Chapter 4

```Chapter 4
Elasticity
End-of Chapter Ex. 4, 8
Elasticity
• It represents the ratio of the % change in one variable to the
% change in another variable
• 1) Price Elasticity of Demand
- measures the responsiveness of quantity demanded for
good x to a change in price of good x
% change in Qx
% change in Px
• 2) Price Elasticity of Supply
- measures the responsiveness of quantity supplied for good x
to a change in price of good x
% change in Qx
% change in Px
Elasticity
%Q

%P
Unit elastic
Elastic
-5
-4
-3
Inelastic
-2
-1
-0.5
0
• Elastic :
-the % change in quantity demanded is larger than the %
change in price
- If elasticity is between -1 and infinity
• Inelastic:
-the % change in quantity demanded is less than the % change
in price
-If elasticity is between 0 and -1
Elasticity
• Unit Elastic,
- Elasticity = -1
- the % change in quantity demanded equals to the % change
in price
P
Unit Elastic
Q
Elasticity
• Perfectly Inelastic
Demand/Supply
• Perfectly Elastic
Demand/Supply
P
P
Elasticity = 0
Elasticity = infinitely
Q
• Ex. Pepsi, coke
Q
• Ex. Tamiflu, Insulin
Elasticity and TE / TR
• If demand is elastic, (% change in quantity demanded
is larger than the % change in price)
• Decrease in price will increase TR
• Increase in price will decrease TR
If Price decrease:
P
% change in Q = 3
% change in P = -0.5
Elasticity = -6 (Elastic)
TR increases
10
5
D
5
20
Q
Elasticity and TE / TR
• If demand is inelastic, (% change in quantity
demanded is less than the % change in price)
• Decrease in price will decrease TR
• Increase in price will increase TR
P
If Price decrease:
% change in Q = 0.4
% change in P = -0.5
Elasticity = -0.8 (Inelastic)
TR decreases
10
5
D
5
7
Q
Elasticity and TE / TR
• If Demand is Elastic, (% change in quantity demanded is larger
than the % change in price), Q and PQ move in the same direction,
similarly to increase in price
P
Q
X
=
PQ
• If Demand in Inelastic, (% change in quantity demanded is less
than the % change in price), P and PQ move in the same direction,
similarly to increase in price
P
X
Q
=
PQ
Elasticity
• 3) Cross-Price Elasticity of Demand
- measure the responsiveness of quantity demanded for good
y to a change in price of good x
% change in Qy
% change in Px
• Substitute goods: Elasticity is positive (Increase in price of
good x will result in an increase in demand of good y)
• Complement goods: Elasticity is negative (Increase in price of
good x will result in a decrease in demand of good y)
Elasticity
• 4) Income Elasticity of Demand
- measure the responsiveness of quantity demanded for good
x to a change in income
% change in Qx
% change in I
• Normal goods: Elasticity is positive (Increase in income will
result in an increase in demand of good x) i.e., Mercedes Benz
• Inferior goods: Elasticity is negative (Increase in income will
result in a decrease in demand of good x) i.e., 2nd hand
clothing
When the price of hot dog is \$1.50 each, 500 hot dogs
are sold every day. After lowering the price to \$1.35
each, 510 hot dogs are sold every day. At the original
price, what is the price elasticity of demand for hot
dogs?
A)
B)
C)
D)
E)
66.67
5
1
0.2
0.015
Calculating Price Elasticity of Demand
%Q

%P
 QNew  QOld   PNew  POld 



QOld

  POld

Q P Q P




Q
P
P Q
Price Elasticity of Demand for Hot Dogs
QOld  500, QNew  510
POld  \$1.50, PNew  \$1.35
Q  510  500  10
P  \$1.35  \$1.50  \$0.15
Q POld
10 1.50



P QOld 0.15 500
 0.2 (D)
For which of the following products is demand likely to
be least price elastic?
A)
B)
C)
D)
E)
Frozen Food
Soft Drinks
Groceries
Diet Coke
Not enough information provided to answer this question
What affects Price Elasticity of Demand?
• One major factor is the availability of substitutes.
• If there are many substitutes for Good X available in the
market, people tend to be very responsive to changes in PX,
and hence, higher elasticity.
• In this question, we check out which option is the most
difficult to be substituted, i.e., necessity good.
• (A) Frozen food can easily be replaced by fresh food.
• (B) Soft drinks and (D) Diet coke can easily find substitutes,
e.g. orange juice, coffee, tea, Zero coke, Diet Pepsi
• (C) Groceries are the hardest to be replaced as they are
necessities.
Ans: C
If the price is \$2 in both locations, the Price
Elasticity of Demand for a candy bar at an airport is
likely to be
the price elasticity for a candy bar
in a grocery store.
A)
B)
C)
D)
E)
Less than
Equal to
Greater than
The reciprocal of
Not enough information to determine
What affects Price Elasticity of Demand?
• Number of sellers within reach.
• Suppose there exists only one kind of candy bar.
• In busy areas where you can find grocery stores, it is more
likely that you can find more than one shop selling candy bars.
• However, in isolated areas such as airports, there may only be
one seller.
• In other words, one will find it difficult to locate an alternative
seller of a certain goods (e.g. candy bars) at the airport.
• A person will still have to buy candy bars from that seller at
the airport even if prices are raised.
• Hence, quantity demanded is less responsive to price changes
compared to shops at other locations.
Ans: a
The Price Elasticity of Demand for apartments is
1.3, while the Price Elasticity of Demand for
toothpicks is 0.4. The likely reason for the
difference is because
A)
B)
C)
D)
E)
There are few substitutes for toothpicks
Apartments are chosen over a long period of time
The fraction of income spent on toothpicks is minuscule
Toothpicks are a necessity
Apartments are a luxury
• Demand for apartments are more price elastic than that for
toothpicks. Why?
• (A & D) are not true because there exist good substitutes for
toothpicks, e.g. dental floss and fingernails.
• (B) is true for many consumers, but is irrelevant, as we are
comparing the Price Elasticity at the same point of time.
• (E) is relevant only if we are talking about Income Elasticity.
What affects Price Elasticity of Demand?
• Budget share: the smaller the budget share of your income, the
smaller the incentive to look for other substitute goods; thus,
smaller the price elasticity of demand.
• People tend not to respond to changes in price of toothpicks
because they are too cheap. \$0.20 a dozen and \$0.40 a dozen do
not bother consumers as they probably do not even notice the
difference.
- the share of your budget is very small in buying toothpick.
• However, buying an apartment is a major choice in life. People
spend most of their savings on acquiring their own homes, and
changes in price of properties are certainly noticeable. As a result,
consumers are more responsive to changes in prices of apartments.
- the share of your budget is very large in buying a house.
Ans: C
Assume the price of gasoline doubles tonight and
remains at that price the next 2 years. The
Demand for gasoline measured tomorrow will be
_____ when compared with the demand for
gasoline measured 2 years from now.
A)
B)
C)
D)
E)
More Elastic
Larger in Absolute Value
The Same
More Inelastic
Less Inelastic
What affects Price Elasticity of Demand?
• Time
• It takes time for people to react to changes in price.
• People wake up tomorrow and find out price of gasoline is
doubled, but they do not have enough time to find substitutes
for gasoline, and hence, the amount of usage will be more or
less the same.
• But, given more time, people can explore other alternatives
(e.g. public transport)
Ans: D
The Cross Price Elasticity for cable TV and satellite
TV is estimated to be -0.3. This implies cable and
satellite TV are:
A)
B)
C)
D)
E)
Normal Goods
Substitutes
Elastic Goods
Complements
Unrelated
• Cross Price Elasticity measures the responsiveness of
quantity demanded for a good to a change in price of the
other good .
• For complement goods, if Px↓ , Qx↑, and Qy also ↑
- The Cross Price Elasticity is negative
• For substitute goods, if Px↓ , Qx↑, and Qy will ↓
- The Cross Price Elasticity if positive
Ans: d
In surveying their alumni, State U’s economics
department discovered that ramen noodle
consumption declined as soon as students
graduated and found jobs. One conclusion the
survey team might draw from this result is that
A)
B)
C)
D)
E)
There is Excess Demand for ramen noodles.
Equilibrium Price for ramen noodles is too high.
College graduates have a high reservation price for ramen
noodles.
Ramen noodles are an inferior good.
Ramen noodles are not nutritious.
were mentioned.
• (C) is not relevant at all because we are not calculating
consumer surplus.
• (E) is not even economics.
• The question talks about Income Elasticity of Demand for
ramen noodles.
- measures the responsiveness of quantity demanded for
a good to the change in income.
- For normal goods, if Income ↑, Qd ↑
- For inferior goods, if Income ↑, Qd ↓
real income.
• The survey relates real income and quantity demanded for
noodles.
• Income ↑, causing Qd ↓ --- inferior good
Ans: D
Period
Income
Px
Qx
Py
Qy
1
8000
24
8
12
40
2
9000
24
9
12
36
a) Given the above information. Calculate the Income
Elasticity of y. Is Good y normal or inferior?
•Recall that Income Elasticity refers to the responsiveness
of quantity demanded for y to a change in Income.
• Mathematically, Income Elasticity of y can be
calculated as: %∆Qy / %∆I.
• To calculate the Income Elasticity of y,
%∆Qy / %∆I
= (∆Qy / original Qy) x (original I / ∆I)
= (-4 / 40) x (8000 / 1000) = -0.8
a) Is Good y normal or inferior?
• Normal goods: Demand for normal goods increases when
income increases.
- Mathematically, the Income Elasticity of a normal good is
positive. (Quantity changes in the same direction as income)
• Inferior goods: Demand for inferior goods drops as Income
increases.
- Mathematically, the Income Elasticity of an inferior good is
negative. (Quantity changes in an opposite direction as
Income)
• Since the Income Elasticity of y is negative, Qy drops as
Income increases.
• Therefore, Good y is inferior.
Period
Income
Px
Qx
Py
Qy
1
9000
24
9
12
36
2
9000
21
12
12
30
b) Given the above information. Calculate the Cross Price
Elasticity of y with respect to a change in Px. Are Good x
and y complements or substitutes?
•
Cross Price Elasticity measures the responsiveness of
the quantity demanded for y with respect to a change in
Px.
• Mathematically, %∆Qy / %∆Px.
• Hence, the Cross Price Elasticity of Demand for y is
%∆Qy / %∆Px
= (∆Qy / original Qv) x (original Px / ∆ Px)
= (-6 / 36) x (24 / -3) = 4/3
b) Are Goods x and y complements or substitutes?
• For complement goods, if Px↓ , Qx↑, and Qy also ↑
- The Cross Price Elasticity is negative
• For substitute goods, if Px↓ , Qx↑, and Qy will ↓
- The Cross Price Elasticity if positive
• In this case, the Cross Price Elasticity of y with respect
to a change in price of x is positive.
• Therefore, Goods x and y are substitutes.
If the Price Elasticity of demand for good X is -3, your
goal is to maximize the revenue, should you raise or
lower the price of good X?
• Recall that whether total revenue increases or
decreases when the price of the good changes
depends on the elasticity of demand.
• If demand is elastic, (% change in quantity demanded
is larger than the % change in price)
• Increase in price will decrease TR
• Decrease in price will increase TR
P
X
Q
=
PQ
• You should decrease the price of good X in order to
maximize Total Revenue.
Chapter 4, Problem #4
Is the demand for a particular brand of car, like a
Chevrolet, likely to be more or less price-elastic than the
demand for all cars? Explain.
•
Price elasticity of a good increases, as more close
Solution to Problem 4(1)
•
Demand for all cars (i.e. Motorcycle, bus, van): hard to find
other substitutes for cars if price of all cars rises, for ex., it is
hard to substitute motorcycle for a car. Highly insensitive to
price change.
•
Demand for specific brand of cars: if price of Chevrolet rises,
people will switch to other brand, say, Toyota. Highly
sensitive to price change.
•
Thus, it is easier to substitute Toyota for Chevrolet than it is
to substitute a motorcycle for a car.
•
Therefore, the market demand curve for cars is likely to be
less elastic than the market demand curve for Chevrolets.
Chapter 4, Problem #8
Suppose that the ingredients required to bring a slice of
pizza to market and their respective costs are as listed in
the table:
Paper plate
2cents
Flour
8cents
Tomato sauce
20cents
Cheese
30cents
Labor (3minutes @ \$12/hour)
60cents
Total cost
120 cents
If these proportions remain the same no matter how many
slices are made, and the inputs can be purchased in any
quantities at the stated prices, draw the supply curve of
pizza slices and compute its price elasticity.
Solution to Problem 8(1)
• The proportions and prices of the ingredients are the same
no matter how many slices are made, meaning that,
• The price of input cost is fixed at 120 cents or \$1.2.
• Therefore, the marginal cost of producing an additional
unit of pizza is constant at \$1.2.
Solution to Problem 8(2)
P
(\$/slice)
1.2
S
Q
(slices per day)
•The price elasticity of supply of pizza is infinite ---- Perfectly Elastic Supply
Curve.
•Highly sensitive to price change - A small change in price, quantity
supplied drops to zero
•Usually occurs when there is a larger number of perfectly substitute goods
•i.e., If the price of an input increases, sellers will switch to another
available substitute goods
End of Chapter 4
```