Why Do People Buy Health Insurance?

The Arithmetic of Risk-Pooling 10-percent chance of hospitalization that costs $10, percent chance of no hospitalization 100 policyholders 10 x $10, x $0 100 = $1000 $100, =

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

“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

Risk-pooling => Averaging (.10 x $10,000) + (.90 x 0) = $ out of 100 consumers pay $1000, get $10,000 of hospital care 90 out of 100 policyholders pay $1000, get nothing back

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

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

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

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 $75 each (and everyone goes to the dentist)? –What is the insurance trade-off for the dental coverage?

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