1 welcome to pmba0608: economics/statistics foundation fall 2006 session 8: october 18 eastern...
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Welcome toPMBA0608: Economics/Statistics Foundation
Fall 2006Session 8: October 18
Eastern campus
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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
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Do you smoke?
Yes No Total
Male 2 9 11
Female 3 4 7
Total 5 13 18
P (male & smoking) = 2/18=0.11
P (male\smoker) =2/5=0.40
P (smoker\male) =2/11=0.18
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Discuss Assignment 31. 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 (H)
High School Graduate
(HG)
Some College
(C)
College Graduate
(CG)
0.27 0.27 0.25 0.18
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1. Application 3.17, Page 110 of Stat
Adult population
P (CG) = 0.24P (B\CG) = 0.18
P(NB\CG) =0.82
P (C)= 0.36
P (NC) = 0.4
P(B\C) =0.25
P(NB\C) = 0.75
P (B\NC) =0.27
P (NB\NC)=0.73Note: 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) = 0.12
P (A) = 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
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2. Application 3.19, Page 110 of Stat
a) P(A) = 0.15b) P (AB & NA) = 0.40.03 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 (A) = 0.5
P (B)= 0.3
P (C) =0.2
P(D\A)=0.99
P (ND\A) =0.01
P (D\B) =0.95
P(ND\B = 0.05)
P (D\C)=0.8
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 =0.5266b) 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 because1. P (x) is between 0 and 12. ∑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
D-50000 0.01
E (G) = 0.99D + 0.01 (D-50000)1000 = 0.99D +0.01D - 5001500 = D
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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.
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Price Elasticity of Demand Measure of the price
sensitivity of buyers
Ed =
Percentage change in quantity demanded as a result of 1% change in price.
$
Computers
P1=$1000
P2=$800
Q1=200 Q2 = 300
D
ΔP%
ΔQ% D
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Price Elasticity of Demand Midpoint Formula
Ed = =
Ed = -[.40/.22] = -1.82
For every 1% decrease in price quantity demanded increases by 1.82%
$
Computers
$1000
$800
Q1 =200 Q2=300
Davg
12
avg
12
PPP
QQQ
9001000800
250200300
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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 =
Ed = -.22/.40 = -0.55 Inelastic, since |E| < 1
5.2/)23(
450/)500400(
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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 =
-0.2 = %ΔQ/0.2
280.120.2
QQQ
avg
12
avg
12
avg
12
PPP
QQQ
%ΔQ = -0.04 or quantity demanded drops by 4%
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Good Price elasticity
Inelastic demand
Eggs 0.1 Beef 0.4 Stationery 0.5 Gasoline 0.5
Elastic demand
Housing 1.2 Restaurant meals 2.3 Airline travel 2.4 Foreign travel 4.1
Some Estimated Price Elasticities of Demand
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Determinants of Elasticity1. 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 Elasticity2. 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
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Determinants of Elasticity
4. Necessities have a lower price elasticity of demand than luxuries
•Ex: E diamonds > E gasoline
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1. D1 is Perfectly Inelastic Everywhere
Why?
Ed =
Ed = 0 Examples?
$
Q
D1
P1
P2
Extreme Cases of Price Elasticity
ΔP%
ΔQ% D
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2. D1 is Perfectly elastic Everywhere
Why?
Ed =
Ed =
Examples?
$
Q
D1P1
∞
Extreme Cases of Price Elasticity
ΔP%
ΔQ% D
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General Rule
The flatter the demand curve the ______ the elasticity
P
QD1
D2
Which demand is more elastic at point A?
A
10
50
12
2540
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Total Revenue, TR
TR = P x Q What does a decrease in P
do to TR? ↓P↓TR ↑Q ↑TR
%Δ TR = %Δ + %Δ P1. If l%Δ Pl > l%Δ Ql
Then TR↓
2. If l%Δ Pl < l%Δ Ql Then TR↑
$
Computers
$1000
200
D
TR = $200,000
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Elasticity and Total Revenue
1. If demand is elastic
|Ed | = | | >1
l%ΔQl > l%ΔPl
If P↓TR↑
ΔP%
ΔQ% D
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Elasticity and Total Revenue
1. If demand is unitary elastic
| Ed | = | | =1
l%ΔQl = l%ΔPl
If P↓TR remains unchanged
ΔP%
ΔQ% D
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Elasticity and Total Revenue
1. If demand is inelastic
| Ed | = | | < 1
l%ΔQl < l%ΔPl
If P↓TR↓
ΔP%
ΔQ% D
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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
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Think about the uses of knowing the price elasticity of demand in your line of work
Share your thoughts with us.
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Other Demand Elasticities
1. Cross-Price Elasticity
Exy =
Examples
Substitutes: Exy > 0Complements: Exy < 0Y
X
ΔP%
ΔQ%
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Example of cross-price elasticities(1977, US)
Note: all of these are examples of substitutes with cross price elasticity
>0
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Other Demand Elasticities
2. Income Elasticity
EI = Normal Goods: EI > 0
Inferior Goods: EI < 0IX
Δ%
ΔQ%
• Examples
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Example of income elasticities(1970, US)
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Price Elasticity of Supply Measure of the price
sensitivity of sellers
Es =
Percentage change in quantity supplied as a result of 1% change in price.
What is elasticity of this supply? (midpoint formula)
$
Computers
P2=$800
Q1=200 Q2 = 300
ΔP%
ΔQ% S
S
P1=$600
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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
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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
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Let’s show this graphically
P
S1
D
S2
$1
$2
10098
$2.80
•Most of the tax (80% of it) is paid by demanders
•If demand is inelastic, consumers end up paying most of the taxCigarettes
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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
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Let’s show this graphically
P
Vitamins
S1
D
S2
$1
$2
10080
$2.40
•Only 40% of tax is paid by demanders
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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)