Economics of Insurance

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Economics of Insurance
Lecture 6
HEALTH AND SAFETY
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Economics of Insurance Health and safety
Overview
This lecture looks in a general way at managing
health and safety risk
It often assumes risk aversion
It introduces the concept of a line of constant
expected value
It revises the concept of certainty equivalent
It looks at various options with regard to
managing health and safety risk
It asks whether the moral hazard involved this
sort of risk management implies that insurance
will AUTOMATICALLY INCREASE RISKS OF AN ACCIDENT
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2 Rules of State Contingent Asset Diagrams
Line of constant expected value
Rule 1 A straight line through an initial
prospect with a slope equal to the ODDS against
the bad event cuts the certainty line at
coordinates equal to the expected value of the
initial prospect
E(V) at basic risk line
Slope odds against event 2
E (V)
E(V) of assets without safety equipment
Initial prospect
X1
E (V)
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2 Rules of State Contingent Asset Diagrams
Line of constant expected value
Rule 1 A straight line through an initial
prospect with a slope equal to the ODDS against
the bad event cuts the certainty line at
coordinates equal to the expected value of the
initial prospect
Proof
The definition of expected value can be
which is an equation for X2 keeping E(V) and odds
(p1/p2) constant
Constant E(V) line
SO
Initial prospect
X1X2
X2
E(V)
Now consider the certainty line
Next consider the point at which the constant
E(V) line crosses the certainty line
X1
Since there are only two possible events
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2 Rules of State Contingent Asset Diagrams
Certainty Equivalent
Rule 2 The CERTAINTY EQUIVALENT of an initial
prospect is at the point where the state
contingent asset curve cuts the certainty line,
at which point its slope is equal to the odds
against event 2
X2
The certainty equivalent (CE) of an initial
prospect is the RISKLESS (i.e. CERTAIN) value of
assets giving the same (i.e. EQUIVALENT) level of
utility as the initial prospect
CE of assets without safety equipment
CE
Initial prospect
X1
CE
The CE must therefore lie on the same state
contingent indifference curve as the initial
prospect
and lie on the certainty LINE
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Will a person buy safety equipment for their
workshop?
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Will safety equipment be bought and installed?
Using expected value (i.e. E(V)) as criterion
X2
E(V) at basic risk line
Installing safety equipment means risk is reduced
so the slope of E(V) line INCREASES
E(V) at reduced risk
E(V) assets HIGHER with safety equipment
E(V) of assets without safety equipment
SO BUY EQUIPMENT
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Using expected value (i.e. E(V)) as criterion
X2
E(V) at basic risk line
Risk of accident reduced, but not by much
E(V) at reduced risk
E(V) of assets without safety equipment
E(V) assets LOWER with safety equipment
SO DONT BUY EQUIPMENT
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Using E(V) as criterion
X2
E(V) at basic risk line
Break-even case
E(V) at reduced risk
E(V) assets SAME with or without safety equipment
E(V) same whether buying safety equipment or not
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Using subjective value (i.e.E(utility)) as
criterion
X2
Risk is reduced (so slope SCIC on certainty line
INCREASES) SCIC SWIVELS
SCIC at basic risk
CE of assets HIGHER with safety equipment
CE of assets without safety equipment
SCIC at reduced risk
SO BUY EQUIPMENT
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Using E(utility) as criterion
X2
Risk is reduced but not much
SCIC at basic risk
SCIC at reduced risk
CE of assets without safety equipment
CE of assets LOWER with safety equipment
SO DONT BUY EQUIPMENT
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Using E(utility) as criterion
X2
Indifferent
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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To insure or not insure?
That is the question.
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Will insurance be bought?
Unfair but low priced insurance
The price of insurance is cheap so the actual of
value of assets if insured
X2
is greater than certainty equivalent of uninsured
assets
Line of constant E(V)
Insurance trading line
E(V) of assets UNINSURED without safety equipment
SO BUY INSURANCE
SCIC at basic risk
Even though, because the insurance is unfair,
the actual value of assets is less than E(V) of
assets
Actual value of assets if INSURED without safety
equipment
CE of assets uninsured
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will insurance be bought?
Unfair and high priced insurance
so the actual of value of assets if
insured
The price of insurance is dear
X2
is less than the certainty equivalent of the
assets uninsured
Line of constant E(V)
E(V) of assets UNINSURED without safety equipment
SCIC at basic risk
SO DONT BUY FULL INSURANCE
Note however that, in this case, partial
insurance is preferable to no insurance
CE of assets uninsured
Insurance trading line
Actual value of assets if INSURED without safety
equipment
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will insurance be bought?
Indifference between insuring or not
X2
Line of constant E(V)
E(V) of assets UNINSURED without safety equipment
SCIC at basic risk
CE of assets uninsured
Insurance trading line
Actual value of assets if INSURED without safety
equipment
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Is there a trade-off between purchasing
insurance and safety equipment?
Is it better to manage risk internally by
buying equipment or adopting practices to REDUCE
RISKINESS
or simply use insurance to compensate if a bad
event happens
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Insurance and Safety Equipment as SUBSITUTES
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Will safety equipment be bought?
Insurance OR safety equipment
Actual value if insured
Certainty equivalent of assets including safety
equipment
gt
X2
E(V) no safety equipment
So insure dont buy
Insurance trading line
Value of assets if insured
CE of assets with safety equipment
SCIC at reduced risk
E(V) of initial assets with safety equipment
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
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Will safety equipment be bought?
Insurance OR safety equipment
X2
Now let the price of insurance increase
E(V) no safety equipment
Buy, Dont Insure (Fully)
SCIC at reduced risk
Insurance trading line
CE of assets with safety equipment
Value of assets if insured
E(V) of initial assets with safety equipment
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
Cost of safety equipment
Now, value of assets insured lt certainty
equivalent of assets INCLUDING safety equipment
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Insurance and safety equipment as complements
(No trade-off)
In this case insurance AND internal risk
management will be undertaken
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Will safety equipment be bought?
Mixture of safety measures and insurance
X2
Risk reduction from safety equipment too small to
make purchase worthwhile
Basic safety and insurance are not trade-offs
BUT CAN INSURE
Insurance trading line
Note that insurance is unfair
CE of assets with safety equipment and insured
SCIC at basic risk
EVEN SO, IT STILL GIVES PREFERABLE POSITION ON
CERTAINTY LINE
SCIC at reduced risk
CE of assets without safety equipment
CE of assets with safety equipment
SO BUY SAFETY EQUIPMENT AND INSURE
Initial (no safety equipment) prospect
Prospect WITH safety equipment
X1
In this case, insurance and installing safety
equipment are COMPLEMENTARY
Cost of safety equipment