Pur Autre Vie

I'm not wrong, I'm just an asshole

Saturday, August 02, 2014

Brute Force, Queues, and the Price System

The price system is generally thought to be a good way to allocate resources.  There are various levels of formality you can adopt in reaching this conclusion.  On an informal level, the basic idea is to force people and businesses to consider the cost of using scarce resources.  If you can make equally good cookies with oat flour or wheat flour, and oat flour is half as expensive (reflecting that it is cheaper to produce or it is inferior for other applications), then the price system will tell you to use oat flour.  In this way wheat flour is preserved for applications in which it is actually superior to oat flour.

On a somewhat more formal level, the price system is thought to address the economic calculation problem.  Prices convey information in an automatic, decentralized way, allowing society to allocate resources without any central direction.  This allows society to solve what would otherwise be an insurmountably complex optimization problem.

And I believe there are much more rigorous "proofs" out there.  I once sat in on a class taught by Gary Becker, and I think he was doing exactly that.

Now there are various ways of critiquing the price system.  One is to observe the social costs and benefits that do not make it into the price - that is, externalities.  Imagine that oats require much less pesticide than wheat.  By itself, that is not necessarily an externality, since the price of the pesticide will be reflected in the price of the wheat flour.  But if pesticides cause damage to people other than the farmer, then the farmer might not take into account all of the costs of the pesticides.  And if that's true, the price of wheat may be "too low" given its overall impact on society.  The prices are sending the wrong signals.

Another critique, or maybe a refinement, of the price system is Coase's theory of the firm.  The allocation of goods across society is generally governed by the price system.  But within a firm, quite often goods are allocated in a centralized manner, by fiat.  The CEO of a car company doesn't make the motor-building division bid against the exhaust-system division for steel.  He simply directs a certain amount of steel to be delivered to each division, regardless of the division's "willingness to pay."  As between the car company and its external counterparties, relations are governed by prices and legal contracts.  Within the company, relations are governed by autocracy.  There is an old Coke ad in which businessmen tell lawyers that they want to sue Coke Zero for "taste infringement" (since Coke Zero tastes so much like original Coke).  We recognize that this is ridiculous, but only because we intuitively understand that for internal purposes a company does not allocate its intellectual property using ordinary market and legal mechanisms.

And so if firms don't find the price system to be an attractive way of allocating resources, we can consider what circumstances might call for centralized resource allocation.

But there is another critique of the price system that I think doesn't get enough attention in economics classes.  While the price system provides a solution to the economic calculation problem, there's nothing to ensure that it's a good solution.  Consider the great famine in Ireland.  During most years of the famine, Ireland was a net exporter of food.  While perhaps a million Irish died of starvation, the price system was telling Irish farmers:  send your food to England, the prices are higher there.  There are English mouths to be fed, chop chop.

If this is how the price system solves the economic calculation problem, then so much the worse for the price system.  But what went wrong?  The answer is that the price system allocates resources according to willingness/ability to pay.  Our cookie manufacturer in the earlier example, who is indifferent between oat flour and wheat flour, will buy whichever is cheaper.  He will have no willingness to pay for the more expensive ingredient, and he won't receive any.  That's all to the good.  Or, if he can't sell his cookies for a high enough price to cover the cost of running his business, he soon won't have enough money to buy oat flour or wheat flour, and he won't receive any.  Again, that's all to the good - his business was a value-destroying proposition, and it should be shut down.  (Unless we can identify some externality that makes his business a net positive for society.)

But the thing about the Irish was that they couldn't pay for food.  And so they were treated just like the unprofitable cookie manufacturer:  the price system didn't allocate any food to them.  But instead of a business going bankrupt, the result was that bodies of children were found along the road, their mouths green and their stomachs bloated from trying to eat grass before they died.

The price system ensures that there is no "shortage" or "surplus" of resources by setting the price so that supply equals demand.  As we've seen, that can be a valuable thing to do.  But in a sense it is a "brute force" solution to the problem.  The reason there will never be a shortage of pencils in a free market economy is that the price will always be set so that anyone who is willing and able to pay for a pencil can get one.  But that's almost tautological:  we've defined "ability to pay" such that the price system can never fail to achieve an efficient outcome, regardless of how far it falls short in actuality.  If there are 10 pencils for 10 million people, and they are allocated by auction, then there is no shortage.  If there are 5 million pencils for 10 million people, and they are sold below the market price so that people queue up for them, then there is a shortage.  Funny how that works, right?  Shortages aren't defined by how far our resources have fallen short of what society needs, they're defined by that most execrable of human institutions, queuing.

We've basically defined efficiency as "what happens when the price system operates without hindrance," with perhaps a slight emendation for externalities.  It's a brute force solution, not in the sense that it requires trying a bunch of different possibilities to find the solution, but rather because it takes whatever solution it produces and labels it "efficient."  And that is just what happened in Ireland.  The deaths of perhaps 1,000,000 Irish people were efficient, according to the price system.  If anything, probably more Irish should have died, since the government intervened to prop up the existence of quite a few Irish people.  And as we've discussed, in the absence of externalities, government intervention is thought to be inefficient.  If the British had sent over food to be sold cheaply to the Irish, and they had queued up for it, it would have been terribly inefficient.  Thank God for Trevelyan.

I feel this example should be taught in introductory economics, so that students will understand the limits of wealth maximization as a moral criterion, and the need for independent assessment of market outcomes.


Anonymous Anonymous said...

I think this is a good post and a good example, but you are misusing terminology in a way that will make the post ambiguous or confusing to those who are used to using it correctly.
Brute force typically is a comp-sci (or sometimes math) term that refers to solving a problem in a very algorithmically unsophisticated way. The classic example being a bunch of nested ‘For’ loops that try literally every possible combination. A smart solution would incorporate some time saving heuristics, like having the traveling salesman try the house that’s next door to the current house rather than picking a random house in the city and trying every set of possible routes.
Markets are actually pretty sophisticated, in terms of the processes they embody. Instead of trying everything, there are lots of decentralized processers each running different algorithms, each of which sees the results but not internals of other units and can update on them, and each of which does a combination of local optimization and hill climbing as well as the occasion big jump.
The problem you identify is a real problem, but its not a problem of markets using a brute force approach.

3:11 PM  
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