Ronald Reagan summarized his case against the economic "failures" of the Carter administration last night, and promised to reduce unemployment, bring down inflation and balance the federal budget "possibly by 1982."

"Yes, the mighty music of American economic progress has been all but silenced by four years of Mr. Carter's failures," Reagan said in a paid 30-minute speech shown on ABC television. "This election will determine whether the nation and the world will again hear that great sound; will determine if the dinner table of your home and the supermarkets of your neighborhood will ever again be places where plans can be made and necessities can be purchased without the gnawing doubt and, yes, fear brought by Mr. Carter's inflation and unemployment."

There is little in the Republican nominee's address that he had not said before, especially in a Sept. 9 speech to the International Business Council in Chicago.

But Reagan was a trifle more optmistic about his economic plan last night than he was in the more detailed message in Chicago. The target for a balanced federal budget in the Reagan economic plan is 1983. Without changing this taraget, Reagan said he was hopeful that the combination of spending cuts and tax reductions he proposes to stimulate production would make it possible to accomplish his goal a year ahead of schedule.

As he had in Chicago, Reagan outlined an eight-point program "that sees the American economic system as it is -- a huge, complex, dynamic system that can work if the American people get a chance to work."

At the heart of the program is a dual plan to "keep the rate of growth of government spending at reasonable and prudent levels" while cutting personal income tax rates 30 percent over three years.

Reagan also proposes to simplify depreciation schedules for business, change or eliminate unspecified federal regulations which discourage economic growth, "establish a stable, sound and predictable monetary policy," promote the export of U.S. products, revitalize American industry and "adopt an energy policy that will allow our economy to grow and our standard of living to rise."

Last night's speech was frankly a political message intended to lay out the Reagan economics plan in the simplest terms.

It was also an attempt to lay out the economics case against Carter, as Reagan has been trying to do since Labor Day.

"By the very standards Mr. Carter himself uses to measure presidential failure, he has failed," Reagan said. "He promised to bring inflation down to 4 percent. It's now at double-digit rates, and hit 18.2 percent earlier this year. The producer price index the past three months has averaged an annual rate of some 13 percent. In fact, between January 1977 and August 1980, consumer prices have risen 42.3 percent.

"In the face of all this economic bad news, Mr. Carter has taken to telling voters that things will get better. But today we found the answer to that. The consumer price index released just this morning showed that the cost of living went up 12.7 percent in September."

He was referring to what the annual rate of inflation would be based on the September index.

Reagan's economics speech came at a time when he is trying to refocus the presidential campaign on Carter's performance. Stumping the South on Thursday, Reagan described Carter as an "incompetent."