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In a perfectly efficient market, this would be the case. But it's easily disproven in practice by the fact that market prices can change by effects which have absolutely no impact on the utility value.
Ie, suppose we have a city with a bunch of plumbers, all of equal plumbing skill/ability, and a company that hires them and manages their distribution to clients, and pays between $80k and $120k depending on how skilled and aggressive the plumber is at negotiating (aggressive meaning they demonstrate an ability/willingness to quit and do a different job instead if they don't get the salary they want). We've assumed by axiom that they provide the same value, and yet get paid different amounts, let's assume the frequency is evenly distributed across this range, such that the average plumber is paid $100k. I suppose you could say that the "utility value" is the highest the company is willing to pay, $120k, and anyone being paid less is simply a bad negotiator, but I'm not sure if you'd say the "market value" is $120k given that most of the plumbers aren't earning that, and a new plumber entering the field is unlikely to get an offer that high.
Suppose then that the plumbers unionize and negotiate that all of them will receive the same pay of $110k. That's now the market value, unambiguously, that's what the market, as created by this single local monopolistic company (which is the only company offering reliable and consistent pay for plumbers in this city) and this one union (which all employees of the company must join) will pay. And yet the utility value of plumbing has not changed, because the union doesn't impact plumbing skill/ability in any way.
Suppose that the company actually takes in revenue of $140k for each plumbing employee it has, and keeps the difference as overhead/profit. There's a sense in which the utility value of a plumber is actually $140k since that's what clients are willing to pay, although if the overhead is necessary then I suppose the utility of the plumber themself is lessened by that. However if a plumbing emergency happens and the company gets a lot more business, earning $150k per employee one year, but takes the extra as profit and changes no salaries, then the utility value of plumbers goes up that year, the market price (from the client and owner's side) goes up, but the market price (from the employees side) remains unchanged.
And suppose that the employer uses local regulations, an army of lawyers, and relationships with local politicians to crush any new plumbers that try to form their own company or go independent in this area. It is not a free market, it is effectively a local monopoly. If you want to be a plumber, you negotiate here, or you leave the city and pay whatever transition costs it takes to uproot your life and your family and be a plumber somewhere else. The fact that this changes market prices but doesn't change the utility value of plumbers should clearly demonstrate that market prices are distinct from utility prices, even if an ideal perfectly efficient and free market would cause them to be equal. In practice, no market is perfectly free, therefore we should expect deviations in precisely the areas where these imperfections drive them apart.
There is an economic concept called "perfect competition" I want to be clear that this economic concept is not required for efficient prices.
And I am talking about efficient prices, not "perfect prices". Prices are a process and a search function for an optimal set of tradeoffs. One of the tradeoffs is information. To perfectly know all the inputs of a product, and to perfectly know the desire for that product would be a very costly search process. There is going to be some fudging of prices and that fudging should be expected given that information itself is not free or costless.
You've created a very long example that kind of assumes away many of the standard market fixes. I do generally like to use theoretical examples for most economic concepts, but I find that they tend to lead people astray when it comes to the nature of prices.
To me your example sounds a bit like this:
"Geologists say that older mountain ranges tend to be shorter and rounder than newer mountain ranges, because wind and erosion will gradually wear mountains down. But that's not always true, imagine there are two mountains. One mountain is 20k feet and in an old mountain ranges. And the other mountain is 10k feet in a newer mountain range. They are both subject to similar levels of erosion, and neither is a volcano. So older mountains can be taller."
You've assumed your position to be true in your example.
And yes the government is fully capable of distorting prices, or assisting companies in distorting prices. I usually bring this up as a reason why government should not have this power, or should at least have many restrictions on the use of this power. But this is also not evidence that prices don't reflect the real world, instead it is more evidence. After all if a government makes it hard to be in the plumber business we should expect the price paid for plumbing services to go up, because the supply of plumbers has been restricted. It would be strange if the government could intervene and not change prices.
Sure, but my example is basically a disproof by counterexample. In this example, prices don't match utility, therefore, the statement "prices always match utility" is logically false. It's really easy to disprove an "always" statement with a single example, even a hypothetical one, because an "always" statement is such a strong claim that it's almost never true. Utility value and market value are different things: sometimes they will be equal, sometimes they will not. I'm not saying they're never equal, I'm not saying they won't usually be close, especially in an efficient market. My point is that markets in the real world are not always efficient, therefore the two values are not always equal in the real world. This should not be controversial.
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