No, it can't.
They are currently riding the coattails of the market economy. There is no way for a price of a good to be determined in the absence of a market to set the price. How much should a #3 spring coil cost? You don't know, and neither does anyone else...until the market demonstrates the price through its allocation of capital and production / consumption processes. You may drastically over or under-value it, simply because you can't foresee every possible alternative use of it within industry.
Right now, they're seeing the prices of goods and capital that other markets are setting, and are able to model their system after it to some extent.
Now, it *may* be possible for a small-sized commune to get along well-enough, but once you get into the complexity of a modern economy, all bets are off. There's no way for all of the economic transactions to be predictable and manageable. A human does not have the capacity, nor does any supercomputer, even in theory.
Imagine the market as a naturally "controlled" chaotic environment consisting of literally
trillions of individual decisions by the people every day. Now imagine trying to figure all that out by committee
We can't even figure out how to stick to the Constitution in the committee known as the U.S. Government...
^^^There's the reason, once again.
I disagree with socialism (communism, fascism, totalitarianism, whatever you want to call it) on moral grounds, too, but that wasn't the question.
It
cannot actually work without relying on capitalism as its guiding light. If one were to assume a hypothetical world socialist state, it would fail, as it would be unable to appropriately allocate production goods, since there'd be no pricing mechanism, since no free market would be around to produce it.
It's nigh impossible to wrap one's head around the complexity and interconnectedness of a market economy. It's STAGGERINGLY complex. There are quite literally billions of separate products in New York city alone, as evidenced by the number of distinct SKU #'s there. Every SINGLE ONE of those has a production process that involves countless resources from many different sources.
As a wild, off-the-wall example of potential pitfalls in complete market planning:
Imagine food rotting on a farm because the train couldn't get there on time to pick it up.
The train was late because the engine failed.
The engine failed because of a broken #3 spring, which could not be replaced
It could not be replaced because the springs were all mis-allocated by a bureaucrat to make pistols for the military.
Now you've lost quite a lot of food.
Yes, that's a crazy and contrived, and over-simplified example, but it's a start in explaining the chaotic, "butterfly effect" of central planning. I'll update it if I can think of a better one.
Size isn't the issue either, as some suggested that Denmark might work because it's small. If you were to imagine this world socialist nation to only have a population of 10,000 people, instead of 6 billion, the same problem is still there: the problem of prices and economic calculation.
There may be a very small commune sized limit where people can limit their production to necessities, which might work without pricing. Barter would work without pricing, but it's a highly limited economic system. Modern economies cannot operate without a free market pricing mechanism to guide them.
If you can prove otherwise, let me know. I'll give you 60% of the book's proceeds

... no one's
ever done it.