Just what do BHP Billiton and Rio Tinto, which plan to lift production even more, think they're doing?

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Politicians, business leaders, and their own shareholders are perplexed. But there's method in their madness. The only self-inflicted harm is BHP's determination to demerge, despite the less than convincing case in the prospectus sent to shareholders.

The truth is the budget deficit would be far worse if the miners dug up less. In the words of the eminent economist Professor Ross Garnaut​: "Growth in resources output is keeping Australia out of recession."

Nobody is suggesting they're motivated purely by the national interest, and definitely not Fortescue's Andrew Forrest or Atlas Iron.

But ramping up production is better than the alternative. The iron ore price would have to halve again for them to lose money.

If they cut production the price would rise, allowing for the fact that China's demand is falling as Garnaut points out but, weird as it sounds, so would their costs.

The reason is they invested a fortune in expanding capacity, which has lifted their fixed costs. It's the old story of economies of scale: the more they produce the lower their unit costs. Only when their variable production costs exceed the extra revenue does it become uneconomic.

That's not to say they read China, by far their biggest customer, correctly. They were wrong on two counts. Demand by exaggerating China's likely growth and then, as it slowed, supply by assuming its high-cost mines would close.

So having dug their hole they must ... well, dig deeper.

Which brings me to BHP's demerger of shunting off the Billiton bit to South32, in which shareholders will get free shares on a one-for-one basis.

It claims this will simplify things no end because BHP will have only its four-and-a-half pillars to worry about – iron ore, oil, coal, copper and potash – and so will be more fleet-footed with maintenance, especially adopting new best practice.

The exercise will cost $US738 million but supposedly save $US100 million a year as BHP manages its coal and copper mines better and they can share the global outsourcing.

Um, how will the demerger do that? Well, since BHP will have fewer assets its  managers can concentrate better.

"The long-term benefits of simplification are multi-faceted and, by their nature, not possible to quantify," says the prospectus. Convinced? Neither am I.

Besides, shareholders will have equal shares in two companies, so what BHP would call a multi-faceted approach is called for.

South32's costs will rise $60 million a year though there's the same claim about managing assets better, this time because its managers will be "incentivised" and won't have their erstwhile rivals in BHP hogging capital.

The bottom line is the whole exercise will save shareholders a net $40 million. That will take 18 years to recoup the cost. Call that a good deal?

@moneypotts