The Economic Calculation debate is one of the most complex and significant debates in all of Economic History, if not the most significant of all. However, despite the complexity of the debate itself, the original argument put forward by Mises is not only fairly simple but was never close to being refuted and actually hardly addressed by the Socialists during the debate due to the differing theoretical frameworks in which everyone was working from, differences not well communicated and only truly realized towards the end of the 20th century. - What is commonly called the "calculation debate" can be best split up into the following sections
The calculation problem states that even if we have all the following conditions 1) Complete information as to every single consumer demand 2) The relevant quantities and qualities of all the different factors of production, both original and produced 3) All of the technological recipes known to man in existence for producing consumer goods 4) Complete agreement on what exact course of action to take regarding what needs to be produced The socialist planner would still not be able to effectively allocate factors of production to there use which best satisfies consumers subjective values (edited)
This problem is an issue which concerns the use of mathematics in order to allocate resources between branches of production in given quantities. This is a problem which concerns the ability to make actual mathematical calculations with the powers that computers and scientists possess, and even with all that they can do, they still are not even close to being able to having the power necessary to plan a modern day market economy even assuming both the calculation problem, knowledge problem and more are assumed away
The knowledge problem consists in questioning the ability of the socialist planners to get information on the following... 1) The demands of consumers (consumers values) 2) The relevant quantities and qualities and different factors of production (both original and produced) 3) The technological recipes to produce consumer goods Socialist planners also have issues creating feedback mechanisms for communicating information and establishing a power structure in which the intentions and incentives of people in control of the means productions are suited to best allocating resources for the good of the masses e.g. allocating resources in a way best fitted to serving subjective values.
Critiques concerning the limitations of static equilibrium and perfect competition models in order to come up with plans for resource allocation in a socialist system. These models usually have huge simplifications in them and assume problems away by there very nature.
All of the following critiques have arguments which fall into these categories, be it one of them or all of them, the categories have different degrees of relevance to different socialist proposals, of which are below (edited)
The socialists attempts at economic allocation takes the following forms, with there being overlap between some socialist proposals:
Solutions that aim at a moneyless society (e.g Communism)
Planning based on labour hours (The Labour Theory of Value)
mathematical Solutions (Equations and trial and error methods)
Those that aim at introducing competitions (Market socialism/"competitive solution")
The argument originally put forward by Mises in 1920 is enough to refute all of these attempts at Economics Calculation, but the debate is not so simple. Mises original argument is what deals with all attempts at calculation in a moneyless socialist society. The second option, attempts at calculation based on the common denominator of labour hour also fails, as it is not enough to have a common denominator, but a common denominator which represents the real world scarcity for factors of production. After 1929 the Socialists would admit the need for money as a common denominator and that the communism imagined by Marx was indeed, nothing but a dream. In response to this the socialists tried to employ a number of Mathematical models (of which most would abandon going into the 1930's) and then attempts at "market-socialism".
The latter two are more complex and involve more moving parts.
I believe the key to dealing with such a complex topic (especially concerning socialist attempts at calculation via mathematical models or market socialism) is to take the form of the fox, but with the heart of a hedgehog
https://b-ok.cc/book/2642098/0f1e65
That being, the route of someone like De Soto, who isolates each of the socialists’ arguments and explains exactly what is wrong with each of them individually, using the original Misesian argument as his pillar. All socialist plans fail to address Mises central critique, but on top of that, each socialist attempt at calculation has unique strengths and weaknesses, but all fail, the fun is figuring out exactly how.
The mathematical solutions are significant in two primary ways
It was during the 1920's that socialists put forward these arguments on there own as ways of allocating resources, but these attempts were almost completely dropped by the 1930's as most socialists moved to market socialism (with Lange making a move back to complete central planning later in life).
Many of the mechanisms used in the mathematical models such as trial and error methods or processes of simultaneously calculated equations would be used in the market socialist models, so understanding the flaws is important.
This section contains sources which question the ability of the central planners to figure out
The demands of consumers (consumers values)
The relevant quantities and qualities and different factors of production
The technological recipes to produce consumption goods
The feedback mechanisms for communicating information
The intentions and incentives of people in control of production
Note: The original Misesian critique shows how the socialist planner cannot allocate resources effectively, even assuming that all of the above are assumed away. This is just icing on the cake as I see it.
The internal debate in Austrian circles revolves around three central questions
Are Mises and hayeks arguments the same?
Did Hayek drop Mises original argument?
Are the arguments of Mises and Hayek compatible?
I would argue that the main focus should not be on whether Hayek dropped Mises argument or not, this is not essential in my eyes. One thing seems for certain though, they are not the same. However, I do believe that the different theories created by Mises and Hayek can be compatible, but the degree to which this is the case depends on the type of socialist argument you're responding to. There is certainly a big difference (which Mises himself notes in the papers he wrote in German during the 1920's) between the calculation based on one central plan and those based on introducing competition. Hayeks writings seem to me to be answers to very specific arguments in very specific contexts.