PPA 220A: Applied Economic Analysis I Meeting 1, Fall 2003 Introduction to Course Munger Chapter 1:

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PPA 220A Applied Economic Analysis I Fall
2003Professor Rob WassmerMeeting
12Probability and Public Policy
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Announcement and HW

• No class next week
• I will assign groups for final on Dec. 2
• Final exam given out Dec. 9
• Describe how article relates to a debate on
  government intervention
• Primary conflicts implied
• Markets vs. experts
• Politics vs. markets
• Politics vs. experts

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Figure 8.1 Three conflicts
Markets

• Equity Policies
• Income Redistribution
• Resource Distribution
• Control Externalities

• Efficiency Policies
• Market structure
• Control Externalities
• Public Goods
• Information Asymmetry

Politics
Experts

• Institutional Reform Policies
• Information
• Values (Efficiency v. Equity
• Institutional Design

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Dense chapter with many statistical formulas
• Only responsible for what covered here
• Discounting Count at less than face value
• Here based upon uncertainty
• Game Offer
• Flip a fair coin (50 heads, 50 tails)
• Receive 5 for head, 1 for tail
• How much are you willing to pay to play?
• Expected value of event
• Payoff from event x probability of event

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Heads 5 0.5 2.50
• Tails 1 0.5 0.50
• Game 2.50 0.50 3.00
• Ever pay to play more than expected value?
• Do you ever go to Reno?
• What would they need to charge to run game?
• Types of risk tolerances
• Risk accepting Willing to pay more than exp.
  value
• Risk neutral Willing to pay exp. Value
• Risk averting Willing to pay less than exp.
  Value
• Also depends on number times played
• Only play once, win 1 or 5

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Policy analysts and probability
• Russian roulette?
• Good policy decision not based upon outcome
• Appropriate decision process
• Two examples Civil rights in South and Kublai
  Khan
• Strengthen levies on Sacramento and American
  Rivers
• Probability concepts
• Expectations about an uncertain future
• PEvent X (number of ways X can occur) / total
  events
• P4 of diamonds 1 / 52 0.0192 or 1.92
• PAce 4 / 52 0.0769 or 7.69
• PRolling 1 or 6 on die 2 / 6 0.333 or 33.3

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Basic rules of probability
• (1) Possible event has a positive probability
• (2) Probability of an event less than or equal to
  one
• (3) Sum of probabilities of all possible events
  is one
• Counting rules
• Total number of events of interest
• Calculate with formula
• Depends if combination (order of events not
  important)
• Depends if permutation (order of events
  important)

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Combination examples
• 6 balls in urn, number 1 to 6, draw 2
• No replacement of ball after drawn, order not
  important
• Outcome of interest 6-1
• Not of interest 1-2, 1-3, 1-4, 1-5, 2-3, 2-4,
  2-5, 2-6, 3-4, 3-5, 3-6, 4-5, 4-6, 5-6
• 15 possible outcomes
• Combinations from N take k (order not important)
• CNk N! / (k! (N-k)!)
• N 6, k 2 (654321) / ( (21) (4321) )
  720 / 48 15
• Probability drawing 6-1 1 / 15 0.067 or 6.7

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Munger Chapter 9 Expected Values, Probability,
and Risk

• What is SuperLotto Plus?
• Taken from http//www.calottery.com/games
• SuperLottoPlus is your chance to win millions of
  dollars! The jackpot ranges from 7 million to
  50 million or more. The jackpot rolls over and
  grows whenever there is no winner. All you have
  to do is pick five numbers from 1 to 47 and one
  MEGA number from 1 to 27 and match them to the
  numbers drawn by the Lottery every Wednesday and
  Saturday.

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Munger Chapter 9 Expected Values, Probability,
and Risk

• First event (N 47, k 5)
• (47!) / ( 5! (42!) ) 2.5959 ( 120 1.4151)
  1,532,544
• Where 2.5959 equals 259 with 57 zeros after it
• Chance of event 1 / 1,532,544
• Second event (N 27, k 1)
• (27!) / ( 1! (26!) ) 27
• Chance of event 1 / 27
• Discuss probability of both events occurring
  later

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Permutation example
• Same as urn example above but order of draw
  counts
• 6-1 not same as 1-6
• Outcome of interest 6-1
• Not of interest 1-2, 1-3, 1-4, 1-5, 2-3, 2-4,
  2-5, 2-6, 3-4, 3-5, 3-6, 4-5, 4-6, 5-6, 2-1, 3-1,
  4-1, 5-1, 3-2, 4-2, 5-2, 6-2, 4-3, 5-3, 6-3, 5-4,
  6-4, 6-5
• 30 possible outcomes
• Combinations from N take k (order important)
• CNk N! / ((N-k)!)
• N 6, k 2 (654321) / (4321) 720 /
  24 30
• Probability drawing 6-1 1 / 30 0.033 or 3.3

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Language of probability
• Independent
• Event A and B are if occurrence of one unrelated
  to other
• Probability of rain today (1 / 10) independent of
  you being elected to CA Assembly (1 / 300)
• Union
• Given A and B are independent the probability of
  A occurs, or B, or both A and B found by adding
  independent probabilities ( 30 / 300 1 / 300 )
  31 / 300
• Intersection
• Given A and B are independent, the probability of
  both occurring
• CA Super Lotto example
• (1 / 1,532, 544) ( 1 / 27) 1 / 41,378,688

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Conditional
• Event A and B are not independent
• Probability of A occurring given that B has
  already
• Formulas in Munger
• Your level of risk aversion
• Two choices (1) sure payoff of 1 and a 20
  chance of winning 5
• Can only play once
• Risk neutral person indifferent
• Risk accepting person takes 5
• Risk averse person takes 1
• What are you? Does it depend upon circumstances?
• What would you like public decision maker to be?

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Policy example
• Sacramento City Manager Stockpile sandbags?
• Chance of flooding in any given year 10
• Is each years flood best considered an
  independent event?
• 100 year flood protection
• Cost of stockpiling in each year 2.5 million
• What outcome variable is needed to make good
  decision?
• Does evaluation of decision quality depend on
  flood occuring?

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Munger Chapter 9 Expected Values, Probability,
and Risk

• Decision analysis
• Map or tree to illustrate consequences of choices
• Method
• Identify mutually exclusive outcomes
• Estimate the value of outcomes if they come to
  pass
• Assign probabilities to outcomes
• Multiply estimated value of each outcome by
  probabilities to obtain expected outcome
• Figure 9.6
• Expected remediation cost for three waste burial
  styles
• Lesson Cheapest up-front alternative is most
  expensive in terms of long-term expected cost

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Fig. 9.6 Simplified Decision Analysis for
Disposal Technology
Human decision
Revealed by nature in future with probability
conditional on prior human decision
Yes 0.6
Remediation Required? Cost if yes40m
Augured Holes (Construction cost 5m)
No 0.4
Yes 0.4
Shallow Land Burial (Construction cost 15m)
Remediation Required? Cost if yes27.5m
No 0.6
Above Ground Vaults ( Construction cost 25m)
Yes 0.1
Remediation Required? Cost if yes10m
No 0.9
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Munger Chapter 9 Expected Values, Probability,
and Risk

• Add construction plus expected remediation costs
• Are constituents risk neutral?
• How far off in the future are remediation costs
• Time value of (covered next time)

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Birthday Problem

• Found at http//www.mste.uiuc.edu/reese/birthday/i
  ntro.html
• How likely is that two people in class have same
  B-day?
• Drawing from an urn of 365 days, N times, with
  replacement
• Formula

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HomeworkDue the Start of Meeting Thirteen

• (1) Do assigned reading and compose a typed and
  well-developed question from the reading assigned
  for thirteenth week that relates to something
  that you do not understand from it.
• (2) Provide a typed and double-spaced explanation
  for the answer given in Munger for question 1 on
  pp. 318-319.
• (3) Write a one to two page, double-spaced
  response to the discussion and advanced questions
  for Chapter 9 at Mungers web site
  http//www.wwnorton.com/college/polisci/analyzingp
  olicy .