Cantor’s diagonal argument: An extension to the socialist calculation debate

Abstract

The standard view of the socialist calculation debate is that Mises and Hayek at best demonstrated the practical impossibility of socialist economy, but that the mathematical solution of economists such as Dickinson showed that “in principle” planners could achieve a rational use of resources without private ownership of the means of production. In the present paper I hoped to show that this view is incorrect, because (if seriously implemented) a socialist planning board would need to publish a list containing an uncountably infinite number of prices. As Cantor’s diagonal argument from set theory shows, it is demonstrably impossible to construct such a list. Therefore, socialist economy is truly impossible, in every sense of the word.