"In other words, your labour is worth nothing unless you produce something other people want."

Karl Marx actually agreed with you there, and wrote about it at length. His concept of "reification" is pretty close to how we describe fiat.

In the real world, the labour theory of value and the market theory of value are tightly coupled, especially for goods and services not easily stockpiled nor transported.

The value estimates only diverge significantly where and when people are not rational economic actors. Market value is not easily predicted under those conditions, either.

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Labor theory is an inversion of reality. Much like most other things socialists believe. The cost of labor has very little to do with the prices people will pay. The cost of labor only determines whether businesses can stay in business at the prices people can pay. This is what unions fail to understand when they work to increase the cost of labor without increasing production efficiency, they are actually just slowly putting whatever portion of industry they control or influence out of business.

Labour theory gives the same value as market value when economic actors are rational, (plus or minus some government-induced labour market friction, and a little speculative market sentiment).

The problem with union leaders isn't their economic models (they have none, fact, I've met a few). Its the old principal-agent problem - they actually don't GAF if their members will have jobs in ten years, because they plan to be in Parliament by then.

The cost to produce the early models of any innovative product is almost never anywhere near the amount the market pays, & the market is not irrarional to place a higher value on a novel & more efficient solution to some real problem. When there are few options, the high profit margins are the signal that "this is the solution we want" which spurs both the innovator to expand & competitors to enter the market & bring the supply more in line with demand. Prices are an information dense language.

“The value estimates only diverge significantly where and when people are not rational economic actors.”

Information asymmetry always exists in the market and so long as it does, estimates of value also will.