Markets and Command in a Modern Economy

The market mechanism is a system of economic organization in which buyers and sellers determine production and prices by free competition. The way that this system solves the problems of how, what and for whom without central planning was dubbed the invisible hand by Adam Smith in his book The Wealth of Nations.
The market only works as advertised in the presence of perfect competition, meaning that no single buyer or seller can affect a price. Perfect competition is compromised by, among others, monopolies and unions. Another cause of market failure is when an economic agent can transfer costs to others involuntarily through spillovers or externalities such as environmental damage. It is also possible that unintended positive effects occur, or that beneficial activities are not undertaken because they are not profitable or cannot be bought and sold in the market or on a pay-per-use basis. The latter are called public goods.

Samuelson formulates the market mechanism with the electoral analogy of dollar votes, and points out the consequence that income inequalities determine for whom the market produces goods. This means that even a perfectly functioning market may result in socially undesirable outcomes, in the sense that some needs of the society are not met because the few agents with the most resources do not have those needs.
Modern mixed economies are based on the market mechanism with the government acting as moderator. The government can help the market operate more efficiently by introducing regulations to improve competition, take into account externalities, and divert resources to public goods. Also, the government can use progressive taxation and transfer payments to reduce income inequalities so the needs of a larger part of society are met by the market mechanism. Finally, the market displays instability, that is, cycles of growth and stagnation that can be extremely damaging to society and the economic system itself, and one of the roles of government is to mitigate the effects of these cycles or reduce their intensity thought fiscal powers (taxing and public spending) and monetary powers (regulating interest rates and the amount of available currency).

Experience seems to indicate that "a market economy cannot simultaneously attain full employment and stable prices".

Economies increase their efficiency through specialization, the use of money and capital investment. Specialization increases the productivity of labour by assigning each individual tasks they can perfom best and fastest. Money streamlines transactions which could otherwise be carried out only through barter. Investing in capital means diverting resources from production of consumer goods to production of tools to imcrease future production, that is, economies grow by trading consumption today for increased production tomorrow. In a market economy, how much is invested in capital versus production of consumer goods is determined by the price of capital, which is interest.

The difference between capitalism and communism is the private versus government ownership of capital.

Critique
Samuelson is unapologetic in stating that "Those without property or education and with skills, color and sex that the market does not value will receive lower incomes", and therefore are less likely to see their needs satisfied by the market. It sounds reasonable when one talks about inefficient businesses being eliminated from the market, but what happens when people themselves get eliminated from the market?

Samuelson calls the economic crisis of the 1970's "foul economic weather" as if the oil crisis, commodity shortages, and a breakdown of international finance and excessive regulation were external to the economic system, and on the same category as bad harvests. More on this later.

It seems that the role of the government in a mixed economy is both that of judge and party: the government judges the quality of competition by ensuring that no single agent can affect prices, but in order to promote public goods it must have the ability to itself affect the prices of public goods favourably. For this the government must have access to a substantial fraction of the available money, and the only way to obtain it is by taxation. Since the government regulates the market, it makes sense that economic activity is taxed (income tax, sales tax, etc). Poll taxes make less sense because they tax entities whether or not they take part in economic exchanges in the market.
If, as in communism, the government has a monopoly on capital, it leads to imperfect competition. In a market economy, everyone should have a share of the capital. But this is not what happens in modern self-described market economies: capital is owned not by people but by corporations. So maybe we are not living in a capitalist system but in a corporatist system, and we all know what Mussolini said about corporatism: "Fascism should more properly be called corporatism because it is the merger of state and corporate power". What we need is a system where individuals not only have their own labour, but they have a share of the capital, and collective ownership of the means of production just does not cut it, whether the collective is the state or a corporation.