Transcript Chapter 4.odd

Chapter 4
Elasticity
Odd-number Questions
Problem #1, Chapter 4
• On the accompanying
demand curve, calculate
the price elasticity of
demand at points A, B, C,
D and E.
Price
100
A
B
75
C
50
D
25
E
0
25
50
75
Quantity
100
Solution to Problem #1 (1)
• Price elasticity of demand refers to the percentage change of
quantity demanded relative to the percentage change of price
• In other words, price elasticity of demand indicates how much
will the quantity demanded change with respect to a 1%
change in price
• Thus, it measures the responsiveness of quantity demanded
to change in price
Solution to Problem #1 (2)
• Price elasticity of demand is always a negative index, as the
demand curve is downward sloping
• For convenience, we always take absolute value of a price
elasticity of demand
• When the absolute value of a price elasticity of demand is
greater than one, that means percentage change in quantity
demanded is greater than percentage change in price
– If this is the case, we regard the highly responsive demand as ELASTIC
Solution to Problem #1 (3)
• When the absolute value of a price elasticity of demand is less
than one, that means percentage change in quantity
demanded is less than percentage change in price
– If this is the case, we regard the weakly responsive demand as
INELASTIC
• When the absolute value of a price elasticity of demand is
exactly equal to one, that means percentage change in
quantity demanded is the same as percentage change in price
– If this is the case, we regard the mirror-responsive demand as
UNITARY ELASTIC
Solution to Problem #1 (4)
• General formula for (Own) Price Elasticity of Demand:
– (Change of quantity demanded / Total quantity demanded) / (Change
of price / Original Price)
– Rearranging terms, we will get
• (Change in quantity demanded / Change in price) *
Price / Total quantity demanded)
• (1 / Slope of the demand curve) * (P / Q)
(Original
• Using the formula, we can derive price elasticity of demand at
any point along the demand curve
Solution to Problem #1 (5)
• Point A
–
–
–
–
–
1 / Slope of the demand curve 1 / (-100/100) = -1
Price is $100 and quantity demanded is 0
Price elasticity of demand = -1 * (100 / 0)
Price elasticity of demand = Infinity
The demand is perfectly elastic
• Point B
–
–
–
–
–
1 / Slope of the demand curve = -1
Price is $75 and quantity demanded is 25
Price elasticity of demand = -1 * (75 / 25)
Price elasticity of demand = -3 (Or 3 in if we take absolute value)
As it is greater than 1, the demand is elastic
Solution to Problem #1 (6)
• Point C
–
–
–
–
–
1 / Slope of the demand curve = -1
Price is $50 and quantity demanded is 50
Price elasticity of demand = -1 * (50 / 50)
Price elasticity of demand = -1 (Or 1 if we take the absolute value)
As it is exactly equal to 1, the demand is unitary elastic
• Point D
–
–
–
–
–
1 / Slope of the demand curve = -1
Price is $25 and quantity demanded is 75
Price elasticity of demand = -1 * (25 / 75)
Price elasticity of demand = -1/3 (Or 1/3 if we take the absolute value)
As it is less than 1, the demand is inelastic
Solution to Problem #1 (7)
• Point E
–
–
–
–
–
–
1 / Slope of the demand curve = -1
Price is $0 and quantity demanded is 100
Price elasticity of demand = -1 * (0 / 100)
Price elasticity of demand = 0 (Or 0 if we take the absolute value)
As it is exactly equal to 0, the price elasticity of demand is zero
The demand is perfectly inelastic- the quantity demanded does not
change regardless of the change in price
Problem #3, Chapter 4
12
Price ($/visit)
• Suppose, while rummaging through
your uncle’s closet, you found the
original painting of Dogs Playing Poker,
a valuable piece of art. You decided to
set up a display in your uncle’s garage.
The demand curve to see this valuable
piece of art is as shown in the diagram.
What price should you charge if your
goal is to maximize your revenues from
tickets sold? On a graph, show the
inelastic and elastic regions of the
demand curve.
0
6
Quantity
(visitors/day)
Solution to Problem #3 (1)
• Where is the source of revenue from displaying the artwork in
your uncle’s garage?
– Selling admission tickets to your uncle’s garage
• How much should you charge in order to maximize the
revenue?
– You should charge a price where the marginal revenue = marginal cost
– However, no supply curve is given in this problem, and we can only
consider the demand curve alone
• How much should you charge then?
– You should charge at the price where it is the midpoint of the demand
curve
Solution to Problem #3 (2)
• At the midpoint of a linear demand curve, the price elasticity
of demand is unitary elastic (1)
– Percentage of change in quantity demanded = Percentage of change in
price
• Left of the midpoint, the price elasticity of demand is elastic
(>1)
– Percentage of change in quantity demanded is greater than
Percentage of change in price
– Increasing the price will lead to an decrease in quantity demanded,
and thus revenue will go down
Solution to Problem #3 (3)
• Right of the midpoint, the price elasticity of demand is
inelastic (<1)
• At the midpoint,
– Further change in price will cause total revenue fall
– The optimal price is settled at the midpoint of a demand curve
• Therefore, you should charge $6 for each admission ticket
where the total quantity demanded is 3
Solution to Problem #3 (4)
Price ($ per visit)
12
Elastic region
Midpoint
6
Inelastic region
Quantity (Visitors per day)
3
6
• Elastic region is located on the left of the midpoint
• Inelastic region is located on the right of the midpoint
Problem #5, Chapter 4
• Among the following groups- senior executives, junior
executives, and students- which is likely to have the most and
which is likely to have the least price-elastic demand for
membership in the Association of Business Professionals?
Solution to Problem #5 (1)
• Senior executives are most likely to have a least price-elastic
demand for membership in the Association of Business
Professionals
• Senior executives have a higher income than junior executives,
while junior executives have a higher income than students
• The membership shares only a small portion of the income
earned by a typical senior executive
– Change in price of the membership causes a small effect on senior
executive
Solution to Problem #5 (2)
• The membership shares a notable portion of the income
earned by a typical junior executive
– Change in price of the membership causes a notable effect on junior
executives
• The membership shares a considerable portion of the income
earned by a typical student
– Change in price of the membership causes a considerable effect on
students
• In general, one earning high income is less likely to respond to
change in price dramatically as the price is actually a very
small portion of one’s consumption budget
Solution to Problem #5 (3)
• Therefore, senior executives have a least price-elastic demand
for the membership
• Which of the three groups has the most price-elastic demand
for the membership?
• Students
– They earning the lowest income among the groups will be
affected the most by the change in price of the membership
as it takes a considerable portion of their income
– Hence, they will probably respond dramatically to change in
the price of the membership
Problem #7, Chapter 4
S
6
Price
• What are the respective price
elasticities of supply at A and
B on the supply curve shown
in the accompanying figure?
Change
in price
4
0
Change in
quantity
9
Quantity
12
Solution to Problem #7 (1)
• Calculating price elasticity of supply is almost identical to
calculating price elasticity of demand, except for the slope of
the curve
• Price elasticity of supply refers to the percentage change of
quantity supplied relative to the percentage change of price
• In other words, price elasticity of supply indicates how much
will the quantity supplied change with respect to a 1% change
in price
• Thus, it measures the responsiveness of quantity supplied to
change in price
Solution to Problem #7 (2)
• Price elasticity of supply is always a positive index, as the
supply curve is upward sloping
• When a price elasticity of supply is greater than one, that
means percentage change in quantity supplied is greater than
percentage change in price
– If this is the case, we regard the highly responsive supply as ELASTIC
Solution to Problem #7 (3)
• When a price elasticity of supply is less than one, that means
percentage change in quantity supplied is less than
percentage change in price
– If this is the case, we regard the weakly responsive supply as
INELASTIC
• When a price elasticity of supply is exactly equal to one, that
means percentage change in quantity supplied is the same as
percentage change in price
– If this is the case, we regard the mirror-responsive supply as UNITARY
ELASTIC
Solution to Problem #7 (4)
• General formula for (Own) Price Elasticity of Supply:
– (Change of quantity supplied / Total quantity supplied) / (Change of
price / Original Price)
– Rearranging terms, we will get
• (Change in quantity supplied / Change in price) * (Original Price /
Total quantity supplied)
• (1/ Slope of the supply curve) * (P / Q)
• Using the formula, we can derive price elasticity of supply at
any point along the supply curve
Solution to Problem #7 (5)
• Point A
–
–
–
–
–
1 / Slope of the supply curve = 1 / (2/3) = 3/2
Price is $4 and quantity supplied is 9
Price elasticity of supply = 3/2 * (4 / 9)
Price elasticity of supply = 2/3
As it is less than 1, the supply is inelastic
• Point B
–
–
–
–
–
1 / Slope of the supply curve = 1 / (2/3) = 3/2
Price is $6 and quantity supplied is 12
Price elasticity of supply = 3/2 * (6 / 12)
Price elasticity of supply = 3/4
As it is less than 1, the supply is inelastic
• At point A on the demand
curve shown, by what
percentage will a 1 percent
increase in the price of the
product affect the total
expenditure on the product?
Price ($/unit)
Problem #9, Chapter 4
6
4
6
Quantity (units/week)
18
Solution to Problem #9 (1)
• In order to answer this question, we will need to compute the
price elasticity of demand
• Applying the general formula, Price elasticity of demand = (1/
Slope of the demand curve) * (P/Q), we get
• Price elasticity of demand
– The absolute value of the slope of this demand curve is 1/3
– Price is $4 and the quantity demanded is 6
– Price elasticity of demand at point A = 3 * (4/6) = 2
Solution to Problem #9 (2)
• Based on the price elasticity of demand, we conclude that a 1percent increase in price will cause a 2-percent decrease in
quantity demanded for the product
• How much does the total expenditure change?
• Total expenditure (TE) = Price (P) * Quantity (Q)
• What will happen if the price increases by 1% and quantity
demanded decreases by 2%?
• Initially, TE = P * Q
• After the change in price, TE will become 1.01P * 0.98Q
Solution to Problem #9 (3)
• From the Total Expenditure function = 1.01P * 0.98Q, a 0.02
decrease in quantity demanded with a 0.01 increase in price
of the product, will approximately lead to a 0.01 (1%)
reduction in Total Expenditure.