> Worse they have incentives to decrease efficiency by increasing paperwork etc.

Money spent on paperwork comes out of the same pile as profit. The MLR cap preserves incentive to reduce paperwork, wherever premiums and payouts sit.

Not internal paperwork. Think in terms of industry wide collusion not a single insurance company. If lobbing or an industry group can drive up healthcare costs via say paperwork or regulations then every health insurance company is “forced” to raise premiums and as the maximum profit per premium ratio is fixed that also increases the total possible industry wide profit.

Of course insurance companies are also in competition so they have individual incentives to keep premiums cost competitive.

I think even in terms of industry-wide collusion, the push of an MLR cap would be to decrease (money spent on) paperwork.

With R = revenue, P = profit, A = administrative expenses, and M = medical expenses, we have:

    R = P + A + M

which we can rearrange a little bit to get

    P = R - M - A

From the point of view of an individual company, clearly increasing our own expenses means less profit:

    P₂ = R - M - (A + δ) = P - δ

But, as you say, if we force everyone to do likewise the situation is better because we can raise prices to raise revenue:

    P₃ = (R + δ) - M - (A + δ) = P

This holds whether or not we have an MLR, but in either case assumes that demand is sufficiently inelastic that we can raise prices enough to make δ more revenue (it won't be a matter of simply raising prices by δ/(number of customers) because some customers may chose to purchase less insurance), and at best it puts is right back where we started.

Does the MLR cap have an impact?

    MLR = M / R
    MLR₃ = M / (R + δ)
    MLR₃ < MLR

By raising our revenues to compensate for the additional expense, we find ourselves with a lower MLR. If we are not near the cap this has no effect; focusing on the other case we are forced to do something to raise the MLR. Where does that come from? Recall our present situation:

    P = (R + δ) - M - (A + δ)

We can lower P or A, but our whole question here is whether we can raise P by raising (everyone's) A so doing the former defeats our purpose and the later contradicts our assumption. We are stuck raising M and further raising R (if market conditions allow it). In a sufficiently inelastic market this is possible, but I really don't see the case where we've forced some extra slop that allows us to raise profit.

Of course if I believe that my company is better able to handle the new paperwork than my competitors, that could help - but if the whole industry believes that's the case then most of them are wrong, and in any event I believe this incentive is weakened not strengthened by the MLR cap.

If paperwork keeps new entrants out of the market, that is something current participants can probably agree on, but that's true in any case and I don't see how the MLR cap makes it stronger.

I don't think this analysis changes if we pull executive compensation out of "administrative expenses" and treat it as something we're maximizing in addition to (or instead of) profit.

Don’t forget a regulation that says Profit <= some percentage of Medical Expenses. In effect you have a normal demand curve but company’s can’t raise prices past some limit. Assuming profit maximization occurs below that limit it has no effect. However, insurance is unusually inelastic in part because much of it is subsidized.

So while thinking in terms of total administrative costs seems reasonable there are two different numbers here, administrative costs for the insurance companies and administrative costs for the healthcare industry and that matters.

So again, assuming it’s the regulation not market forces limiting profits increasing Ma directly increases profits. Up to some limit rather than P < (Mm + Ma) * X% it’s P = (Mm + Ma) * X%. Thus creating incentives to increase Ma.

Ah, yes, administrative costs within the medical organizations are presumably paid by passing those costs on to (payers including) insurance companies as "medical costs" and that is presumably counted in the M in the MLR (I could imagine a system that avoids it - at, ironically, the cost of some more paperwork - but I don't expect it's what we do).

It is true that the MLR cap does nothing to motivate insurance companies to avoid increasing hospital paperwork. I don't see that it produces incentive to create it - yes, increasing payments to hospitals increases allowable profit, but in order to make that profit you need sufficient revenues and customers aren't paying because they want hospitals to do paperwork. I'm of a mind that (at the margin) increasing legitimate (or nearly legitimate) medical spending is typically pretty easy so there is no need to find alternative ways of paying hospitals more; if I'm mistaken about that then you raise an important point that probably deserves attention (if it hasn't got it in some way I'm unaware of).

This is not remotely true.