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Why Do People Buy Health Insurance?

Explore why people buy health insurance through risk-pooling calculations. Learn about actuarially fair premiums, risk reduction, and insurance trade-offs. Includes group exercises for practical application.

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Why Do People Buy Health Insurance?

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  1. Why Do People Buy Health Insurance?

  2. 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 $100,000 = = $1000 100 100

  3. .10 N x $10,000 + .90 N x $0 N With N policyholders N (.10 x $10,000 + .90 x $0) (factor out N) N (.10 x $10,000) + (.90 x 0) (N’s cancel) .10 x $10,000 = $1000

  4. “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

  5. 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

  6. 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

  7. 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

  8. The Insurance Trade-off • Give up premium ($1000) • To avoid risk of much bigger loss(10-percent chance of $10,000) ??

  9. 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?

  10. 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

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