—Interest Praxeology—
Praxeology is, traditionally, the theory of human action, of why humans take certain actions in certain circumstances through purposeful behavior.

In Yoggist terms this would translate to how followed beliefs, or action-guiding beliefs, cause one to act to achieve some end; aka to fulfill some interest.

Interest here is defined as merely that which a sentient being's behavior tends towards. The end a being is attempting to achieve by engaging in a purposeful action, is the interest.
 

—Behavior and Wants are Separate—
Here we can define a "want" or an intrinsic interest:
That which a being's behavior tends towards, regardless of external factors.
Regardless of external factors here is a distinguisher between interests that are merely due to some current limiting factor, and interests more inherent to the being possessing them.

Imagine a person stuck in a cage, with a guard stationed outside ready to shoot them if they attempt to leave. In such a situation, the person does not have an interest in leaving the cage, in the sense that their behavior will not tend toward that end, because doing so will result in bodily harm.

With this being said, they do have an intrinsic interest in leaving the cage, they 'want' to leave the cage, which is what is normally meant by someone saying they have an interest in leaving the cage.

It isn't that they will try to leave the cage right now, instead right now they would rather stay in the cage, not because of their own preferences, but rather due to an external factor beyond their control that artificially limits the fulfillment of their interests.

This immediately demonstrates a critical difference between a being having a mere interest in something in some sense, and them actually wanting something, having an intrinsic interest in some end. In this case we can say they may have an interest in leaving the cage, because absent the external factors "spooking" them into staying in the cage, they would leave it immediately.

We can then say them not leaving the cage is merely them placing a separate interest above their own freedom of movement, their interest in not dying. Such an interest acts as a conduit for many other interests, as dying prevents fulfillment of most other interests that are relative to a being's actions in the world.

Such an interest that acts as a conduit for other interests can be described as being entangled with many other interests, such an interest is an "Inherent Interest" and is the interest appealed to when acting against an Intrinsic Interest.
 

—The Problem of Market Demand—
The problem with the Austrian conception of "free markets", markets that are mostly or entirely unregulated, or Pure Markets as they will be referred to as here as to not confuse moral language with legal detail, is that the logic in favor of them confuses market demand with people's wants.

The traditional praxeological argument in favor of Pure Markets is the idea that people's wants generate economic demand, and in an unregulated marketplace sellers will prop up to take advantage of the demand. The demand creates an incentive to give a fairly priced supply, specifically the pricing necessary to make a profit.

With competition, overpricing when possible becomes rarer because it becomes less possible, as people can simply go to another seller. Depending on the good being sold, they can also simply stop buying the good.
This is the basis of most economics, supply and demand. The more people willing to buy, the more people are incentivized to sell.

This demand is not the same thing as actual wants though, as this only measures non-intrinsic interests, or Relative Interests, interests that are relative to the present conditions, taking in all 'spooking' external factors influencing how someone acts according to their interests.
This includes economic externalities, coercion, irrational judgement, cultural spooks, lack of information, among many other things.

Because of this, a Pure Market only works well if there is fair and plentiful competition. Some industries are harder to enter than others, which creates a loophole wherein if an industry is hard to enter but easy to stay afloat, competition will be low and incentive to act against people's actual wants will be high.
 

—Where Austrian Economics Loses its Grip—
Especially for libertarians wanting deregulation, they run into a problem where they make a sharp distinction between someone being coerced by force into acting against their actual wants, and someone being coerced by their own conditions, manipulations, and other "spooking" external factors into acting against their actual wants, or into allowing their wants to be frustrated.

The libertarian argument is that the latter isn't coercion at all, and that any circumstance where they make a voluntary exchange isn't inconsistent with their interests or anything else because such an exchange is always mutually beneficial. They then say this is true because any exchange that isn't mutually beneficial is an exchange a rational human would not partake in.

The problem here is that, relative to interests, the distinction between what they consider coercion and not, is arbitrary; and the exact same logic can be used against involuntary exchange as well.

For someone to stay in a cage because the alternative is death, is them engaging in a mutually beneficial exchange. The guard doesn't want them to leave the cage, and probably doesn't want them dead, just imprisoned. The prisoner doesn't want to die, and views their interest in not dying above their interest in freedom of movement.

Yet the libertarians argue allowing criminals to hold people at gunpoint and use that to their advantage in the market, would not protect anyone or ensure adequate supply of goods relative to people's actual wants. This is a contradiction.
 

—Economic Information is Concealed by Absolute Property—
Libertarians talk of economic information, a possible argument in their favor is that use of force conceals information in the economy. If Bob is offered a purchase of their land for $100,000, this brings the information of whether they value their land more or less than $100,000 into the market, allowing supply and demand for such land to adjust accordingly.

If Bob is instead threatened with force to lose their land, well.. information is still revealed, they value their land less than their own life.

The argument from libertarians is such information is less meaningful, less relevant to the economy, that such information doesn't change supply and demand for such land because any seller can assume most people value their own life over their land, or other property for that manner.
As such, markets that don't allow such force conceal less information which in turn leads to the market being more efficient, and allowing supply and demand function better.

The problem with this idea is that it may be true in a simplistic example such as this, but information is still concealed when people's interests are not given bargaining power; and interests are still frustrated without the use of force.

As explained before, the coercive nature of force expands to other domains, and results in very similar results. Imagine a situation where a gay man lives in a town that hates gay people. The threat of him being ostracized acts as a "spook" against his interests, leading to the information of him being gay, being concealed from the market.
Similarly, a situation where someone is forced to pay extra for rent from a landlord or work in a very dangerous job simply because they are impoverished and have nowhere else to go, is a situation where their preferences are being hidden from the market.

Any case of this will create inefficiency, and this can be logically proven. Inefficiency in a market is measurable by whether there exists an allocation of resources that could make someone better off without making anyone else worse off than they were before. The more such allocations exist, the more inefficient. It can also be measured as whether decentralized actors are unable to coordinate production between each-other using relevant knowledge.
If a market contains external factors that distort the expression of intrinsic interests, market demand cannot be assumed to accurately represent those interests, which results in an inefficiency in both market coordination and supply and demand.

This can be shown regardless of which measure of inefficiency you choose.

 

—A Proof that Austrian Economics results in Inefficiency—
–Premises:
(P1): Market demand reflects the behavior of people under their existing conditions, and therefore reflects their relative interests, rather than necessarily their intrinsic interests or wants independent of external constraints.
(P2): An interest that is fulfilled or pursued only because of the present conditions affecting an agent's behavior, is a relative interest rather than an intrinsic interest. (Definition)
(P3): External factors can alter the conditions under which a person acts according to their interests, causing them to pursue relative interests that differ from their intrinsic interests.
(P4): When a person's relative interests differ from their intrinsic interests due to external factors, their behavior does not fully reveal to the market the intrinsic interests that would otherwise guide their actions.
(P5): A market allocation is inefficient when there exists an alternate allocation that can better fulfill the interests of at least one person without reducing the fulfillment of the interests of others, or when relevant information necessary for decentralized coordination is concealed.

–Logic:
(L1): From (P2), interests that are relative to the existing conditions of an agent are distinguishable from intrinsic interests that would remain present regardless of those conditions.
(L2): From (P3), external factors can cause a person's behavior to be directed towards a relative interest rather than the intrinsic interest that would otherwise guide their behavior.
(L3): From (L1 + L2), when external factors cause a person's behavior to be directed towards a relative interest that differs from their intrinsic interest, the behavior of the person is not necessarily representative of their intrinsic interest.
(L4): From (P4), when a person's behavior is directed towards a relative interest that differs from their intrinsic interest, their behavior does not fully reveal the intrinsic interest that would otherwise guide their actions.
(L5): From (L3 + L4), when external factors cause a person's behavior to be directed towards a relative interest that differs from their intrinsic interest, the intrinsic interest that would otherwise guide their behavior can be concealed from the market.
(L6): From (P1 + L5), market demand can therefore reflect behavior directed towards relative interests while failing to reveal the intrinsic interests of the people generating that demand.
(L7): From (P5), when relevant information necessary for decentralized coordination is concealed, the resulting market allocation is inefficient.
(L8): From (L6 + L7), whenever market demand fails to reveal intrinsic interests that are relevant to the allocation of resources, the resulting market allocation can be inefficient.

–Conclusion:
From (L8): Therefore, Pure Markets do not necessarily produce efficient allocations, because market demand can reflect relative interests created by external conditions rather than the intrinsic interests of the people involved, allowing relevant information about interests to be concealed from the market.
 

—Libertarian Slavery and Wage Labor—
Some might think that market efficiency and ethics are separate, based on the idea that slave labor for example can be used to enhance market efficiency, making production of goods cheaper.
Libertarians who follow Austrian Economics would instead argue such slavery conceals important information from the market such as which people are best at which labor, since the labor is supplied involuntarily giving an incentive to hide your skills from your slave owner.

Information is also hidden involving how much of specific products to make, whereas extra production can be done in areas that might not make much sense, simply because production in certain industries may have a disproportionate advantage given by slave labor.

In the same way though, abusive wage labor also conceals information even when force is not used. In an unregulated market, people who seek employment simply because of their external conditions and not as an intrinsic interest, conceal from the market information about what jobs they actually want, what jobs are actually needed, and how much their own labor is worth.
 

—Worker-Ownership, Interest Alignment, and Information—
The hidden information and thus inefficiency is a side-effect of Interest Misalignment, where the interests of employee and employer, worker and owner, are misaligned to the detriment of the market. Interest Alignment on the other-hand, implies an ability to ensure proper coordination relative to the interests of the parties involved, and thus knowledge of how they manage scarce resources.

An enterprise that is entirely worker-owned, has all the knowledge of the interests of all parties involved internally, as such no information is lost in internal organization.

Consumer bargaining power has a similar effect, the NAP though can disincentivize these types of arrangements, because in an absence of appropriate regulation those looking to hold on to "dictatorial" power over enterprise and the overall economy will use every means to do so, and this is true historically.

The more interests are not being subordinated, the more information is revealed to the market and the better the outcomes.