The funny thing about Krugman choosing this particular subject to complain about is that he's the Keynesian: You know, the pay-a-man-just-to-dig-a-hole crowd. Here he is quoting from Keynes famous parable:
If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coalmines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez-faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.
He was right then, and I’m right now — and if you find it strains your personal credulity, so what?
You'd think, therefore, that Krugman would be utterly thrilled with Spread Networks' project. They paid folks $300 million of their own (and their investors') money---as opposed to taxing the average citizen---to dig holes. And, again, if their project fails, the average citizen's good money won't chase after bad to clean up, and maintain in perpetuity, the mess---as it would a failed government project (although that wouldn't be Krugman's concern). Again, Krugman ought to love this one!
P.s. Before you challenge me on the cumulative hit to the small investor resulting from the front running (afforded by the three milliseconds) by some high frequency traders (not saying it's by any means right), know that spreads are substantially narrower (investors are paying far less per trade) than they were before the advent of high frequency trading.