WHATEVER you may think of President Regan's tax bill as public policy, it is going to launch this country on a highly interesting experiment. Precisely as he intended, the president has accomplished a sharp break with recent tradition.The first question is the response of investment and business to this sudden relaxation of taxes. How much of their tax savings will people put into productive investment, as Mr. Reagan expects, and how much into vacatons in Acapulco or condominiums in Florida? Nobody knows. The next question, and for Mr. Reagan the crucial one, is the response of the political system. How will middle-income Americans react -- with gratitude for the cuts in their own taxes, or with resentment against the disproportionately larger ones for wealthier people? How sensitive are American voters to questions of income distribution? Since the distribution of income has not changed for more than 30 years, no one can really say.But an answer will emerge in the next few years' elections.

This tax program is not quite so totlly new as Mr. Reagan's more enthusiastic supporters claim. It points in the direction in which the country was moving in the generation following the Civil War and again, for not quite so long a time, after World War I. The ideas behind the Reagan tax bill are the same familiar ones that seem to recur periodically, after times of national strain, when Americans suddenly decide that they are fed up with hearing about the national community and its social responsibilities. But if the theory has a certain history, the country and its people have changed profoundly since its last visit.

The economics of the Gilded Age, with its emphasis on wide disparities between rich and poor to heighten incentives, has been pursued in recent years mainly in the Third World. The most conspicuous example has been Brazil. In the industrial world, most people currently seem to believe that very large differences in wealth, from one family to another, are not compatible with democratic standards. But opinion on this point has always been a little less firm in the United States than in most other rich countries. Americans are now going to press the accustomed limits of economic inequality a bit, and see what happens.

The enactment of this tax bill will make continuous inflation more dangerous than ever to the Reagan administration. Voters will quickly perceive tht some of its tax reductions risk being offset by inflation, while others are inflation-proof. Generally speaking, it is the benefits for the middle range of incomes that are most vulnerable. If your income is now around the average, the current inflation -- if it continues undiminished for the next three years -- threatens to leave you with a higher tax burden than today's. But if you are now in the top bracket, your marginal rate will drop from 70 percent to 50 percent, regardless of inflation.

The higher the inflation from now until 1984, the greater the differences in this bill's treatment of average incomes and very high ones. Since this tax bill is also likely to contribute strongly to further inflation, the results promise to be too interesting for comfort.