Download Session 8

Welcome to
PMBA0608:
Economics/Statistics
Foundation
Fall 2006
Session 8: October 18
Eastern campus
1
I prefer not to post the slides
before each class…..why?
1) I would like to encourage you to
 Think in class
 Respond in class
 Interact in class
 Learn in class
2) I don’t know how much I will cover in class.
3) Reading the assigned sections of the book ahead of
time is a good substitute for having the slides a head
of time.
4) Don’t write everything down in class as the slides will
be posted after class.
5) Write down what is not in the slide.
6) I have the slides numbered now. So you cans just
refer to them by their numbers in your notes
2
Do you smoke?
Yes No
Male
Total
2
9
11
Female 3
4
7
Total
13
18
5
P (male & smoking) =
2/18=0.11
P (male\smoker)
=2/5=0.40
P (smoker\male)
=2/11=0.18
3
Discuss Assignment 3
1. Application 3.17, Page 110 of Stat
The table shows proportion of adults (in each
category) who find the ads believable. (B)
•
18% of college grads find the ads believable
(82% don’t, NB) (We are not saying that 18% of
believers are college grads.)
Less than High School
High
Graduate
school (H) (HG)
Some
College
(C)
College
Graduate
(CG)
0.27
0.25
0.18
0.27
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1. Application 3.17, Page 110 of
Stat
P (B\CG) = 0.18
P (CG) = 0.24
P(NB\CG) =0.82
P(B\C) =0.25
P (C)= 0.36
P(NB\C) = 0.75
Adult
population
P (B\NC) =0.27
P (NC) = 0.4
P (NB\NC)=0.73
Note: 27 percent and 27 percent is not
54%. It is 54 per 200 or 27 percent.
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1. Application 3.17, Page 110 of
Stat (Part a)




We know that P(CG ) = 0.24
We also know that P (NB\CG) = 0.82
We want to know P (NB & CG)
Conditional Probability
 P(NB\CG)= P (NB & CG)/P (CG)
 0.82 = P (NB & CG) /0.24
 P (NB & CG)= 0.24 * 0.82 = 0.1968 0r
19.68%
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1. Application 3.17, Page 110 of
Stat (Part b)
 P (NB\C)=?
 P (NB\C) = 1- P (B\C) =1 – 0.25 =
0.75 or 75%
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1. Application 3.17, Page 110 of
Stat (Part c)






P (HG U H) = 0.4= P (NC)
P (B\NC) =0.27
P (NC & B) =?
P (B\NC) = P (NC &B) /P (NC)
0.27 = P (NC & B) / 0.4
P (NC & B) = 0.27 * 0.4 = 0.108 or
10.8%
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2. Application 3.19, Page 110 of
Stat (categories are mutually exclusive)
Antilock
Brakes
(AB)
No Antilock
Brakes
(NAB)
Accident
(A)
P (AB & A)
= 0.03
P (NAB & A) P (A) =
= 0.12
0.15
No
Accident
(NA)
P (AB &
NA) = 0.4
P (NAB &
NA) = 0.45
P (NA) =
0.85
P (AB) =
0.43
P(NAB) =
0.57
1
9
2. Application 3.19, Page 110 of
Stat
a) P(A) = 0.15
b) P (AB & NA) = 0.4
0.03 is joint probability. You want
the conditional probability)
 P (AB\A) =?
 P (AB\A) = P (AB & A) / P (A)
 P (AB\A) = 0.03/0.15= 0.2 or 20%
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3. Application 3.27, Page 115 of Stat
(D= detection, ND =no Detection)
P(D\A)=0.99
P (A) = 0.5
P (ND\A) =0.01
P (D\B) =0.95
P (B)= 0.3
P(ND\B = 0.05)
P (D\C)=0.8
P (C) =0.2
P (ND\C) =.2
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3. Application 3.27, Page 115 of Stat
(D= detection, ND =no Detection)
a) P(A\D) =?
 P (A\D) = P (A & D)/ P (D)




P (A & D) = 0.5 * 0.99= 0.495
P(D) = P (A & D ) + P (B & D) + P ( C & D)
P (D) = 0.495 + 0.3 * 0.95 + 0.2* 0.8
P (D) = 0.495 + 0.285 + 0.16=0.94
 P (A\D) = 0.495/0.94 =0.5266
b) P (C\D) =P (C & D) / P (D)
 P (C\D) = 0.16/0.94 = 0.1702
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4. Exercise 3.31, Page 123 of Stat
 a is a probability distribution because
1. P (x) is between 0 and 1
2. ∑p (x) =1
 b is not a probability distribution because
conditions 1 and 2 are not met.
 c is not a probability distribution because
condition 2 is not met
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5. Application 3.33, Page 123 of
Stat
• P (theft) = 0.01, Value = $50,000
– Let D = premium
– G =insurance company’s gain
G
P(G)
D
0.99
E (G) = 0.99D + 0.01 (D-50000)
1000 = 0.99D +0.01D - 500
1500 = D
D-50000 0.01
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Assignment 4
(due on or before October 25)
 Questions 1, 2, 6, Page 110
of Econ.
 Questions 11 & 13, Page 111
of Econ.
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Next Class
 Saturday, October 28 in Athens
 Study
 Chapter 4 of Stat
 Chapter 23 of Econ
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Chapter 5 of Econ Book
 Price of gas goes up by 10%
 Do we buy more or less?
 How much less?
 Price of restaurant meals goes up by 10%
 Do we buy more or less?
 How much less?
 We are more sensitive to changes in the
price of restaurant meals than to changes
in the price of gasoline.
17
Price Elasticity of Demand
 Measure of the price
sensitivity of buyers
% ΔQ D
 Ed = % ΔP
 Percentage change in
quantity demanded as
a result of 1% change
in price.
$
P1=$1000
P2=$800
D
Q1=200
Q2 = 300
Computers
18
Price Elasticity of Demand
 Midpoint Formula
Q 2  Q1
Q avg
Ed = P  P
2
1
Pavg
300  200
250
= 800  1000
900
Ed = -[.40/.22] = -1.82
For every 1% decrease
in price quantity
demanded increases
by 1.82%
$
$1000
$800
D
Q1 =200
Q2=300
Computers
19
Degree of Sensitivity
 Elastic: |Ed| > 1
 Unit:
|Ed| = 1
 Inelastic: |Ed| < 1
• In our example |E| > 1, so demand
for computers is elastic
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Let’s practice
 When the price of milk is $2 per gallon,
consumers buy 500 gallons. When the price
rises to $3 per gallon, consumers buy only 400
gallons. What is the elasticity of demand and
how would you classify it?
 Ed =
(400  500) / 450
(3  2) / 2.5
 Ed = -.22/.40 = -0.55
 Inelastic, since |E| < 1
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Let’s practice
 Question 3a Page 110
 Price elasticity of demand is 0.2
 If price increases from $1.80 to $2.20, what
happens to quantity demanded?
 Ed =
 -0.2 =
Q 2  Q1
Q avg
P2  P1
Pavg
Q 2  Q1
Q avg
2.20  1.80
2
 -0.2 = %ΔQ/0.2
%ΔQ = -0.04 or quantity
demanded drops by 4%
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Some Estimated Price Elasticities of Demand

Good

Inelastic demand
Eggs
Beef
Stationery
Gasoline

Price elasticity
0.1
0.4
0.5
0.5
Elastic demand
Housing
Restaurant meals
Airline travel
Foreign travel
1.2
2.3
2.4
4.1
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Determinants of Elasticity
1. Number of substitutes
 The greater the # substitutes, the
greater the elasticity
 The narrower the definition of the
market, the greater the elasticity
 Ex:Ecars < Echevys < Ecamaros
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Determinants of Elasticity
2. Item’s share of consumer budget
 The greater the share of budget, the greater
the elasticity
 Ex:
Ehousing is ______ than Esalt
3. Time
 The longer the time horizon, the greater the
elasticity
 Ex: Gasoline Demand: ELR is ____
than ESR
25
Determinants of Elasticity
4. Necessities have a lower price
elasticity of demand than luxuries
•Ex: E diamonds > E gasoline
26
Extreme Cases of Price Elasticity
1. D1 is Perfectly
Inelastic
Everywhere
 Why?
% ΔQ D
% ΔP

Ed =


Ed = 0
Examples?
$
P2
D1
P1
Q
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Extreme Cases of Price Elasticity
2. D1 is Perfectly
elastic Everywhere
 Why?
 Ed =
% ΔQ D
% ΔP
 Ed = ∞
$
P1
D1
Q
 Examples?
28
General Rule
 The flatter the demand curve the
______ the elasticity
Which demand is more
elastic at point A?
P
A
12
10
D2
D1
25
40
50
Q
29
Total Revenue, TR
TR = $200,000
 TR = P x Q
 What does a decrease in P
do to TR?
 ↓P↓TR
 ↑Q  ↑TR
 %Δ TR = %Δ + %Δ P
1. If l%Δ Pl > l%Δ Ql
 Then TR↓
$
$1000
D
200
Computers
2. If l%Δ Pl < l%Δ Ql
 Then TR↑
30
Elasticity and Total Revenue
1. If demand is elastic
% ΔQ D
 |Ed | = |
| >1
% ΔP
 l%ΔQl > l%ΔPl
 If P↓TR↑
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Elasticity and Total Revenue
1. If demand is unitary elastic
% ΔQ D
 | Ed | = |
| =1
% ΔP
 l%ΔQl = l%ΔPl
 If P↓TR remains unchanged
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Elasticity and Total Revenue
1. If demand is inelastic
% ΔQ D
 | Ed | = |
|<1
% ΔP
 l%ΔQl < l%ΔPl
 If P↓TR↓
33
Let’s practice
 Question 9, page 111
 Should you increase or decrease the
price of admissions to a museum to
increase revenue?
 Is demand for museum likely to be
elastic or inelastic?
 Elastic
 Decrease price
34
Think about the uses of knowing the
price elasticity of demand in your line of
work
Share your
thoughts with
us.
35
Other Demand Elasticities
1. Cross-Price
Elasticity
 Exy =
% ΔQ X
% ΔPY
Substitutes:
Exy >
0
Complements: Exy < 0
 Examples
36
Example of cross-price elasticities
(1977, US)
Note: all of these are examples of
substitutes with cross price elasticity >0
37
Other Demand Elasticities
2. Income Elasticity
 EI =
% ΔQ X
%Δ I
Normal Goods:
EI > 0
Inferior Goods:
EI < 0
• Examples
38
Example of income elasticities
(1970, US)
39
Price Elasticity of Supply
 Measure of the price
sensitivity of sellers

% ΔQ S
Es =
% ΔP
S
$
P2=$800
P1=$600
 Percentage change in
quantity supplied as a
result of 1% change in
price.
 What is elasticity of this
supply? (midpoint formula)
Q1=200
Q2 = 300
Computers
40
Application of elasticity
 Who pays taxes?
 If government imposes an excise tax
of $1 per pack on cigarettes, who
ends up paying the tax?
 Is demand for cigarettes elastic or
inelastic?
 Inelastic
41
Who is the tax collected from?
 Supplier
 What does this do to the supplier’s
cost?
 What does this do to supply curve?
 Decreases (shifts leftward)
 By how much?
 $1 per pack
42
Let’s show this graphically
S2
P
$1
S1
•If demand is
inelastic,
consumers
end up paying
most of the
tax
$2.80
$2
D
100
98
•Most of the
tax (80% of
it) is paid by
demanders
Cigarettes
43
Now let’s suppose government collects a
$1 excise tax from producers of
vitamins
Is demand for vitamins more
or less elastic than demand
for cigarettes?
 More elastic
44
Let’s show this graphically
S2
P
$1
S1
•Only 40% of
tax is paid by
demanders
$2.40
$2
D
80
100
Vitamins
45
All else equal
The higher the elasticity of
demand, the higher the
______tax burden.
The higher the elasticity of
supply, the higher the
demanders’ tax burden (show
this graphically)
46