Transcript Session7-ElasticityandItsApplication

Economic Analysis
for Business
Session V: Elasticity and its Application-1I
Instructor
Sandeep Basnyat
9841892281
[email protected]
APPLICATION: Does Drug Interdiction Increase or
Decrease Drug-Related Crime?

One side effect of illegal drug use is crime: Users
often turn to crime to finance their habit.

We examine two policies designed to reduce illegal
drug use and see what effects they have on drugrelated crime.

For simplicity, we assume the total dollar value of
drug-related crime equals total expenditure
on drugs.

Demand for illegal drugs is inelastic, due to
addiction issues.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Policy 1: Interdiction
Interdiction
Price of
reduces
Drugs
the supply
of drugs.
P2
Since demand
for drugs is
inelastic,
P1
P rises proportionally more
than Q falls.
new value of drugrelated crime
S2
D1
Result: an increase in
total spending on drugs,
and in drug-related crime
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
S1
initial value
of drugrelated
crime
Q2 Q 1
Quantity
of Drugs
Policy 2: Education
Price of
Education
reduces the Drugs
demand for
drugs.
new value of drugrelated crime
D2
D1
S
P and Q fall.
Result:
A decrease in
total spending
on drugs, and
in drug-related
crime.
initial value
of drugrelated
crime
P1
P2
Q2 Q1
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Quantity
of Drugs
Income Elasticity of Demand

The income elasticity of demand measures the
response of Qd to a change in consumer income.
Percent change in Qd
Income elasticity
=
of demand
Percent change in income
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Calculating Income Elasticity of Demand

Arc Elasticity:
Q
% Q
Q Y
Q
x 


Y
% Y
Y Q
Y
◦ where Y stands for income.

Example
◦ If a 1% increase in income results in a 3% decrease in quantity
demanded, the income elasticity of demand is x = -3%/1% =
-3.
Numerical Example
a) Suppose the demand for an automobile as a function of
income per capita is given by:
Q = 50,000 + 5I
What is the income elasticity of demand when per capita
income increases from $10,000 to $11,000?
Numerical Example
a) Suppose the demand for an automobile as a function of
income per capita is given by:
Q = 50,000 + 5I
What is the income elasticity of demand when per capita
income increases from $10,000 to $11,000?
Solution:
When I1 = 10,000 Q1 = 100,000
When I2 = 11,000, Q2 = 105,000
Percentage Change in Q = 4.88
Percentage Change in I = 9.52
Income Elasticity of Demand = 4.88 / 9.52 = 0.512
Numerical Example-Point Income Elasticity
b) Suppose the demand for an automobile as a function of
income per capita is given by:
Q = 50,000 + 5I
What is the income elasticity of demand at the income level
of $10,500?
Numerical Example
b) Suppose the demand for an automobile as a function of
income per capita is given by:
Q = 50,000 + 5I
What is the income elasticity of demand at the income level
of $10,500?
Solution:
When I = 10,500;
Q = 102,500
dQ / dI = b = 5
Income Elasticity of Demand = b x (P/Q)
= 5 x (10500 / 102500)
E = 0.512
Necessities, Inferior goods and luxuries
Elasticity measurement as:
 E<0
: Inferior goods (negative)
 0 < E ≤ 1 : Normal goods or necessities
 E>1
: Luxuries
 An increase in income causes an increase in
demand for a normal good and luxuries.
 An increase in income causes a decrease in
demand for inferior goods.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Cross Price Elasticity of Demand

The cross-price elasticity of demand measures the
response of demand for one good to changes in the price
of another good.
% change in Qd for good 1
Cross-price elast.
=
of demand
% change in price of good 2
 For substitutes, cross-price elasticity > 0 (positive)
E.g., an increase in price of goat meat causes an
increase in demand for chicken.
 For complements, cross-price elasticity < 0
(Negative)
E.g., an increase in price of computers causes
decrease in demand
for software.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Calculating Cross Price Elasticity of Demand

Arc Elasticity,
Q
% Q
Q po
Q


po
% po
po Q
po
◦ where Po stands for price of another good.

Example
◦ If a 1% increase in the price of a related good results in a 3%
decrease in quantity demanded, the cross-price elasticity of
demand is = -3%/1% = -3.
Numerical Example
Demand for a publisher’s book is given as:
Qx = 12,000 – 5,000Px + 5I + 500Pc
 Px = Price of the book = $5
 I = Income per capita = $10,000
 Pc = Price of the books from competing publishers = $6
1.
2.
3.
Find Price elasticity of demand for the book. What
effect a price increase would have on total revenues?
Find income elasticity of demand for the book. Find if
the book is inferior good, normal good or luxury.
Assess the probable impact on demand for the book if
competing publishers raise their prices. Are the books
substitute for each other or complements?
Numerical Example
1) a) Find Price elasticity of demand for the book.
b) What effect a price increase would have on total revenues?
Solution:
a) Substituting the values of I and Pc
Qx = 12,000 – 5,000Px + 5(10000) + 500(6)
Or, Qx = 65,000 – 5,000Px
When Px = $5 (given), Qx = 40,000
Now, dQx/dPx = b = - 5000
Therefore, E p = -5000 x (5 / 40000) = - 0.625
b) Since, the demand for the book is inelastic, an increase in
the price of the book would increase total revenue.
Numerical Example
Demand for a publisher’s book is given as:
Qx = 12,000 – 5,000Px + 5I + 500Pc
 Px = Price of the book = $5
 I = Income per capita = $10,000
 Pc = Price of the books from competing publishers = $6
Find Price elasticity of demand for the book. What
DONE 1.
2.
3.
effect a price increase would have on total revenues?
Find income elasticity of demand for the book. Find if
the book is inferior good, normal good or luxury.
Assess the probable impact on demand for the book if
competing publishers raise their prices. Are the books
substitute for each other or complements?
Numerical Example
2) a) Find income elasticity of demand for the book.
b) Find if the book is inferior good, normal good or luxury.
Solution:
a) Substituting the values of Px and Pc
Qx = 12,000 – 5,000(5) + 5I + 500(6)
Or, Qx = - 10,000 + 5I
When I = $10000 (given), Qx = 40,000
Now, dQx/dI = b = 5
Therefore, E I = 5 x (10000 / 40000) = 1.25
b) Since, the E I > 1 for the book, the book is luxury.
Numerical Example
Demand for a publisher’s book is given as:
Qx = 12,000 – 5,000Px + 5I + 500Pc
 Px = Price of the book = $5
 I = Income per capita = $10,000
 Pc = Price of the books from competing publishers = $6
Find Price elasticity of demand for the book. What
DONE 1.
effect a price increase would have on total revenues?
DONE 2.Find income elasticity of demand for the book. Find if
the book is inferior good, normal good or luxury.
3. Assess the probable impact on demand for the book if
competing publishers raise their prices. Are the books
substitute for each other or complements?
Numerical Example
3) a) Assess the probable impact on demand for the book if
competing publishers raise their prices.
b) Are the books substitute for each other or complements?
Solution:
a) Substituting the values of Px and I
Qx = 12,000 – 5,000(5) + 5(10000) + 500Pc
Or, Qx = 37,000 + 500Pc
When Pc = $6 (given), Qx = 40,000
Now, dQx/dPc = b = 500
Therefore, Cross price elasticity of demand for the book
E c = 500 x (6 / 40000) = 0.075
1% increase in competitor’s book price will increase the demand
for the book by 0.075%
b) Since, the E C > 0 for the book, the book is substitute to
competing producer’s book.
Basic Concept on Marginal Effects
Consider a simple linear equation for a demand curve:
Q =180 -2p ………………………….……(i)
When p = 5; Q = 180 - 2 x 5 = 170
P = 6; Q = 168
P = 7; Q = 166
For every 1 unit increase in the p, Q decreases by 2 units.
So, -2 = Marginal effect of Price on Quantity
Similarly for multivariate equation:
Q = a + bP + cI
‘c’ is the Marginal Effect of Income on quantity.
For the inverse demand function of equation (i) above,
P = 90 - 0.5Q
Q is the marginal effect of quantity on price.
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
Where;
Q = quantity demanded per month
P=price of the product
A=firm’s advertising expenditure per month
Y=per capita disposable income
P *=price of BJ Corp
a) During the next five years, per capita disposable
income is expected to increase by $2,500. What effect
will this have on the firm’s sales?
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
a) During the next five years, per capita disposable
income is expected to increase by £2,500. What
effect will this have on the firm’s sales?
Solution:
For 1 unit increase I Y; Q increases by 2.8 unit
For 2500 units increase in Y; Q increases by 2500 x
2.8 units.
Therefore, Increase in sales = 7000 units.
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
b) What is the relationship between the products of PK
and BJ??
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
b) What is the relationship between the products of PK
and BJ??
Solution:
For 1 unit increase Price of BJ (P*); Quantity of PK (Q)
decreases by 1.2 units
Therefore Cross price elasticity of Demand is negative
(<0)
Hence, both companies are producing complementary
products.
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
c) PK intends to charge $15 and spend $10,000 per
month on promotion, while it believes per capita
income will be $12,000 and BJ’s price will be $3,
calculate the income elasticity of demand. What
does this tell you about the nature of PK’s product?
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
c) PK intends to charge $15 and spend $10,000 per
month on promotion, while it believes per capita
income will be $12,000 and BJ’s price will be $3,
calculate the income elasticity of demand. What
does this tell you about the nature of PK’s product?
Solution:
YED = 2.8 x (12000 / 41665.4) = 0.806
PK is selling normal goods.
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
d) What effect would an increase in advertising of
$1000 have on profitability, if each additional unit costs
$10 to produce?
Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows:
Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*
d) What effect would an increase in advertising of
$1000 have on profitability, if each additional unit costs
$10 to produce?
Solution:
If Increase in A = 1; Increase in Q = 0.8 = 800 units;
Increase in R = 800 x 15 = $12,000
Increase in Costs = 800 x 10 + advertisement
(A)$1000= $9,000
Thus every additional $1,000 spent on advertising
increases profit by $3,000.
Basic Concepts on Power form Elasticity
Recall the basic non-linear (power form) function:
Q = Pα
Here, Price Elasticity of Demand = α
Eg. If, Q = P2
PED = 2
Meaning: for 1 % increase in the P, Q decreases by 2%.
Analysis can be extended to a multivariate functions:
Q= aPb Ac Yd P0e
Here, P = price of the good
A = Advertisement expenditure
Y = Income level of the people
PO = Price of other goods.
Basic Concepts on Power form Elasticity
Consider a non-linear demand function:
Q = 9.83P-1.2A2.5Y1.6P01.4
Here, P = price of the good =$60
A = Advertisement expenditure = $120,000
Y = Income level of the people = $28,000
P0 = Price of other goods = $45
Find the equation for the demand curve.
Basic Concepts on Power form Elasticity
Consider a non-linear demand function:
Q = 9.83P-1.2A2.5Y1.6P0-1.4
Here, P = price of the good =$60
A = Advertisement expenditure = $120,000
Y = Income level of the people = $28,000
P0 = Price of other goods = $45
Find the equation for the demand curve.
Solution:
Q = 9.83P-1.2(120000)2.5(28000)1.6(45)-1.4
Q = 3100718641762767839.13P-1.2
Price Elasticity of Supply
Price elasticity
of supply

Percentage change in Qs
=
Percentage change in P
Price elasticity of supply measures how
much Qs responds to a change in P.
 Loosely speaking, it measures the pricesensitivity of sellers’ supply.
 Again, use the midpoint method to compute
the percentage changes.
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Price Elasticity of Supply
Price elasticity
of supply
Example:
Price
elasticity
of supply
equals
16%
= 2.0
8%
Percentage change in Qs
=
Percentage change in P
P
S
P rises
P2
by 8%
P1
Q1
Q rises
by 16%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q2
Q
The Variety of Supply Curves
Economists classify supply curves according to
their elasticity.
 The slope of the supply curve is closely related
to price elasticity of supply.
 Rule of thumb:
The flatter the curve, the bigger the elasticity.
The steeper the curve, the smaller the elasticity.
 The next 5 slides present the different
classifications, from least to most elastic.

CHAPTER 5 ELASTICITY
AND ITS APPLICATION
“Perfectly inelastic” (one extreme)
0%
% change in Q
Price elasticity
=
=
of supply
10%
% change in P
P
S curve:
vertical
S
P2
Sellers’
price sensitivity:
0
Elasticity:
0
=0
P1
P rises
by 10%
Q1
Q changes
by 0%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Inelastic”
< 10%
% change in Q
Price elasticity
=
=
of supply
10%
% change in P
P
S curve:
relatively steep
S
P2
Sellers’
price sensitivity:
relatively low
Elasticity:
<1
<1
P1
P rises
by 10%
Q1 Q2
Q rises less
than 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Unit elastic”
% change in Q
Price elasticity
=
=
of supply
% change in P
=1
10%
P
S curve:
intermediate slope
S
P2
Sellers’
price sensitivity:
intermediate
Elasticity:
=1
10%
P1
P rises
by 10%
Q1
Q2
Q rises
by 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Elastic”
> 10%
% change in Q
Price elasticity
>1
=
=
of supply
10%
% change in P
P
S curve:
relatively flat
S
P2
Sellers’
price sensitivity:
relatively high
Elasticity:
>1
P1
P rises
by 10%
Q1
Q2
Q rises more
than 10%
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
“Perfectly elastic” (the other extreme)
any %
% change in Q
Price elasticity
= infinity
=
=
of supply
0%
% change in P
P
S curve:
horizontal
Sellers’
price sensitivity:
extreme
Elasticity:
infinity
S
P2 = P1
P changes
by 0%
Q1
Q2
Q changes
by any %
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Q
The Determinants of Supply Elasticity
The more easily sellers can change the quantity
they produce, the greater the price elasticity of
supply.
 Example: Supply of King’s Way property is
harder to vary and thus less elastic than
supply of new cars.
 For many goods, price elasticity of supply is
greater in the long run than in the short run,
because firms can build new factories, or
new firms may be able to enter the market.

CHAPTER 5 ELASTICITY
AND ITS APPLICATION
3:
Elasticity and changes in equilibrium
ACTIVE LEARNING
The supply of beachfront property is
inelastic. The supply of new cars is elastic.
 Suppose population growth causes
demand for both goods to double
(at each price, Qd doubles).
 For which product will P change the most?
 For which product will Q change the most?

41
ACTIVE LEARNING
3:
Answers
Beachfront
property (inelastic
supply):
When supply
is inelastic,
P
an increase in
D1 D2
demand has a
bigger impact
on price than P
2
on quantity.
P1
S
B
A
Q 1 Q2
Q
42
ACTIVE LEARNING
3:
Answers
When supply
is elastic,
an increase in
demand has a
bigger impact
on quantity
than on price.
New cars
(elastic supply):
P
D1 D2
S
P2
P1
B
A
Q1
Q2
Q
43
How the Price Elasticity of Supply Can Vary
P
Supply often
becomes
less elastic
as Q rises,
due to
capacity limits.
S
elasticity
<1
$15
12
elasticity
>1
4
$3
100 200
Q
500 525
CHAPTER 5 ELASTICITY
AND ITS APPLICATION
Thank you