < 1. Coke and Pepsi, then, are considered weak substitues.
CPE > 1: goods are close substitutes
CPE < 1: goods are weak substitutes
A and B are complements:
Milk and cookies are complements. If the price of milk decreases (∆P M↓), more people will be cookies (∆QC↑). Therefore,
Q C %
CPE =
0
PM %
If the CPE is, therefore, negative, we conclude that the goods are complements. Again, in addition to the sign of the CPE,
the magnitude of the coefficient is also important. if,
|CPED| > 1: goods are close complements
|CPED| < 1: goods are weak complements
Income Elasticity of Demand
Income elasticity of demand is a measure of how much the demand for a good is affected by changes in consumers’
incomes.
IE =
Q%
I%
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Normal goods
A good is considered a normal good if people buy more of that good when their income increases. Therefore, income
Q%
elasticity for a normal good is positive. IE =
>0
I%
If income-induced response to the demand of a good is strong, then IE > 1. The demand is income-elastic. This would
indicate that the good is a luxury good. If the response is not strong, then IE < 1. The demand is income-inelastic. This
would indicate that the good is a necessity.
IE > 1: demand is income elastic (luxury goods—vacation homes; international travel)
IE < 1: demand is income inelastic (necessities—food and clothing)
Inferior goods
A good is considered an inferior good if people buy less of that good when their income increases. Income elasticity for an
Q%
inferior good is, then, negative. IE =
< 0. Examples of inferior goods are: rental housing and public transportation.
I%
Price Elasticity of Supply
The price elasticity of supply measures the degree of suppliers’ response to a change in the price of the good being
supplied. Since the relationship between price and quantity supplied is always direct, the coefficient of price elasticity of
supply is always positive.
PES =
Q S %
P%
Factors determining the elasticity of supply
 Availability of inputs— If inputs are readily available to expand output in response to a price increase, then supply
is elastic.
 Time— The price elasticity of supply tends to increase as producers have more time to respond to a price change.
The long-run elasticity of supply is greater than the short-run elasticity.
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