2. 1 Welcome to PMBA0608: Economics/Statistics Foundation Fall 2006 Session 8: October 18 Eastern campus

3. 2 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

4. 3 Do you smoke? YesNoTotal Male2911 Female347 Total51318 P (male & smoking) = 2/18=0.11 P (male\smoker) =2/5=0.40 P (smoker\male) =2/11=0.18

5. 4 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 (H) High School Graduate (HG) Some College (C) College Graduate (CG) 0.27 0.250.18

6. 5 1. Application 3.17, Page 110 of Stat Adult population P (CG) = 0.24 P (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)=0.73 Note: 27 percent and 27 percent is not 54%. It is 54 per 200 or 27 percent.

7. 6 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%

8. 7 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%

9. 8 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%

10. 9 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 1

11. 10 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%

12. 11 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

13. 12 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

14. 13 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

15. 14 5. Application 3.33, Page 123 of Stat P (theft) = 0.01, Value = $50,000 –Let D = premium –G =insurance company’s gain GP(G) D0.99 D-500000.01 E (G) = 0.99D + 0.01 (D-50000) 1000 = 0.99D +0.01D - 500 1500 = D

16. 15 Assignment 4 (due on or before October 25)  Questions 1, 2, 6, Page 110 of Econ.  Questions 11 & 13, Page 111 of Econ.

17. 16 Next Class  Saturday, October 28 in Athens  Study Chapter 4 of Stat Chapter 23 of Econ

18. 17 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.

19. 18 Price Elasticity of Demand  Measure of the price sensitivity of buyers  E d =  Percentage change in quantity demanded as a result of 1% change in price. $ Computers P1=$1000 P2=$800 Q1=200Q2 = 300 D

20. 19 Price Elasticity of Demand  Midpoint Formula E d = = E d = -[.40/.22] = -1.82 For every 1% decrease in price quantity demanded increases by 1.82% $ Computers $1000 $800 Q1 =200Q2=300 D

21. 20 Degree of Sensitivity  Elastic: |E d | > 1  Unit: |E d | = 1  Inelastic: |E d | < 1 In our example |E| > 1, so demand for computers is elastic

22. 21 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?  E d =  E d = -.22/.40 = -0.55  Inelastic, since |E| < 1

23. 22 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 %ΔQ = -0.04 or quantity demanded drops by 4%

24. 23  Good Price elasticity  Inelastic demand Eggs 0.1 Beef 0.4 Stationery0.5 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

25. 24 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: <<E cars E chevy s E camaros

26. 25 Determinants of Elasticity 2. Item’s share of consumer budget The greater the share of budget, the greater the elasticity  Ex: E housing is ______ than E salt 3. Time The longer the time horizon, the greater the elasticity  Ex: Gasoline Demand: E LR is ____ than E SR

27. 26 Determinants of Elasticity 4. Necessities have a lower price elasticity of demand than luxuries Ex: E diamonds > E gasoline

28. 27 1.D1 is Perfectly Inelastic Everywhere Why? E d = E d = 0 Examples? $ Q D1D1 P1P1 P2P2 Extreme Cases of Price Elasticity

29. 28 2. D1 is Perfectly elastic Everywhere  Why?  E d =  Examples? $ Q D1D1 P1P1 ∞ Extreme Cases of Price Elasticity

30. 29 General Rule  The flatter the demand curve the ______ the elasticity P Q D1 D2 Which demand is more elastic at point A? A 10 50 12 25 40

31. 30 Total Revenue, TR  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 ↓ 2.If l%Δ Pl < l%Δ Ql Then TR ↑ $ Computers $1000 200 D TR = $200,000

32. 31 Elasticity and Total Revenue 1.If demand is elastic  |E d | = | | >1  l%ΔQl > l%ΔPl  If P ↓  TR↑

33. 32 Elasticity and Total Revenue 1.If demand is unitary elastic  | E d | = | | =1  l%ΔQl = l%ΔPl  If P ↓  TR remains unchanged

34. 33 Elasticity and Total Revenue 1.If demand is inelastic  | E d | = | | < 1  l%ΔQl < l%ΔPl  If P ↓  TR↓

35. 34 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

36. 35 Think about the uses of knowing the price elasticity of demand in your line of work  Share your thoughts with us.

37. 36 Other Demand Elasticities 1.Cross-Price Elasticity  E xy =  Examples Substitutes: E xy > 0 Complements: E xy < 0

38. 37 Example of cross-price elasticities (1977, US) Note: all of these are examples of substitutes with cross price elasticity >0

39. 38 Other Demand Elasticities 2. Income Elasticity E I = Normal Goods: E I > 0 Inferior Goods: E I < 0 Examples

40. 39 Example of income elasticities (1970, US)

41. 40 Price Elasticity of Supply  Measure of the price sensitivity of sellers  E s =  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=200Q2 = 300 S P1=$600

42. 41 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

43. 42 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

44. 43 Let’s show this graphically P S1 D S2 $1 $2 100 98 $2.80 Most of the tax (80% of it) is paid by demanders If demand is inelastic, consumers end up paying most of the tax Cigarettes

45. 44 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

46. 45 Let’s show this graphically P Vitamins S1 D S2 $1 $2 100 80 $2.40 Only 40% of tax is paid by demanders

47. 46 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)