President Reagan today described the November election as a clear choice between his view of "having given government back to the people" and Walter F. Mondale's "philosophy of bigger government."

"Everything we have done, everything we mean to do, is to give the American people opportunities to make this great, free nation greater and freer still," Reagan said. "That's why the choice in 1984 is so clear because my opponent's policies would take us off the path toward an opportunity society and put us back on the path toward defeatism, decline and despair."

After a week of focusing on foreign policy, Reagan's focus today was on economic optimism, which his advisers say they believe will be decisive in the presidential election.

Reagan mentioned his Friday meeting with Soviet Foreign Minister Andrei A. Gromyko only once, in response to a written question after a speech to the Detroit Economic Club. The question was whether he and Gromyko could become friends.

The president said he didn't know whether friendship was possible but said the talks were "constructive" and necessary because the United States and the Soviet Union each had the power to "destroy the world" or "save the world."

" . . . We are ready to join with them in approaching this principal problem of runaway armaments in the world," Reagan said.

In his speech, Reagan repeatedly mocked Democratic economic policies which he said Mondale had supported throughout his career.

"My opponent, who opposed our tax program, said it would be murderously inflationary before inflation went down," Reagan said. " He said there would be no recovery, before recovery began, then said recovery would be only anemic before the strongest economic expansion in 30 years. He now says there is no denying that the deficit must be reduced with tax increases.

"Forgive me, but judging from the record of those who are philosophically or constitutionally opposed to what we are doing, we might be better off if we consulted astrologers about what the deficit will be in 1989," Reagan said. "But there are two things we do know that are not a matter of prediction: First, my opponent is committed to large spending increases and a tax increase . . . and, second, those policies . . . gave America an economic hangover that we must never -- ever -- suffer through again."

Reagan's speech, laden with statistics, appeared to be a dress rehearsal for Sunday's nationally televised debate with Mondale in Louisville.

Summing up what he said was the choice in the November election, Reagan said of Mondale, without mentioning him by name: "He puts his faith in more power for government. We place ours in more opportunity for people. He sees America wringing her hands. We see America using her hands.

"He sees America divided by envy, each of us challenging our neighbor's success. We see an America inspired and uniting for opportunity, all of us challenging the best in ourselves. We believe in knowing when opportunity knocks. He goes out of his way to knock opportunity."

Before speaking to the Economic Club, the president presided at the swearing-in of 1,548 new U.S. citizens from 82 countries. The largest contingents were 214 new citizens from Iran and 167 from Lebanon.

"You have joined a country that has been called the least exclusive club in the world with the highest dues," Reagan said. "America was founded by men and women who understood that freedom does not come free. It has a cost. But I don't suppose anyone would know the cost of freedom better than you."

Reagan departed from Detroit for a campaign speech in Gulfport, Miss., where he spent the night. He is scheduled Tuesday to campaign in Texas.

Reagan's polls show him with a big lead in all three states he is visiting on this swing, his last before Sunday's debate. Campaign aides also were heartened by a poll published Sunday in the Detroit Free Press which showed Reagan leading Mondale in Michigan by a 54-to-37 percent margin.