[Evan]

There are three parts of the insurance bussiness to think about:
1) Underwriting profit/loss
2) Amount of float (cash)
3) Retun on investments

A very basic way to understand their interaction is:
(2*3)+1 = Profit

Increasing any of these, all else remaining equal, will increase profit. Obiovusly though, increasing one will usually adversely affect another. In your example, your car insurance company sacrificied a portion of 1 to increase 2.

First of all, you were right about one part. It allows them to reduce staff and billing activities. In doing this it cuts their SGA costs. This means that they don't reduce #1 by as much as you think; althought they do reduce their top line, by x%, they improve margins and don't hit their bottom line quite as hard.

Whether or not their return is high enough to justify the price cut, I obviously can't tell you because I don't know who it is, how much float they're managing, what their actuarial assumptions are or how accurate they are.

This is a complicated business that relies VERY heavily on completely fabricated assumptions. I don't mean to imply that that's not accurate, because that's not true. My point is that it's extremely tough to analyze a single decision in a vacuum. My guess would be that if they're offering the discount it makes them more money, and not by a small margin.