Prices are how subjective value becomes information other people can act on. Every price compresses how badly someone wants something, relative to everything else it could be used for — scarcity, effort, substitutes, all folded into one number.
No single person, or committee, needs to know any of that underlying detail. A carpenter doesn’t need to know why lumber got scarcer this month — he just sees the price rise and economizes accordingly. This is what solves the knowledge problem: the price system spreads the calculation across every participant in the market instead of routing it through one throughput-limited authority.
Lumber gets scarce -> price rises
Carpenter sees the price, not the reason
Carpenter substitutes, conserves, or pays up
No central authority had to know why
Remove market prices — as Socialism does by abolishing private ownership of capital goods — and this signal disappears with them. That’s the mechanism behind the economic calculation problem: without prices, there’s nothing left to economize with.