Leastcost risk bearing

1
Least-cost risk bearing

• Sciences Po
• F.H. Buckley
• Goetz 75-95, 99-102

2
The problem

• Where seller sells a product which has a defect
  which imposes a risk of loss, should the risk
  fall on the buyer or seller?
• The economist asks how the parties would bargain
  to allocate the risk.

3
Goetzs whizbang Questions on p. 76
4
The whizbang50 chance of a whiz, 50 of a bang
It might go whiz or it might go
bang
5
What are the utility levels of Sehler and Beyer
after the sale?Assuming that Beyer bears the risk

• After the sale, Sehler has 500 and Beyer 1000
• The whizbang imposes a 50 percent probability of
  a cost of 250

6
What is the utility level of Sehler after the
sale?U 100M1/2

• Sehler has 500 and no risk of loss (caveat
  Beyer).
• What is Sehlers utility level?
• USehler 1005001/2 2,236.07

7
What is the utility level of Beyer after the
sale?Assuming that Beyer bears the risk

• After the sale, Beyer has 1000 plus the risk of
  loss
• Beyer has .5(1000) .5(750)

8
What is the utility level of Beyer after the
sale?U 100M1/2

• Beyer has .5(1000) .5(750)
• UBeyer .510010001/2 .51007501/2
• 1,581.14 1,369.31
• 2,950.05

9
What are the utility levels of Sehler and Beyer
after the sale?U 100M1/2

• USehler 2,236.07
• UBeyer 2,950.05

10
Show that Beyer would pay up to 129.48 to avoid
the risk

• With the risk, UBeyer 2,950.05
• Without the risk, UBeyer U1000-129.48
• U1000-129.48 U870.52
• 100870.521/2
• 2950.05

11
Will Sehler buy the risk?

• Show that seller is indifferent between 500 and
  632.82 plus the risk
• U500 (.5)U632.82 (.5)U(632.82-250)
• U500 2,236.07
• (.5)U632.82 (.5)U382.82 1257.80 978.30
  2,236.1

12
Will the parties trade the risk?

• Beyer will pay at most 129.48 for Sehler to take
  the risk
• Sehler wont assume the risk for less than 132.82
• So no deal. Risk stays with Beyer.
• Does this tell you anything about least-cost risk
  bearing? The wealthier are more willing to accept
  risks.

13
Will Beyer sell the risk to Sehler?

• What do you think happens when the multiplier is
  not 100 but 1000,
• i.e., U 1000M1/2?

14
Suppose the risk of a bang is only 10

• What is the expected range or dispersion of
  Beyers payoffs?

15
Dispersion of outcomes
10 chance of 750, 90 chance of 1,000
16
Dispersion of riskA 10 probability of a 250
loss
EMV .1(250) 25
17
Beyer now joins a risk-pool with 19 other
whizbang purchasers

• What change in his risk?

18
Risk pooling reduces the dispersion of risk Page
78A risk pool of 20 and a probability of 10
19
Risk pooling reduces the dispersion of risk, not
the size
EMV 25
20
The mean (EMV) remains 25, but (1) the risk
(mean-preserving spread) is smaller, and (2) the
maximum exposure is about 7.00, not 250
21
Dispersion of outcomes
EMV 25
22
What happens when the risk pool increases?

• Cf. pp. 80-81
• What do you think happens with a risk pool of
  1,000,000 people?

23
What happens when the risk pool increases?

• Cf. pp. 80-81
• What do you think happens with a risk pool of
  1,000,000 people?
• The loss of 25 becomes a certainty, with no
  dispersion from the mean

24
What happens when the risk pool increases?

• Cf. pp. 80-81
• What do you think happens with a risk pool of
  1,000,000 people?
• The loss of 25 becomes a certainty, with no
  dispersion from the mean
• Assuming risk aversion, what would you prefer a
  sure thing loss of 25, or a 10 chance of losing
  250?

25
What happens when the risk pool increases?

• Cf. pp. 80-81
• What do you think happens with a risk pool of
  1,000,000 people?
• The loss of 25 becomes a certainty, with no
  dispersion from the mean
• What does this tell you about insurance companies?

26
Now we have two senses of least-cost risk bearing

• Assuming diminishing marginal utility, wealthier
  people are better able to bear risk (Beyer and
  Sehler)
• Poorly diversified parties may reduce their risk
  by selling it to a better diversified party.

27
Heres a third kind of least-cost risk bearing

• There is a 10 percent probability of a loss of
  250
• Sehler (but not Beyer) can eliminate this risk at
  a cost of 10

28
Heres a third kind of least-cost risk bearing

• There is a 10 percent probability of a loss of
  250
• Sehler (but not Beyer) can eliminate this risk at
  a cost of 10
• In a Coasian world, would it matter who is
  assigned the risk?

29
Heres a third kind of least-cost risk bearing

• There is a 10 percent probability of a loss of
  250
• Sehler (but not Beyer) can eliminate this risk at
  a cost of 10
• In a Coasian world, would it matter who is
  assigned the risk?
• What if its not a Coasian world?

30
Do these three factors come together in products
liability?

• The manufacturer is wealthier
• Who can spread the risks better
• What about the third factor harm reduction?

31
The case of Martin WurrierGoetz p. 83

• The Law of Damages Damages are meant to
  compensate the plaintiff for his loss by putting
  him in the same position he would be in had the
  breach not occurred
• Liquidated damages and Penalty Clauses. The
  parties may stipulate for a liquidated damages,
  which are a genuine pre-estimate of compensatory
  damages on breach but if they want more, this
  amounts to a penalty and is unenforceable.
• One cant insure for a penalty.

32
The case of Martin Wurrier

• Are barriers to penalty clauses inefficient?
• The problem of idiosyncratic harm.
• What do you think motivated this rule?

33
The case of Martin Wurrier
SHYLOCK This kindness will I show.Go with me to
a notary, seal me thereYour single bond and, in
a merry sport,If you repay me not on such a
day,In such a place, such sum or sums as
areExpress'd in the condition, let the
forfeitBe nominated for an equal poundOf your
fair flesh, to be cut off and takenIn what part
of your body pleaseth me.ANTONIO Content, i'
faith I'll seal to such a bondAnd say there is
much kindness in the Jew.
34
Who do you think should bear Wurriers risk?

• Who is best able to cure the problem?
• What could the bus company do to minimize the
  risk?
• What could Wurrier do? The problem of moral hazard

35
Moral hazard

• Do you drive faster when you have a seatbelt on?
• Or when you have full coverage for automobile
  insurance?
• Does absolution give rise to an incentive
  problem?

36
Efficient Care LevelsWhat level of care will
Reliable take?

• CW pH, where
• CW is the Cost to Wurrier
• P is the probability of an accident
• H is Wurriers subjection valuation of the harm
  10,000.
• If Reliable is liable for H, it will take
  precautions provided that the cost of one more
  precaution is less that the benefit in terms of
  harm reduction

37
Reliables Marginal and Total Cost of Care
38
Reliables Marginal Cost Curve

Each unit of care costs Reliance 10
MC Care
10
Units of Care
39
Each unit of care reduces the ex ante probability
of an accident

• The benefit of taking additional care is the
  reduction of the ex ante cost of harm pH.
• We will assume that investments in care will
  reduce p but not H

40
Lets make up some numbers for pHpH Total Harm
41
The marginal decline in Total Harm rH is the
marginal benefit of care
42
The marginal decline in Total Harm rH is the
marginal benefit of care
43
So how much care will Reliable take, if it is
liable?
44
So how much care will Reliable take, if it is
liable?
45
Why Reliance takes exactly x units of care

Can Reliance save money by taking one more unit
of care at x-1?
MC Care
MB10,000
Units of Care
x
46
Why Reliance takes exactly x units of care

Will Reliance want to move from x to x1 units
of care?
MC Care
MB10,000
Units of Care
x
47
MC MB as a point of optimality The
Goldilocks standard

• At the table in the kitchen, there
• were three bowls of porridge.
• Goldilocks was hungry.  She
• tasted the porridge from the first bowl. 
• "This porridge is too hot!" she exclaimed.
• So, she tasted the porridge from the second bowl.
• "This porridge is too cold," she said
• So, she tasted the last bowl of porridge.
• "Ahhh, this porridge is just right," she said
  happily and she ate it all up.

48
How do you think Reliable will react if it is
liable for only 1,000 in damages?

• Reliable will now take H to be 1,000, not
  10,000
• The value it gives to pH and rH will therefore
  decline

49
Marginal Benefit of Harm ReductionWhat happens
when liability is reduced by non-enforcement of
penalty clauses

MC Care
MB10,000
MB1,000
Units of Care
x
X
50
National Steel v. GibbonsGoetz p. 88

• Some legal jargon
• What is strict liability?
• Why strict liability for abnormally dangerous
  activities?
• What is res ipsa loquitur?
• What is a common carrier?
• What are the duties of a common carrier with
  respect to carriage of goods?
• Can you think of any reason for special
  exemptions from liability for common carriers?

51
Why did the court nevertheless impose strict
liability?

• Can you list the reasons?

52
Why did the court nevertheless impose strict
liability?

• Can you list the reasons?
• Carriers are in general better able to pass on
  the risk (better diversified?)
• Carriers are in a better position to solve the
  informational problem
• Carriers are in a better position to reduce the
  probability of harm

53
Risk and Fairness A Theory of Justice
The greatest happiness principle The good is
whatever brings the greatest happiness to the
greatest number of people.
(Jeremy Bentham 1748-1832)
54
How would a utilitarian choose amongst rule
sets?Assume were measuring utils
55
Rawls Difference Principle
Difference Principle Social and economic
inequalities should be arranged so that they are
both (1) to the greatest benefit of the least
advantaged persons (maxmin), and (2) attached
to offices and positions open to all under
conditions of equality of opportunity A Theory
of Justice 1971.
John Rawls 1922- 2002
56
So how would a Rawlsian choose?
57
So how would a Rawlsian choose?
Set 3 is max-min
58
Is this insensitive to anything other than
minimum payouts?
59
How about now?
Does the Difference Principle posit extreme risk
aversion?
60
How about now?
Is Underdog looking a little envious?
61
Whats so bad about envy?

• A deadly sin
• For the economist, an externality
• Can you offer an economic defense of envy? As
  well as the economists understanding of when
  envy is inefficient (i.e., sinful)?

62
Divide and ChooseGoetz p. 94

• Consider divide and choose played by children
  over cake. Oldest cuts, youngest picks. Is this
  fair? What is the best strategy for the divider?
• What about question 4 on p. 95. Still fair?
• Is there anything different in the Doris and
  Cloris example? If so, what makes the difference?

63
Divide and Choose If you were Doris, how would
you divide?
64
Divide and Choose If you were Doris, how would
you divide?
For Chloris, 20 gt 16
65
Divide and Choose But if you were Chloris, how
would you divide?
66
Divide and Choose But if you were Chloris, how
would you divide?
For Doris, 14 gt 10
67
Plea Bargains

• How do plea bargains work?

68
Plea Bargains

• Why are they permitted? Is there an element of
  unfairness for the accused?
• Lets supposed you are charged with an offence of
  which you are innocent. There is nevertheless a
  10 probability of conviction, with a sentence of
  20 years. The prosecutors offers you one year in
  exchange for a plea. What do you do?
• Suppose I have persuaded you that plea bargains
  are unfair to the accused. If they are not
  enforced, is he better off?

69
How does an accused react to the Parrish case? An
intermediate solution

• Plea bargains arent banned. But neither are they
  always enforced.
• Can you express the accuseds choice in a
  formula?
• Plead if pUB (1-pU)SNU lt pTST, where
• pU Probability that the bargain will be upheld
• B Prosecutors deal
• SNU Sentence if deal not upheld
• pT Probability of conviction if a trial
• ST Sentence at trial