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Why Do People Buy Health Insurance?
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The Arithmetic of Risk-Pooling
• 10-percent chance of hospitalization
that costs $10,000
• 90-percent chance of no hospitalization
• 100 policyholders
10 x $10,000 + 90 x $0
100 = $1000
$100,000
100=
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With N policyholders
.10 N x $10,000 + .90 N x $0
N
.10 x $10,000 = $1000
(.10 x $10,000) + (.90 x 0)
N (.10 x $10,000 + .90 x $0)
N
(factor out N)
(N’s cancel)
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“Actuarially fair premium” or“actuarial value”
(.10 x $10,000) + (.90 x 0) = $1000
= total claims divided by number of policies
= expected (or average) claims per policy
= break-even premium
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Risk-pooling => Averaging
(.10 x $10,000) + (.90 x 0) = $1000
• 10 out of 100 consumers pay $1000, get $10,000 of hospital care
• 90 out of 100 policyholders pay $1000, get nothing back
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Insurance reduces risk
(.10 x $10,000) + (.90 x 0) = $1000
Suppose everyone has $7000 income
• 10 out of 100 policyholders pay $1000,have $6000 to live on
• 90 out of 100 policyholders pay $1000, have $6000 to live on
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Without insurance
(.10 x $10,000) + (.90 x 0) = $1000
Suppose everyone has $7000 income
• 10 out of 100 policyholders have -$3,000 to live on
• 90 out of 100 policyholders have $7,000 to live on
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The Insurance Trade-off
• Give up premium ($1000)
• To avoid risk of much bigger loss(10-percent chance of $10,000) ??
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Group Exercise (Part 1)
• What premium will cover claims if everyone has a 20% chance of $8,000 hospitalization?– What is the insurance trade-off?
• What additional premium will cover claims if add 2 regular dental checkups @ $75 each (and everyone goes to the dentist)?– What is the insurance trade-off for the dental
coverage?
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Group Exercise (Part 2)
• What premium will cover claims for 1000 policyholders if– 500 have 5-percent risk of $10,000 hospitalization
– 500 have 10-percent risk of $10,000 hospitalization
• What premium will cover claims for 1000 policyholders if– 800 have 5-percent risk of $10,000 hospitalization
– 200 have 10-percent risk of $10,000 hospitalization