The benefit of an ideal free market is that it is extremely efficient at allocating resources. We have briefly mentioned how your preferences and overall budget determine how much of any item you will want to buy at a given price (its “utility” to you), and how that scales up to form the demand curve for everyone.

For a specific product, ideal free market conditions mean that exactly the “right” amount of resources will be devoted to producing it. Competition ensures that suppliers will be optimally efficient in producing the product in the quantity where the demand and supply curves meet.

Scaling up from one product to the entire market, producers of all products compete for resources, so under ideal free market conditions, there will be an optimal allocation of resources throughout the economy. This “ideal allocation” ensures that resources are used in a perfectly efficient way to maximize the satisfaction (utility) of consumers subject to their budget constraints.

Given the conditions that define an economist’s ideal free market and utility, the above can be shown mathematically.

One can appreciate the power of the free market by considering the alternative of a planned economy where what is produced and in what quantity is centrally decided. Since there is essentially a monopoly on production, the competitive incentive to reduce the costs of production is missing. The state does not have to produce goods in quantities that satisfy consumers desires, thus reducing overall “utility”. There is little incentive to introduce new goods or services. Even in market economies, there may be times when a government wants to put a thumb on the scales of what is produced (and what is not produced), but the history of fully planned economies shows pretty clearly that they don’t work as well as market economies. The Chinese economic miracle is largely due to their decision to abandon planning in favor of free markets. 

Which brings us briefly to note that economic systems don’t necessarily align tidily with political systems. One can have a capitalist free market economy in an absolute dictatorship as easily as in a democracy. It is also possible to have a vibrant free market economy with substantial state ownership. Singapore, which has been ranked as having the most open economy in the world, and the most “pro-business” one, has large state-owned enterprises^[1]. It also has one of the highest per capita incomes in the world, higher than the US.

^[1] https://www.weforum.org/agenda/2019/10/competitiveness-economy-best-top-first-singapore-secret-consistency/