REAGAN

President Reagan publicly opposes tax increases, saying he would raise them in a second term only as a ''last resort.'' But since his inauguration in 1981, Mr. Reagan has signed four bills increasing various taxes.

''I don't have a plan to tax or increase taxes; I am not going to increase taxes'' in a second term, Reagan said in his Oct. 7 debate with Democratic challenger Walter Mondale.

In 1981, the Reagan administration shepherded through Congress legislation trimming tax rates 5 percent in 1981 and 10 percent in each of the next two years. The President argues that these tax cuts were ''very instrumental in bringing about this economic recovery.''

So last Aug. 4, Reagan said he would ''veto any tax bill that would raise personal income-tax rates.'' He has left himself maneuvering room, however, on increasing tax revenue in other ways.

Reagan says he favors simplifying the current tax system and in January asked the Treasury Department to study various options and report on them in December.

Treasury Secretary Donald T. Regan says the administration is leaning toward proposing a modified flat tax. In such a tax system many deductions are eliminated so that the rate at which income is taxed can be lowered.

The President has promised, however, to keep the home mortgage deduction.

In a ''pure'' flat tax, all deductions are wiped out and all individuals are taxed at the same rate.

In a modified flat tax, some deductions are preserved, and there are several tax brackets, so that the rate at which an individual is taxed rises with his taxable income.

Reagan says he does not want the revised tax plan to raise any more revenue than the existing tax system.

Rather than boosting taxes, the President favors reducing the federal deficit by encouraging continued rapid economic growth and by reductions in the rate of increase in federal spending.

The administration argues that such a prescription for erasing the deficit is possible, in part, because the deficit will be smaller in coming years than many private economists forecast. For example, by assuming steady, strong economic growth and declining interest rates, the Office of Management and Budget predicts a deficit of $139 billion in fiscal 1989. By contrast, using less optimistic assumptions about growth and interest rates, the nonpartisan Congressional Budget Office projects a deficit of $263 billion the same year.

If the President is wrong and taxes must be increased to narrow the deficit, it will not be the first time Reagan has given his reluctant approval to a tax increase.

In 1982, he signed the Tax Equity and Fiscal Responsibility Act, which raised

Later that year, Congress passed and the President signed a 5-cent-a-gallon increase in the federal gasoline tax, designed to raise $5.5 billion a year for road repair.

As part of the bipartisan plan to rescue social security, in 1983 the President signed the Social Security Amendments, which, among other things, raised payroll taxes.

And this year the President signed the Tax Reform Act of 1984 - the so-called deficit down payment - which raised taxes $50 billion through fiscal 1987.