Under the tax proposals President Reagan announced last night, the federal tax burden would still go up this year, to 21.1 percent of gross national product, then steadily recede to 19.3 percent by 1984.

That is the same level that prevailed in 1978. The basic Reagan program -- three years of 10 percent cuts each in individual income tax rates, and more generous depreciation writeoffs for business -- would put the tax take back just where it was three years ago.

The president promised in his address that he will propose additional tax cuts "at an early date," to reduce the so-called marriage penalty, whereby two earners pay more if married than they would with the same incomes if single; to index tax brackets so that they rise with inflation; to provide tuition tax credits to college and perhaps private-school students and their parents; and to give further relief from inheritance taxes on family-owned farms and businesses.

Treasury Secretary Donald Regan refused yesterday to say how these additional tax cuts would be paid for. He told reporters that enterprise zones, providing tax incentives for business to invest in depressed areas, will probably also be included in a second tax bill.

Under the president's plan the first tax cut would show up in pay checks as of July 1 this year, when withholding would be reduced 10 percent. This would be equivalent to a rate cut of 5 percent for the whole year, and will cut individual taxes on average by 5.1 percent.

The business tax cut, which provides for much simpler and more generous depreciation allowances on investment, would be made retroactive to Jan. 1 of this year and be fully phased in over five years.

The tax plan would cost the government an estimated $8.9 billion in fiscal 1981, $53.9 billion in 1982 and $221.7 billion by 1986. Individuals would get $162.4 billion of the 1986 cut, business $59.3 billion.

When fully effective the Reagan cuts would reduce business taxes 40 percent from what they otherwise would be, while individual taxes would be cut by somewhat less than 33 percent. Individual taxes would otherwise have gone up because of inflation and higher Social Security taxes; these are the factors that this year will lift the tax burden even if the Reagan cuts are enacted.

The president also proposed a few minor revenue-raisers, increasing the cost of air travel and imposing charges on boat owners to pay for Coast Guard services which benefit them.

Individuals at all income levels would have roughly equal cuts in their tax liabilities in percentage terms, but with much larger dollar amounts for the well-to-do. Regan commented to reporters yesterday morning that it was important to cut taxes for those in upper-income brackets as they are the ones who save and invest most.

Next year, under the president's proposals, a family of four earning $20,000 a year would have a tax cut of $470, equivalent to a $15.1 percent cut in tax liability. For a family earning $50,000, a cut of the same proportion would be $1,883.

By 1984 the Reagan proposals would cut taxes for a four-person family earning $20,000 a year by $578 or 29 percent. A similar family with an income of $30,000 a year would pay $1,063 less tax a year, equivalent to a 27 percent cut. In upper-income brackets, $7,469 a year would be cut from the tax bill of a $100,000 family that got all its income from investment and $6,869 from one that earned all its income from working. These cuts are equivalent to 26 1/2 percent and 24 1/2 percent respectively.

Although the tax cuts are similar in proportional terms they have a very different impact on after-tax incomes. Because the rich pay out more of their incomes in taxes, a cut in their tax bill gives them a bigger rise in their take-home pay, in percentage as well as in dollar terms, than it gives lower-income families.

Treasury background papers yesterday stressed the importance of the cuts in tax rates, saying that they "are designed to improve the economy by improving incentives." The plan for individual tax cuts closely follows the Kemp-Roth proposal endorsed by Reagan during the election campaign and backed by "supply siders" who believe that cutting tax rates spurs people to work harder and save more, and that this stimulates the economy and raises investment and productivity.

The business tax proposal is a modified form of the so-called 10-5-3 plan which puts all investment into one of three groups for writeoff over ten, five or three years. This gives a huge tax break to profitable firms investing in long-lived equipment and builders, and a smaller one to those with shorter-lived assets. It breaks the connection between depreciation allowance and expected life of the investment.

The administration has decided to ask Congress to pass a "clean" tax bill, with few or no amendments, with the promise of a vehicle for congressmen's "pet projects" later in the year. But unless it includes substantial revenue-raisers, the cost of the second bill could upset the rest of the budget figuring.

After cutting taxes by 5 percent in 1981, the president's proposal would give future rate cuts of 10 percent in 1982 and 1983 and a final 5 percent in 1984. He proposed no change in the personal exemption and zero bracket amount (equivalent to the old standard deduction) which are critical for the lower-paid.

Although the capital gains tax exclusion would be unchanged, there would be a sharp drop -- from 28 percent to 20 percent -- in the maximum effective tax on capital gains, because of the successive rate cuts.