With only three weeks to go in the presidential election campaign, the economic issue finally has been fully joined.

For weeks Republican Ronald Reagan has been hammering away at President Carter's economic record, emphasizing the recession, 7 1/2 percent unemployment and, during the first quarter of 1980, inflation in consumer prices running at an 18 percent annual rate.

In a network radio speech Sunday and another speech yesterday at the National Press Club, the president began to strike back strongly, defending his record but stressing the major differences between his proposals for the future and those of Reagan.

And late Monday, independent John Anderson offered a detailed analysis of the impact of his economic policy proposals, while criticizing those of both his opponents.

One of the "central issues of this campaign," Carter said at the Press Club, is "do we want policies that encourage growth without driving inflation up -- through needed investments in new plant and new equipment?Or do we want to place our emphasis on immediate consumption through a quick, regressive, across-the-board tax cut" that would be inflationary?

While Reagan would not agree his proposals are either regressive or inflationary, he likely would agree that the differences in the candidates' tax proposals, along with the estimates of their impact on the economy, do constitute a "central" issue of the campaign.

Reagan has been campaigning hard for a quick 10 percent across-the-board personal income tax cut, with another 20 percent slash in the following two years. Such a cut, he and his advisers argue, would revitalize the economy by giving individuals a new incentive to save and invest. At the same time, he would cut business taxes by allowing companies to write off their investments in plants and equipment more rapidly.

The tax cuts would not be inflationary, Reagan maintains, because he still would balance the federal budget by 1983 by eliminating "fraud and waste" in spending programs.

Carter ridiculed this claim yesterday, saying his opponent's tax proposals including tuition tax credit for parents whose children attend private schools -- and plans for added spending for defense, merchant marine subsidies and elimination of the "work-test" for receiving Social Security benefits "would add $130 billion to the 1983 budget deficit."

"He has not specified which programs would be cut," the president said of Reagan. "I call upon him to do so."

For his part, Carter wants a $27.6 billion tax cut in 1981, more than half of which would go to business in the form of investment incentives and much of the remainder to offset the impact of higher Social Security taxes scheduled for Jan. 1. Reagan's cuts for 1981 are estimated to total $38.9 billion, rising to $80.1 billion in 1982.

Anderson on Monday took a leaf from both his opponents' campaign books. "In 1976, the voters elected a candidate for president who promised lower defense spending, a balanced budget, 4 percent unemployment, 4 percent inflation, labor law reform, comprehensive national health insurance, comprehensive welfare reform and a host of other initiatives that remain unrealized 48 months later," his statement declared.

"In 1980, a new candidate is in the running," Anderson continued, referring to Reagan. "He promises to cut personal income tax rates by one-third, substantially hike military spending and still balance the federal budget . . . sdespite a near-record $63 billion federal budget deficit for the fiscal year that ended less than two weeks ago."

The independent's own program contains few such promises. In particular, Anderson noted, "It makes no attempt to win votes with the promise of immediate tax relief -- relief that would soon be negated by the rising inflation that would result from a large tax cut at this time."

All the candidates agree the economy is in trouble and that one essential ingredient for improvement in the future is a higher level of business investment. Carter's tax cuts are focused precisely to encourage more investment. Reagan's rely far more on a broad-brush approach in which generally lower taxes are supposed to accomplish the same goal.

The candidates also agree that regulation of American business has, in some instances -- on just how many instances there would not be much agreement -- gone too far. Reagan constantly emphasizes the "overregulation" of the economy and suggests Carter has been responsible for much of it. Carter, in reply, points to deregulation of airlines, railroads, financial institutions, energy, truck lines, and communications industries during his term in office, a record unmatched by any previous administration.

Reagan blames Carter's economic policies for double-digit inflation. The president, for the most part, blames OPEC oil price increases and notes that inflation is coming down. To keep it coming down, Carter touts his own brand of fiscal restraint: "The rate of real growth in government spending is half what it was when I took office, and the budget deficit is less than half as large a portion of the gross national product," he told the Press Club audience.

The president also suggested that, if reelected, he probably would propose the use of future tax reductions to help "moderate the wage and price spiral," a reference to a so-called tax-based incomes policy, or TIP.

Reagan would have nothing to do with a TIP, nor would he continue Carter's present voluntary wage-price standards program. Anderson believes a TIP should be part of any attack on inflation.

Carter also emphasizes the reduction on U.S. oil imports by 2 million barrels a day. "No other country can match that record," he said proudly, adding, "We have loosened, but we have not yet broken, the grip of foreign oil dependency."

In an obvious dig at Reagan, Carter continued, "Those who ignore this challenge, those who discount conversation, those who believe we can leave the energy challenge to the oil companies alone have failed to grasp what may well be the central challenge of our time."

Reagan wants to disband the Department of Energy and to deregulate oil and gas prices as soon as possible as part of a move to an unfettered energy market.