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Welcome to PMBA0608: Economics/Statistics Foundation

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

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Welcome to PMBA0608: Economics/Statistics Foundation

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  1. Welcome toPMBA0608: Economics/Statistics Foundation Fall 2006 Session 8: October 18 Eastern campus

  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

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

  4. 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.) Discuss Assignment 31. Application 3.17, Page 110 of Stat

  5. 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.

  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%

  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%

  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%

  9. 2. Application 3.19, Page 110 of Stat (categories are mutually exclusive)

  10. 2. Application 3.19, Page 110 of Stat • P(A) = 0.15 • 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%

  11. 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

  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

  13. 4. Exercise 3.31, Page 123 of Stat • a is a probability distribution because • P (x) is between 0 and 1 • ∑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

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

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

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

  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.

  18. 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. $ P1=$1000 P2=$800 D Q1=200 Q2 = 300 Computers

  19. Price Elasticity of Demand • Midpoint Formula Ed = = 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

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

  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? • Ed = • Ed = -.22/.40 = -0.55 • Inelastic, since |E| < 1

  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%

  23. Some Estimated Price Elasticities of Demand • GoodPrice 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

  24. Determinants of Elasticity • 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

  25. 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

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

  27. Extreme Cases of Price Elasticity • D1 is Perfectly Inelastic Everywhere • Why? • Ed = • Ed = 0 • Examples? $ D1 P2 P1 Q

  28. Extreme Cases of Price Elasticity 2. D1 is Perfectly elastic Everywhere • Why? • Ed = • Ed = • Examples? $ D1 P1 ∞ Q

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

  30. 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 • If l%Δ Pl > l%Δ Ql • Then TR↓ • If l%Δ Pl < l%Δ Ql • Then TR↑ $ $1000 D 200 Computers

  31. Elasticity and Total Revenue • If demand is elastic • |Ed | = | | >1 • l%ΔQl > l%ΔPl • If P↓TR↑

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

  33. Elasticity and Total Revenue • If demand is inelastic • | Ed | = | | < 1 • l%ΔQl < l%ΔPl • If P↓TR↓

  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

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

  36. Other Demand Elasticities • Cross-Price Elasticity • Exy = • Examples Substitutes: Exy > 0 Complements: Exy < 0

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

  38. Other Demand Elasticities 2. Income Elasticity • EI = Normal Goods: EI > 0 Inferior Goods: EI < 0 • Examples

  39. Example of income elasticities(1970, US)

  40. 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) S $ P2=$800 P1=$600 Q1=200 Q2 = 300 Computers

  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

  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

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

  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

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

  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)

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