For the United States and the other industrialized countries, the politics of the new year are mostly in place. At the center is the unresolved problem of the last decade -- the famous mix of slow growth and rising prices known as stagflation.

The rhetoric of those has recently changed -- from liberal to conservative. But it remains in doubt whether the government that counts most, the government of this country, will tackle basic troubles or, like its predecessor, merely attack the symptoms.

Continuing inflation is deeply embedded in most of the industrial world. In this country, which is better than average, the core rate of inflation -- that is to say, the increase in prices that business must impose to stay abreast of rising costs -- now amounts to about 10 percent annually. Uncertain political conditions in the Persian Gulf and bad harvests ensure higher prices for energy and food. Unless measures are taken, inflation of over 10 percent is guaranteed for the United States and most European countries.

Slow growth in national output arises from inflation -- and the half-measures taken to stem it. The combined effect of high interest rates and reductions in government spending and private investment works to reduce to about 2 percent the growth outlook for the next 18 months for the United States, Britain, Canada, Germany and France.

Between rates of growth and political coloration there exists a connection. When there are surpluses to divide, societies seem ready to leave the task to political leaders. When disposable income falls and the task is distributing sacrifice, people turn self-reliant.

So the 1960s were halcyon days for believers in government management of the economy -- Democrats in the United States, Labor in Britain, Gaullists in France, Social Democrats in West Germany and Scandinavia. But lately, parties and persons known to favor the free play of markets have surged forward. Hence the recent success of the Tories in Britain; Helmut Schmidt and his coalition partners, the Free Democrats, in West Germany; President Giscard d'Estaing and the Independents in France. The Republican victory of Ronald Reagan last fall is the American counterpart of a general drift.

But are free marketers any better in dealing with stagflation than believers in government direction? Recent experiences in Japan, Germany and Great Britain, apart from being special in each country, cancel each other out. Nor is a true test apt to come with the Reagan administration in this country.

Reagan supporters, to be sure, have surfaced two coherent strategies for dealing with stagflation. There is the emergency program favored by Jack Kemp, the New York congressman, and David Stockman, the Michigan congressman who will be Reagan's budget director. It features a tight lid on credit, bit cuts in taxes and government spending and deregulation on the grand scale, including decontrol of oil and gasoline.

Then there is the foreign policy strategy. The idea is to live with stagflation and concentrate on making a few gains in dealing abroad. Later, when the government acquires strength and confidence, there can be an emerging drive on the economic problems with some effort to get directly at the transmitter of inflation -- the wage-price cycle.

But Reagan's closest advisers have explicity repudiated both strategies. More important, the Cabinet selection has been a disavowal of any strategy. The incoming administration is conspicuously lacking in an economic guru. It is significant that Donald Regan, the broker designated to be secretary of the treasury, is noted for open-mindedness and an eclectic approach. The nominee for secretary of state, Gen. Alexander Haig, while having many merits, has been much more a reflector of other person's strategic views than an independent source of light.

As distinctive as the lack of a strong conceptual scheme is the presence of a random collection of naysayers to past Democratic positions. The Reagan Cabinet personifies a medley of complaints -- against big spending, big government, heavy regulation, elaborate social programs and deep concern for the environment. These negative views make up less a government policy than the jagged edges of an opposition. But if the new administration does not solve basic problems, it can, with luck, avoid the blame for failure.