Since 2008, Somali pirates operating in the Gulf of Aden have made about $120 million per year in net profits. But they've cost the shipping industry far, far more than that — between $900 million and $3.3 billion per year.

Not an efficient business model.

That's according to an offbeat recent paper (pdf) by Timothy Besley, Thiemo Fetzer and Hannes Mueller that tries to break down the economics of Somali piracy. The authors find that piracy has increased shipping costs in the region by 8 percent since attacks ramped up in 2008.

Among other things, the shipping industry has had to pay for armed security, ransoms, safer ships and even taxes for an increased military presence in the region. All told, these extra costs come to between $900 million and $3.3 billion per year. The authors also found a seasonal fluctuation — it's about 14 percent cheaper to charter a ship through the Gulf of Aden during the summer monsoons, when fewer pirates are out, than during the spring.

As Tim Fernholz points out at Quartz, the numbers here suggest that piracy is an extremely inefficient form of wealth transfer. (Not to mention deadly.) It would be cheaper, though unrealistic, for the shipping industry to just hand over $120 million to the pirates. Alternatively, the authors estimate that just $1.3 billion in extra costs would be enough to employ 1.5 million workers in Somalia at prevailing wages.

Here's the paper's conclusion: "The analysis further underlines the difference between organized extraction by the state in the form of taxation and disorganized predation. We estimate that the latter is at least ten times more costly."

In any case, there's now a question of whether Somali piracy is still as big a problem as it once was. Recent reports suggest that attacks are down two-thirds since last year. That might be because of all the extra actions taken since 2008 — from stepped-up security on ships to the international armada off the Horn of Africa. Or, as the Economist notes, Somali pirates might just be biding their time during a period of bad weather.

Related: For more on the economics of piracy, here's a recent paper (pdf) by three European researchers on the strategies used during negotiations. Here's one summary:

They found that Somali pirates pretend to be more sophisticated than they are, whereas shipowners pretend to be poorer. Nowadays both sides have an interest in a speedy resolution, since a prolonged negotiation incurs costs. For the shipowner, the cargo spoils and the ship goes unused. For the pirates, the captured crew must be fed and the ship guarded. And pirates cannot last long without a resupply ofqat, which is to them as rum is to Captain Jack Sparrow. Settle too quickly, though, and one side or other is likely to get a poor deal.