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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)