Transcript ECON 1001 AB Introduction to Economics I Dr. Ka-fu WONG Fourth week

ECON 1001 AB
Introduction to Economics I
Dr. Ka-fu WONG
Fourth week of tutorial sessions
KKL 925, K812, KKL 106
Clifford CHAN
KKL 1109
[email protected]
Covered and to be covered
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Covered last week
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Dr. Wong finished up to kf004.ppt
You should have at least read up to Chapter 4 Elasticity.
If not, please press hard on them. We are getting to the first midterm!
Start reading Chapter 5 Demand: The Benefit Side of the Market
Your first midterm covering chapter 1 – chapter 4 will be held on this
Saturday October 6, 2007 at 9am
To be covered in the tutorial sessions this week
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Problems in chapter 4: #1, #3, #5, #7 and #9
You are advised to work on the even ones as well
Problem #1, Chapter 4
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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)
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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)
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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
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If this is the case, we regard the highly responsive demand as
ELASTIC
Solution to Problem #1 (3)
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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
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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
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If this is the case, we regard the mirror-responsive demand as
UNITARY ELASTIC
Solution to Problem #1 (4)
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General formula for (Own) Price Elasticity of Demand:
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(Change of quantity demanded / Total quantity demanded) /
(Change of price / Original Price)
Rearranging terms, we will get
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(Change in quantity demanded / Change in price) *
(Original Price / Total quantity demanded)
(1 / Slope of the demand curve) * (P / Q)
Using the formula, we can derive price elasticity of
demand at any point along the demand curve
Solution to Problem #1 (5)
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Point A
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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
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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)
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Point C
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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
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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)
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Point E
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1 / Slope of the demand curve = -1
Price is $0 and quantity demanded is 100
Price elasticity of demand = -1 * (0 / 100)
Price elasticity of demand = 0 (Or 0 if we take the absolute value)
As it is exactly equal to 0, the price elasticity of demand is zero
The demand is perfectly inelastic- the quantity demanded does
not change regardless of the change in price
Problem #3, Chapter 4
Suppose, while rummaging through
your uncle’s closet, you found the
original painting of Dogs Playing
Poker, a valuable piece of art. You
decided to set up a display in your
uncle’s garage. The demand curve to
see this valuable piece of art is as
shown in the diagram. What price
should you charge if your goal is to
maximize your revenues from tickets
sold? On a graph, show the inelastic
and elastic regions of the demand
curve.
12
Price ($/visit)
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0
6
Quantity
(visitors/day)
Solution to Problem #3 (1)
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Where is the source of revenue from displaying the
artwork in your uncle’s garage?
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How much should you charge in order to maximize the
revenue?
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Selling admission tickets to your uncle’s garage
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?
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You should charge at the price where it is the midpoint of the
demand curve
Solution to Problem #3 (2)
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At the midpoint of a linear demand curve, the price
elasticity of demand is unitary elastic (1)
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Percentage of change in quantity demanded = Percentage of
change in price
Left of the midpoint, the price elasticity of demand is
elastic (>1)
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Percentage of change in quantity demanded is greater than
Percentage of change in price
Lowing the price will lead to an increase in quantity demanded,
and thus revenue will go up
Solution to Problem #3 (3)
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Right of the midpoint, the price elasticity of demand is
inelastic (<1)
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At the midpoint,
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Percentage of change in quantity demanded is less than
Percentage of change in price
Increasing the price will only lead to a slight decrease in quantity
demanded, and thus revenue will go up
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
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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
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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)
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Senior executives are most likely to have a least priceelastic 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
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Change in price of the membership causes a small effect on
senior executive
Solution to Problem #5 (2)
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The membership shares a notable portion of the income
earned by a typical junior executive
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The membership shares a considerable portion of the
income earned by a typical student
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Change in price of the membership causes a notable effect on
junior executives
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)
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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
What are the respective
price elasticities of supply
at A and B on the supply
curve shown in the
accompanying figure?
B S
6
Price
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4
0
Change
in price
A
Change in
quantity
9
Quantity
12
Solution to Problem #7 (1)
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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)
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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
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If this is the case, we regard the highly responsive supply as
ELASTIC
Solution to Problem #7 (3)
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When a price elasticity of supply is less than one, that
means percentage change in quantity supplied is less
than percentage change in price
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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
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If this is the case, we regard the mirror-responsive supply as
UNITARY ELASTIC
Solution to Problem #7 (4)
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General formula for (Own) Price Elasticity of Supply:
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(Change of quantity supplied / Total quantity supplied) /
(Change of price / Original Price)
Rearranging terms, we will get
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(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)
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Point A
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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
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1 / Slope of the supply curve = 1 / (2/3) = 3/2
Price is $6 and quantity supplied is 12
Price elasticity of supply = 3/2 * (6 / 12)
Price elasticity of supply = 3/4
As it is less than 1, the supply is inelastic
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At point A on the demand
curve shown, by what
percentage will a 1
percent increase in the
price of the product affect
the total expenditure on
the product?
Price ($/unit)
Problem #9, Chapter 4
6
4
A
6
Quantity (units/week)
18
Solution to Problem #9 (1)
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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
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1 / Slope of the demand curve = 1 / (-1/3) = -3
Price is $4 and the quantity demanded is 6
Price elasticity of demand = -3 * (4/6) = -2 (Or 2 if we take the
absolute value)
As it is greater than 1, the demand is elastic
Solution to Problem #9 (2)
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Based on the price elasticity of demand, we conclude
that a 1-percent 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)
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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.
The end
Thanks for coming!
Good luck in your
midterm!!!