President Reagan's new tax-cut plan is smaller than the first proposed and would probably result in lower federal deficits, lower interest rates and somewhat slower economic growth for the next several years than under his original proposal.

It would also leave many individuals with rising rather than diminished tax burdens once inflation and already scheduled Social Security tax increases are taken into account.

Reagan noted in a speech to a joint session of Congress last month that even his original plan would not have been enough to offset these increases.

Now, as part of an effort to gain votes for his plan, he has reduced those cuts. However, while many taxpayers would only break even or fall behind, taxpayers in the highest brackets would come out ahead under the new Reagan plan, and do so immediately.

Reagan's original proposal was criticized from several quarters as too large and inflationary. His revised, scaled-back personal and business tax proposals for the years 1981 through 1984 would reduce some of the pressure on him to find new ways to cut the budget in those years.

But while they would cost less in the immediate future, by 1984 the new proposals would cost nearly as much as the old. The tax cuts then would be only $4.7 billion smaller than originally proposed, still leaving Reagan the difficult problem of coming up with nearly $40 billion of additional spending cuts if he is to balance the budget that year.

The biggest impact from the changes Reagan made would come next year when the total tax-cut package would be worth only $37.4 billion compared to his original $55 billion. But postponing the effective date of the personal tax cuts and trimming them also means this year's budget deficit will be lower by $6.7 billion than under the first plan.

These smaller cuts should ease pressures in financial markets where the prospect of continued large budget deficits has helped keep long-term interst rates high, much to the consternation of the administration. The relief would come because with smaller tax cuts the government would have to borrow less to finance the deficit, leaving more money for private borrowers.

Wall Street praised Reagan's changes for this reason. Business executives, on the other hand, complained bitterly since their tax break would be considerably smaller.

While the administration has provided no estimates of how different income groups would fare under his proposals, the nature of the changes suggests his modifications this week tilted the proposed relief slightly more toward middle- and upper-income taxpayers.

Under the new plan, some taxpayers would find that as a result of inflation they would still be pushed into higher tax brackets. Some would find their marginal tax rate -- the rate on their last dollar of taxable income -- higher in 1984 than in 1980.

Some lower-income taxpayers would find their marginal rates and their total tax burdens higher in 1984, since Reagan did not decide to include in his package any increase in either the $1,000 personal exemption or in the "zero-bracket amount" (formerly the standard deduction), which helps set the threshold for income taxes. Moreover, these taxpayers would be slightly worse off under Reagan's modified plan than they would have been under his first one.

Taxpayers with high incomes, however, would get substantial cuts immediately through a lowering of the top marginal rate of investment income from 70 percent to 50 percent on Jan. 1. It is already 50 percent on income from work.

Except for those in the top brackets, exactly whether particular taxpayers would be better off under the new package or the original one depends on how they would benefit from some of added features, such as a new income exclusion for married couples with two incomes, higher limits on contributions to individual retirement accounts, and major new income exclusions for Americans working abroad.

For instance, a family of four with a $25,000 income and average deductions last year paid $2,901 in income tax, which was 11.6 percent of its income. If the family had only one income, and it were to rise in line with inflation, by 1984 its tax bill would be equal to 10.9 percent under the new plan. But if both spouses had equal $12,500 incomes, the new added exclusion intended to offset the so-called marriage penalty, would cut the tax bill to only 9.8 percent of income.

But under Reagan's original plan, the family's tax liability would have fallen to about 9.8 percent of its in come regardless of whether it had one income or two. Now, because rates would be cut only 25 percent over three years instead of the 30 percent Reagan first proposed, taxpayers, except those at the top, who do not qualify for one of the special breaks would not fare as well.

Business executives, who were briefed at the Treasury Department before the White House announced its new plan, complained bitterly that the increase in tax write-offs they were expecting for investments in new plants and equipment was not significantly smaller.

Both the House and Senate taxwriting committees probably would have made changes similiar to those Reagan opted for even if the president had stuck with his first plan.

Nevertheless, this particular break would be smaller by $9 billion in fiscal 1984 than it other would have been, Treasury officials said. Some other business cuts were added to the package, however, including a new tax credit for certain research and development expenses and a 10 percent investment credit for rehabilitation of older structures.

Some tax experts said Reagan's changes in the depreciation allowances greatly simplified the new scheme and would mean that different industries would get more equal treatment than under the original plan.

While the sum of the changes in the tax package will provide some relief on the budget front for the next few years, after 1985 the impact would go the other way.

Originally, Reagan proposed no more cuts in tax rates after 1984. He still doesn't, but the other parts of the package become more expensive in terms of lost revenue after 1985 than the savings from holding the cut in personal tax rates to 25 percent instead of 30 percent.

Some analysts said that from about 1984 on, the impact on the economy from the new package would be little different from the original, but that since some revenue from those later years is not committed, there will be less room for added spending or tax cuts then.