Here’s a letter to a new correspondent (who offers only one name):
Mr. or Ms. Ashu:
Thanks for your e-mail, the full content of which reads:
P vs NP is one of the millennium problems that are unsolved.
The problem, in short, can a computer calculate something in a polynomial (P) amount of time. Since I heard of your claim that economic calculation (I think on a blog) without out a price system is impossible can you show that it is an NP type of problem? Sorry if I sent this multiple times.
If you don’t know about this type of math do you know any other Austrian who can?
First, the argument that economic calculation is impossible without a price system isn’t mine. It was first made by Ludwig von Mises in 1920, refined and defended by F.A. Hayek throughout the 1930s and ‘40s, and further developed by subsequent scholars, most especially in 1985 by Don Lavoie.
Second and more fundamentally, this Austrian insight is not that the mathematics of economic calculation is so difficult as to be impossible in practice. Instead, this insight is that the challenge of economic calculation is to incite multitudes of strangers to act productively in response to an inconceivably vast number of dispersed, often conflicting, and frequently fleeting bits of information. Coordinating the plans and choices of individuals spread across the globe, and even across time, requires that information about the consumption preferences of individuals – as well as of availabilities of billions of different inputs and of the likely relative values of a practically uncountable number of different input combinations – somehow be transmitted far and wide and in ways that prompt each of these multitude of strangers to make both production and consumption decisions in ways that yield something approaching maximum possible economic output.
This problem is not one of getting the mathematics correct; it’s one of information collection and use, where much of the information is not even in principle quantifiable.
A system of prices reckoned in terms of money and set in competitive markets for private property rights is the only known ‘mechanism’ for eliciting enough such information, transmitting it in readable form to where it is most useful, and then prompting individuals – consistently if never perfectly – to act on this information in ways that raise over time the standard of living of nearly everyone.
That the general features of this astonishingly complex system of economic coordination can be usefully described with mathematics is beyond doubt. That it is fundamentally impossible for knowledge of mathematics to substitute for the information-generation and information-processing achievements of competitive markets is, however, even more certain.
Donald J. Boudreaux
Professor of Economics
Martha and Nelson Getchell Chair for the Study of Free Market Capitalism at the Mercatus Center
George Mason University
Fairfax, VA 22030