Do our intuitions about deadweight loss break down at very small scales?

I’ve been thinking about high-frequency trading again.  Some of the issues surrounding HFT may come from whether our intuitions break down at very small scales.

Take the ordinary arbitrage of bananas.  If one banana sells for $1 and another for $2, no one worries that the arbitrageurs, who push the two prices together, are wasting social resources.  We need the right price signal in place and the elimination of deadweight loss is not in general “too small” to be happy about.

But at tiny enough scales, we stop being able to see why the correct price is the “better” price, from a social point of view.  Think of the marginal HFT act as bringing the correct price a millisecond earlier, so quickly that no human outside the process notices, much less changes an investment decision on the basis of the better price coming more quickly.  (Will we ever use equally fast computers to make non-financial, real investment decisions in equally small shreds of time?  Would that boost the case for HFT?  Is HFT “too early to the party”?  If so, does it get credit for starting the party and eventually accelerating the reactions on the real investment side?)

HFT also lowers liquidity risk in many cases (it is easier to resell a holding, especially for long-term investors, as day churners can get caught in the froth), and thereby improving the steady-state market price, again especially for long-term investors.  That too could improve investment decisions, even if the improvement in the price is small in absolute terms.

Some decisions based on prices have to rely on very particular thresholds.  If no tiny price change stands a chance of triggering that threshold, we encounter the absurdity of there being no threshold at all.  We fall into the paradoxes of the intransitivity of indifference and you end up with too many small grains of sugar in your coffee.

So maybe a tiny price improvement, across a very small area of the price space, carries a small chance of prompting a very large corrective adjustment, with a comparably large social gain.  Yet we never know when we are seeing the adjustment.  The smaller the scale of the price improvement, the less frequently the real economy gains come, but in expected value terms those gains remain large relative to the resources used for arbitrage, just as in the bananas case.  It’s not obvious why operating on a smaller scale of price changes should change this familiar logic.  Is the key difference of smaller scales, combined with lumpy real economy adjustments, a greater infrequency of benefit but intact expected gains?

In this model the HFTers labor, perhaps blind to their own virtues, and bring one big grand social benefit, invisibly, every now and then.  Occasionally, for real investors, their trades help the market cross a threshold which matters.

I am reminded of vegetarians.  Say you stop eating chickens.  You are small relative to the market.  Does your behavior ever prompt the supermarket to order a smaller number of chickens based on a changed inventory count?  Or are all the small rebellions simply lost in a broader froth?

What is the mean expected time that HFT must run before it triggers a threshold significant for the real economy?

Aren’t the rent-seeking costs of HFT near zero?  Long-term investors do not have to buy and sell into the possible froth.  HFTers thus “tax” the traders who were previously the quickest to respond, discourage their trading, and push the rent-seeking costs of those traders out of the picture.  More fast computers, fewer carrier pigeons.  Are there models in which total rent-seeking costs can fall, as a result of HFT?  Does it depend on whether fast computers or pigeons are more subject to production economies of scale?