Mere arithmetic suggests that Phase II of President Carter's anti-inflation program will yield to Phase III. But does it follow as the night they day that, because Phase II features voluntary controls on wages and prices, Phase III will bring in mandatory controls?

Many people think so. Liberals argue that the voluntary program won't work and that when failure becomes clear the only alternative will be direct controls. Conservatives claim the Carter administration itches to interfere with the private sector anyway and won't miss this opportunity.

But the content of policy, as distinct from the arithmetical metaphor, points in the other direction. Far from seeking to control the economy, the Carter administration differs from recent Democratic predecessors in wanting to achieve public policy objectives by widening the options open to the private sector. Even if Phase II doesn't work, the signs will be ambiguous and there are many steps available tothe administration before direct controls.

Consider first the four elements making up Phase II of the anti-inflation effort. The ceterpiece is the voluntary guidepost program on wage and price increases. The aim of the guideposts is to give business enough muscle in dealing with labor so that the next round of wage increases can be held around 7 percent annually.

The guidepost program also affords some leeway to labor. It lies in the real wages insurance guarantee. That would give tax rebates to workers to make up the difference, if any, between a 7 percent wage hike and the annual rise in the consumer price indec. So, far from controlling business and labor, the administration merely widens their opportunities to play roles more consistent with the public interest in stopping inflation.

The second feature of the program is budgetary stringency, particularly in the welfare field. By cutting government spending, the president, rightly or wrongly, implicitly passes on to the private sector responsibility for those who have traditionally been the wards of federal programs.

The third feature of the program is a commitment to support the dollar with high interest rates and a slush fund of some $30 billion. That commitment was forced upon the administration by complaints from financial markets that the sinking dollar destroyed confidence and impaired investment. So the administration has reversed itself, and is now propping up the dollar to create a climate for more activity by the rivate sector.

Fourth, and least noticed, there is deregulation. The administration is not merely promoting more competition in the trucking and railroad industries and in airlines. It also means to dismantle some of the environmental and safety control applied by previous administrations. The aim, once more, is to lift burdens from the private sector, and give business a chance to show its stuff.

The sum of these measures presents a powerful showing of the president's commitment against interference in the marketplace. Indeed the preference for letting a disencumbered private sector achieve public policy objectives is perhaps the historic mark distinguishing this administration from past Democratic regimes. In any case it seems clear that Carter went to voluntary controls precisely in order to get a handle on inflation without having to go to mandatory controls.

The present policy may, of course, fail. In particular it seems doubtful that the big wage contracts can be held precisely at the 7 percent level. But the end results are bound to be cloudy, and there will be obscure differences between say the teamster contract, which comes up first, and the auto worker and rubber worker negotiations, which come later. No one will really be clear as to whether the policy has succeeded for many, many months.

Even if failure is evident, moreover, there are lots of alternatives remaining to the president. For example, suppose that, as many fear, high interest rates required by the commitment to support the dollar generate a recession in 1979. The president could then come back in 1980 with an appeal for stimulus by a tax cut. Which is not exactly bad political medicine for an election year.

What all this says to me is that those who predict mandatory controls on wages and prices are dead wrong. The president is going the other way. Phase III can turn out to be many things, including even a recession, but one of them is clearly not mandatory controls on wages and prices.