In reality there are no totally free or ideal markets in operation. Lack of perfect knowledge, monopolistic practices, cartels, taxes and government regulation bias the equilibrium points of most large markets in existence today. Participants engage in information bias practices such as insider trading and price fixing. Some believe that the notion of a free market is inherently inachievable because they believe that governments are fundamentally involved in markets through the creation and enforcement of property rights. Others argue that the concept of property comes from natural law and therefore it is incorrect to see governments as creating markets.
In the ideal free market, the law of supply and demand functions, influencing prices toward an equilibrium that balances the demands for the products against the supplies. At these equilibrium prices, the market distributes the products to the purchasers according to each purchaser's use (or utility) for each product and within the relative limits of each buyer's purchasing power. In the limited mathematical ideal market this distribution of products is Pareto Optimal (see Pareto efficiency), meaning that no purchaser could have their purchasing limits filled in a way more useful to them without reducing the usefulness of some other purchaser's bundle of products. This type of optimality doesn't necessarily have anything to say about the distribution of purchasing power itself (which is often an input to the mathematical ideal market) - the optimality generally refers to the distribution of products given the pre-existing purchasing power of the purchasers. The necessary components for the functioning of such a free market include no artificial price pressures from taxes, subsidies, tariffs, or government regulation, perfect (or at a minimum, equivalent) knowledge about the value of the goods, geographic availablity of goods to all people, and no artificial monopolies or other forms of economic coercion on the part of the actors.
The distribution of purchasing power in an economy depends to a large extent on the Labor market and the Financial markets, but also on other things such as family relationships, inheritance, gifts and so on. The ideal free market does not explain particularly well the performance of many real markets such as the Labor market, or Financial markets. It explains better the markets for consumers products.
The economic and political application of the concept of the ideal free market is known, primarily by detractors, as neoliberalism.