WHEN PRESIDENT REAGAN signs that tax cut later this year, how much will you increase your savings in response to it?The administration argues -- vigorously -- the you will save more of your income -- and this assertion is central to its whole tax strategy. The future savings rate is crucial to the president's claim that his tax cut -- despite the large budget deficit that would continue next year -- can encourage investment without increasing inflation. In our own view, the president is mistaken. With the negotiations between the White House and Congress now apparently approaching a climax, the underlying issues of savings and investment require careful attention.

Saving equals investment, the textbook equation says. But the term "savings" is not quite so simple as it looks. The money that you put in the teapot is certainly savings. The profits that corporations reinvest are also savings. The country's net imports, oddly, count as savings. And most emphatically, a government budget surplus -- if there were one -- would be savings. The present deficit is negative savings.

The point here is the increasing any category of savings is the same as increasing any other, it its effect on investment and the financial markets. Specifically, an increase of $1 in your savings has the same effect for investment as a decrease of $1 in the federal deficit.

Americans currently save about 5 percent of their after-tax income. A rise of only one percentage point next year would mean an additional $23 billion in personal savings -- with the same meaning for the nervous financial markets and investors as reducing the federal deficit almost by half. The Reagan administration is telling the business and financial crowd not to get obsessed with the federal deficit because, even though the tax cut will keep it high, relief is coming from another direction.

That's why it is essential for the administration to show that a tax cut will actually increase personal savings. Donald Regan, the secretary of the Treasury, returned to this argument again yesterday when he appeared on "Issues and Answers." On the opposite page today, Charles E. Walker ably summarizes the evidence to support this proposition.

Should you be persuaded? It's quite true that the famous 1964 tax cut increased the rate of saving. The country was in the third year of a tremendous boom that was rapidly raising incomes. Inflation was low and the tax cut was, as economists say, real; even after inflation, tax rates were sharply lower. But at the inflation rates that the administration itself foresees, the Reagan tax bill would offer substantial real cuts only to a small minority of wealthy taxpayers. For everyone else, it would provide very little change. Inflation would keep pushing them up into higher tax brackets nearly as fast as the Reagan bill reduced the rates for each bracket.

If there is little real tax cut for the vast majority of people, savings rates won't rise. If savings don't rise, there's nothing to offset the financial pressure of continuing budget deficits. The tax cut will merely feed consumer demand, with the usual acceleration of inflation. The famous 1964 tax cut, incidentally, not only increased savings. It also pushed up interest rates -- and inflation as well.