Principles of Microeconomics / Unit 15 MIC 1406 worked example, 60 to 90 seconds
Pooled and Fair Premiums
The idea
From a table of how many in a pool suffer each size of loss, compute the total expected claims and divide by the number insured: that is the pooled premium when nobody can be told apart. Then compute each risk group's actuarially fair premium, its own expected loss per member. Compare: members below the pooled premium subsidize those above it, and the gap is what classification would remove.
In practice
Worked example: one hundred drivers. Seventy will have two hundred dollars of damage, twenty will have two thousand, and ten will have twelve thousand: fourteen thousand plus forty thousand plus one hundred twenty thousand, one hundred seventy-four thousand in all. Pooled premium: one thousand seven hundred forty each. Fair premiums by group: two hundred, two thousand and twelve thousand. The seventy safe drivers each pay fifteen hundred forty more than their risk; the ten worst each pay ten thousand two hundred sixty less.
Where people slip
The pooled premium is fair to the pool, not to any member; whether the safe should subsidize the risky is an equity question the arithmetic does not settle. And the insurer's costs and profit sit on top of these figures, which cover claims only.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Something wrong in this lesson? Flag it