MR. CARTER'S last budget -- his would-have-been budget -- is a dare to Mr. Reagan. It dares him to try bringing down the deficit without either wrecking the social programs or raising taxes. As for Mr. Carter himself, in this budget for the fiscal year 1982, he comes out unequivocally for a large tax increase.

In the conventional terms that have prevailed until now, it's a tight budget. It increases very little more than the inflation rate, and that little is wholly concentrated on defense spending. To cut the present deficit in half, he would impose a walloping tax increase of about $35 billion in real terms -- that is, above inflation. Part of it is the increase in the gasoline tax, a thoroughly good idea but one one that Mr. Carter has proposed before without success. Most of this tax increase is the familiar process by which inflation pushes people into higher income tax brackets.

This tax increase would raise federal revenues to more than 22 percent of the gross national product -- three percentage points higher than when he took office and slightly higher than the previous high water mark in World War II. Four years ago he had pledged to hold this crucial ratio below 21 percent. In this budget, his last opportunity to set the terms of the debate over his presidency and its aftermath, he has chosen to defend his party's spending commitments at the cost of his own fiscal conservatism.

The federal deficit? Last year, counting off-budget spending, it was $74 billion. This year, Mr. Carter's budget reveals, it will be around $78 billion. Next year, if you cross out the Carter tax increase and substitute the Reagan tax cut, it would remain in just about the same range. That's the magnitude of the job awaiting Mr. Reagan as he tries to move it toward balance.

The most valuable contribution of Mr. Carter's budget -- an utterly non-partisan one, for which Mr. Reagan owes him genuine gratitude -- is to open the sensitive issue of the current formulas indexing benefits to inflation.This budget drives home the lesson of the enormous complexity of indexation and the constant stimulus that it provides to future inflation. It's not just the magnitude of these increases that attracts the eye, but the incredible sensitivity of these costs to what seem like minor technicalities. A change in the law last year would adjust food stamp benefits next year not just for the previous 12 months of inflation, but for the inflation expected in the next three months as well. Cost? Almost half a billion a year. Giving retired federal employees two cost-of-living increases a year, instead of one, costs over a billion dollars a year. And if the Consumer Price Index did not overcompensate for housing costs, next year's budget would be $13 billion lower. These formulas urgently need revision.

An outgoing president's budget can never do more than put questions to his successor.Mr. Carter's budget puts the right questions, crisply and clearly. The incoming administration will seize this budget and, over the next month, impose its own first round of revisions. That's the point at which the country will begin to see, in hard numbers, Mr. Reagan's answers.