usps insurance rates

What do USPS insurance rates tell us about its operations? Here is a 2007 document regarding insurance rates for domestic mail:

Prices for insurance coverage changed as follows:
Value up to $50 is $1.65.
$50.01 to $100 is $2.05.
$100.01 to $200 is $2.45.
$200.01 to $300 is $4.60.
The price per additional $100 of insurance, valued over $300 up to $5,000, is $4.60 plus $0.90 per each $100 or fraction thereof.

Crudely taking the mid-point of each bracket up to $300, we get implied loss rates of 6.6%, 2.73%, 1.63%, 1.84%, respectively. The rate converges asymptotically to $0.90/$100, or 0.9% implied loss. The numbers have such a wide range that it’s worth taking a closer look.
(Read the article)

optimizing insurance ordering

Sometimes the order in which procedures are performed has an effect on the payout from insurance. This is the case when there is both a deductible and a coinsurance.

Suppose the deductible is \(d\), and the price and coinsurance of the \(i\)-th procedure performed are \(p_i\) and \(c_i\) respectively, then the total out-of-pocket cost is:

\(d + (p_1 – d) c_1 + p_2 c_2 + \cdots = (1-c_1) d + \sum_i p_i c_i\)

The second term is fixed cost; it’s the coinsurance on the first procedure that matters. This shows that to minimize out-of-pocket cost, one should, somewhat surprisingly, get the procedure with the highest coinsurance first. Essentially, every dollar of the deductible paid is subsidizing what the insurance company might have paid, but for a procedure with very high coinsurance, the subsidy is not very much to begin with.