The title of this post might seem somewhat strange because on the surface the concepts of roundaboutness and market socialism are not directly related. However, bear with me until the end of this post and I hope that I will be able to demonstrate that these things are tightly connected.
I explain why the notion of aggregate roundaboutness of the economy is probably meaningless in this latest short paper of mine:
It is not even clear that the notion of the economy’s total roundaboutness may be ascribed a determinate meaning. Consider the fact that even the decision about what to consider the beginning of production of a certain good is necessarily going to be arbitrary. Even the moment of extraction of the relevant raw materials used in its production is probably not the right starting point because the extraction of those raw materials requires investments of other resources and so on ad infinitum.
The realization that there is no point where the production of a unit of a certain good is started ex nihilo has an important corollary which is relevant to the subject of this post. The corollary is that the production of any input requires obtaining other inputs. This is what is needed to demonstrate that market socialism is untenable.
Recall that market socialism a la Oscar Lange is a system under which price mechanism exists for consumer goods but all the factors of production are owned or hired (in the case of labor) by the state. The traditional argument against this set-up has been that there is no competition in this system. But the response of a market socialist may be that nothing theoretically prevents the government from instructing the appointed managers to compete with one another for producing better consumer goods. Of course, opponents of market socialism may respond that, without being owners of their enterprises, the appointed managers will have weaker incentives to innovate. But this argument is merely psychological and vulnerable to counter-arguments appealing to the fact that in many modern corporations the key entrepreneurial decisions are made by appointed top-managers who rarely own a large enough stake in their companies.
But the observation that I made above about the necessity of other inputs for production of any inputs provides the basis for a praxeological argument against market socialism. Since it is the state and not the managers who will own the money from the sale of consumer goods, the state may not allow the managers to freely decide how to spend the money on inputs because in such case there is no socialism here. The state must thus decide according to some principle where inputs are going to be used and in what quantities and combinations. And the state may not replace input markets by auctioning the inputs exactly because the state does not itself produce and sell some output. Thus, market socialism is untenable.
UPD: What I wrote in the last paragraph probably requires some clarification. The idea is that due to the Hayekian critique market socialism can only succeed if it can combine the advantages of the capitalist system with the absence of property rights in the inputs and the money received for them. Thus, the state cannot just assign some specialized managers to run different enterprises producing inputs as they wish. It must dispose of the inputs or at least the profits itself. More precisely, if the state auctions the inputs as they are produced to retain the prices for them, it may not merely transfer the money to the managers running the enterprises producing the auctioned inputs because such an arrangement will just be capitalism made less efficient by artificially forcing everyone to buy inputs at institutionalized exchanges. Thus, the state must itself decide how to invest either the whole amounts of money it gets for the inputs or at least the difference the input producers make between the price at which the inputs are auctioned and the prices at which they buy the inputs they need at other auctions.
In the first case, the state will quickly find itself displacing all the appointed specialized managers in deciding about the allocation of the inputs. But even in the second case the Hayekian critique still applies in full force because it is not the specialized managers with the relevant knowledge who will have to decide how the profits will be invested but some central bureaucrats.