Hello, everyone thank you for your patience with me and thank you Jon Irenicus and Truth and Liberty for the responses. I’ve thought about it before going to sleep and I seem to have solved the problem.
This is basically the solution just a bit more technical.
Firstly we work under the assumption that entrepreneurs in this imagined society are perfect in their loyalty to the state, this does not mean they imitate free market incentives, just that there is no problem for them meeting some set of objectives given by the state. So the incentives don’t perfectly replicate the incentives of free market profits, instead I assumed the incentive is “to maximize revenue” since this is the only quantitative measure of performance that can be made into an incentive and has some relation to prices, when profits do not exist.
Secondly, this produces prices that have a tendency to allocate capital goods so as to equalize revenues everywhere which is a result very different from a configuration of capital goods that maximizes consumer welfare produce, and a result that makes no sense.
Each market will tend to the revenue maximizing price, which is the midpoint of the demand curve.
But if the revenue of each market is maximized, then how can all markets have the same total revenue? How can markets ever hope to have the same total revenue?
As more people move from a lower revenue yielding market towards a higher yielding revenue market, the price per unit of the lower yielding market goes up, but at this point you’re above the midpoint of the demand curve in the lower revenue yielder and below the midpoint of the demand curve in the higher revenue yielder meaning revenues aren’t maximized in either one. Furthermore it is indeed mathematically possible even in an equilibrium construct that two markets can never have the same total revenue if there must be a trade off between production in one market and production in another market.
So, to put it simply, if entrepreneur’s are given full control of what they produce and simply act as revenue maximizes they will engage in actions which are largely irrational. Consumer welfare will indeed have little to no bearing on their decisions as revenue cannot measure this. The only force which will guide their decisions is the mysterious invisible hand of the socialist market which would move them to attempt to maximize and equalize revenues everywhere, which would lead to the complete destruction of some markets and gross over investment in others, the impact of this on the prices of capital goods will skewer their true worth as an imputation of consumer demand and lead to utter chaos.
This means the socialist market must indeed control what industries exist and how many competitors are in each. If this is done then capital goods prices cannot but hope to yield results even close to the efficiency of the market. If it is not done then calculation still remains impossible as there is no way of measuring performance or a rational basis for making entrepreneurial decisions.
I just did.
The socialist can say “look the market just solves equations a computer can do this” to which you can respond, “no there is something called disequilibrium and the market process”
Then he can say “look a computer can just intelligently guess at prices and you’ll get the same results as the market” to which you can respond “no, for the prices to start off the same the computer would have to accurately arrive at a price containing all the expectations, knowledge and values of entrepreneurs which is limited if they do not have control over what they’re purchasing”
To which our friend will reply “Fine, give them full control over what to produce, but it will be a cold day in hell before I see another industrialist live like a king while the workers kiss his feet” to which you can put the final blow “Without profits there is no way to actually measure performance, the items produced and the quantities produced will be completely out of wack compared to a capitalist society. If entrepreneurs act as revenue maximizers their decisions will be irrational. This will lead to complete chaos and will be once again reflected as such in the price system”