The so-called Austrian school of economics makes much of what they call the socialist calculation problem. They argue that a society based on social ownership could not have an effective price system and therefore could not have the decentralized decision-making we see in a market economy.
The claim was first made by Ludwig Von Mises in the 1920s. Really all he is saying is that transfers between enterprises using a decentralized price system must be market exchanges. Without explaining why, he rules out the possibility of such transfers occurring between socially owned enterprises where there is no exchange of ownership but simply a transfer of socially owned property from one custodian to another. I am thinking here of a transfer between a supplier and user of some component in production. Without predicting what will actually happen in the communist future we could easily imagine production units using decentralized pricing to determine least costs methods of production and assigning output to the highest bidder. We could also easily imagine such a system being ultimately driven by consumer demand.
Then we had the intervention of Frederick Hayek in the 1930s and 40s. He demolished the rather lame decentralized socialist model devised by the economist Oskar Lange. That model confines decentralized price adjustments to consumer goods while price adjustments for intermediate goods are carried out by a central agency that is keeping an eye on inventory levels. Hayek correctly points out the inadequacy of such an arrangement and how it does not represent a fully functioning price system. Discrediting the Lange model is all very well, but Hayek did not then go on to show that an economy based on social ownership would in fact be limited to the Lange model. In other words he did not show that there is something about social ownership that would prevent the use of decentralized price adjustment in the allocation of intermediate goods. So I think I can justly say that all that Hayek has done is refute a straw man.
OK now we come to the final version of the argument and this was developed in the 1980s by Don Lavoie of George Mason University. He conceded that a socially owned economy could have a price system but that it would not be a very good one. In his book Rivalry and Economic Planning, he contends that any price system under social ownership would be inferior to a market based one because it would be unable to reflect the discovery process that emerges from competition between market participants. According to Lavoie, it is important, in the presence of uncertainty, to have numerous participants trying out different approaches to problems, based on their own opinions, guesses and hunches. Those who come up with the best and most highly valued products using the cheapest methods win out in this competitive contest. I fully agree with what he is saying. However, if, as I contend, decentralized custodianship is an important part of social ownership, diversity of approach should not be a problem.
Under social ownership, it would still be very common for an individual enterprise or facility to be just one of many producing the same good or close substitutes and each of them would be free to try out different production methods and product designs. Some would be new entrants who were either existing enterprises moving into a new field with synergies or starts ups established by enthusiasts with ideas that the incumbents were not open to or capable of developing. This diversity would be greatly assisted by having numerous independent agencies being responsible for disbursing funds in each industry and making their own assessment of what were good investments. At the same time, enterprises would be free to choose their suppliers based on cost and quality, and would have to outbid other users of a resource or intermediate good. Discovering and adopting the best methods and products would of course mean that it would be common to see activities abandoned and enterprises closed or reorganized. So, the only real obstacle to a decentralized price system would be the absence of daring and conscientious custodians and this gets us back to the question of whether we can do without the profit motive. Can we do our best just because we enjoy the work and want to contribute? As I argue elsewhere this does not strike me as being all that fanciful if we are sharing high and increasing affluence and all the unpleasant work is performed by robots and computers.
So the calculation argument is not a separate argument from the standard one about whether we need the profit motive.
I think it is appropriate to point out that there is no reason to be smug about economic calculation under capitalism. Communist workers could hardly do a worse job of allocating investment funds than do highly fluctuating interest rates and exchange rates produced by capitalist finance. And there are good reasons for thinking that economic decision-making would be far superior to that under capitalism. To begin with, the absence of ownership barriers would increase the scope for coordination, and lessen the scope for secrecy and deception.
So to sum up. My basic point is that when it comes to economic calculation, communism will be able to do anything capitalism can and do a better job of it.
I have links below to a number of articles that go into more detail on this topic.
http://www.simplymarxism.com/model.html (April 2020)
A podcast discussion of the model: