Among the many insights Mises provides in his magnum opus, Human Action, there are crystal-clear considerations about the price mechanism, the role entrepreneurs play in fostering efficient resource allocation, and how socialism is detrimental to the economy, insofar as it disrupts the smooth interplay of prices, entrepreneurship, and resources’ allocation.
Prices and Subjective Value
In an unhampered market economy, the price mechanism is the tool conducive to the most efficient—i.e., desired by consumers—allocation of resources. Why? Because prices stem from the different subjective values human beings attach to the various consumer goods and services available in the economy.
When one consumer subjectively values the good s/he owns less than the good owned by another one, and vice versa, the two of them exchange their respective possessions—selling and buying. In Mises’s own words,
it is precisely the disparity in the value attached to the objects exchanged that results in their being exchanged. People buy and sell only because they appraise the things given up less than those received. (Human Action,  1998, p. 205)
By repeatedly exchanging, sellers discover the values subjectively attached to consumption goods by demanders—i.e., the market value of goods. In other words, they understand which consumer values any single available good most, thus allowing each good to find the most eager owner.
Notice that subjective appraisement of goods’ values is possible if and only if goods are privately owned by the exchanging agents. In fact, without private ownership of goods, exchanging agents could not enjoy the profit rewarding the discovery of the most eager desirers of the goods they want to exchange on the market—they would not be able to attain the highest possible reward from the exchange. Analogously, absent private ownership of goods, exchanging agents could not possibly experience losses—in the form of missed satisfaction of wants—when exchanging with those who are not the most eager desirers of the goods the former supply.
Entrepreneurship and Resource Allocation
However, before being exchanged and consumed, consumers’ goods need to be produced: here is where entrepreneurs enter the scene. As a matter of fact, entrepreneurs receive mandates from consumers: consumers value—and desire—specific goods, and thus provide entrepreneurs with incentives to discover what those desired goods are and choose the most efficient ways (and means of production) to produce them. Thus, entrepreneurs earn their profits over the speculative difference between costs of production and revenues from sales to consumers. As Mises writes,
The direction of all economic affairs is in the market society a task of the entrepreneurs. Theirs is the control of production. They are at the helm and steer the ship….They are bound to obey unconditionally the captain’s orders. The captain is the consumer….If a businessman does not strictly obey the orders of the public as they are conveyed to him by the structure of market prices, he suffers losses, he goes bankrupt, and is thus removed from his eminent position at the helm. Other men who did better in satisfying the demand of the consumers replace him. (Human Action,  1998, p. 270, bold added)
It’s easy to understand that the role of entrepreneurs is not easy at all. They are at the same time owners (and/or acquirers) of the means of production—thus shouldering the risk of wrong allocation of scarce resources, i.e., malinvestment—and vested with the task of correctly anticipating the sorts, the quantities, and the subjective valuations of goods consumers demand. Therefore, among their many roles, entrepreneurs need to be speculators of sorts: their role (in part) is to correctly guess the future wants of consumers, in order to avoid malinvestment and make profits.
Were entrepreneurs to be wrong in their speculations about the future, they would suffer losses. In fact, entrepreneurs first pay in advance in order to acquire the means of production and are later rewarded with revenues. If entrepreneurs do not interpret correctly the future desires of consumers—they first make the outlays but later do not reap (enough) revenues. As Mises explains,
Entrepreneurs often err. They pay heavily for their errors….Yet the real entrepreneur is a speculator, a man eager to utilize his opinion about the future structure of the market for business operations promising profits….He sees the past and the present as other people do; but he judges the future in a different way. (Human Action,  1998, p. 582, bold added)
In the light of what has been expounded so far, it’s evident that entrepreneurs are essential and indispensable cogs in the economic machinery, at least as long as the world we inhabit features uncertainty about the future and scarcity of means of production with alternative—and mutually exclusive—uses.
Socialism Is Economically Impossible
Here is the problem with socialism: without private ownership, market prices—stemming from subjective valuations—cannot surface, the price mechanism is impaired, and entrepreneurs can no longer appraise means of production for their usefulness in satisfying consumers’ wants. Entrepreneurs are left with no usable calculating tool when it comes to future speculation and are thus unable to choose how to allocate means of production. In Mises’s own words,
Profit tells the entrepreneur that the consumers approve of his ventures; loss, that they disapprove. The problem of socialist economic calculation is precisely this; that in the absence of market prices for the factors of production, a computation of profit or loss is not feasible. (Human Action,  1998, p. 701, bold added)
And even if human beings could attain perfect technological knowledge, it would be of no avail. In fact, technological knowledge is value-free by definition; it can explain how to attain something, but it cannot answer two questions: Is it worth the effort? Is it what we desire? In other words, technological knowledge is useful when it comes to recipes and mixes, but entirely useless when it comes to evaluations and decisions. As Mises explains,
The art of engineering can establish how a bridge must be built in order to span a river at a given point and to carry definite loads. But it cannot answer the question whether or not the construction of such a bridge would withdraw material factors of production and labor from an employment in which they could satisfy needs more urgently felt. (Human Action,  1998, p. 209, bold added)
Hence, even conceding to socialists the scenario most favorable to them (i.e., perfect technological knowledge), they would nonetheless be at a loss when planning production within the economy: absent subjective values and prices, they would not be able to choose what to produce and what to forego.
Prices, stemming from exchanges among agents attaching different subjective values to goods, constitute the signal whereby economic agents (consumers and producers/entrepreneurs) can allocate any economic good to where it is needed the most—the price mechanism emerges.
The price mechanism can properly work if and only if economic goods are subjectively valued. But subjective valuation of goods requires private ownership: without private ownership, profits and losses are not privately enjoyed or suffered, providing no incentive to allocate resources in the most efficient way.
Socialism, imposing common ownership, makes subjective valuation of goods impossible, thus impairing the price mechanism. Without prices, entrepreneurs cannot calculate and efficiently allocate resources. Hence, socialism is doomed to economic failure.