President Reagan turned to the familiar medium of radio yesterday in an effort to persuade an increasingly skeptical public that his economic program will begin by summer to reverse the recession that has left nearly 9.9 million people out of work.

In the first of a series of five-minute radio speeches to be broadcast live at midday on 10 consecutive Saturdays, Reagan said his program has not yet worked because "it hasn't really started".

"The 10 percent tax cut in July will be the real beginning of our program," he said, discounting the spending and tax cuts that took effect last year.

He repeated his resolve to resist pressures for any "quick fix" to stimulate the economy although he indicated he might be willing to make "some compromise" to end the stalemate with Congress over the budget--so long as it did not involve tampering with his tax cuts.

"Now, I know you've been told by some that we should do away with the tax cuts in order to reduce the deficit," he said, in reference to the clamor in Congress over the $91.5 billion in red ink he is forecasting for next year. "That's like trying to pull a game out in the fourth quarter by punting on the third down."

Speaking with reporters after the radio broadcast from the Oval Office, Reagan repeated his belief that his tax cuts would eventually bring about sustained economic recovery unlike, he said, the temporary resurgences in the past when "hyping the money supply" and "stimulating government spending" were the methods used to bring the nation out of recession. These policies only had the effect, he said, of spurring new rounds of inflation.

"Now inflation does have a temporary stimulative effect by its very nature, kind of like a warm bath," he told reporters. "At first it feels good, but then it gets too hot."

Aides said Reagan turned to the older medium of radio partly to avoid having his words filtered through television network news programs. Choosing a time when Americans are busy waxing the car, cutting the lawn or driving to the supermarket or hardware store, the president spoke in a personal, easy-going radio announcer's style. "I'll be back every Saturday, same time, same station. I hope you'll be with me," he said at the beginning of his address. Aides said he wrote the address himself in longhand after rejecting a draft his speechwriters had prepared.

Franklin D. Roosevelt as president had skillfully used his radio "Fireside Chats" as a regular means of communicating with the public. More than any other president since Roosevelt, Reagan is a skilled performer in the medium. It was radio that gave Reagan his first real job after college nearly 50 years ago--$5 a game broadcasting University of Iowa football games.

In time he became one of the leading play-by-play sports announcers in the Midwest. When he left office as governor of California in 1975, he began a series of two-to-three minute radio commentaries which were broadcast by about 300 radio stations across the country.

He stopped these broadcasts when he ran for the Republican presidential nomination in 1976. But he resumed the five-day-a-week program from the time he lost the primary battle to President Ford until he announced in late 1979 his intention to run for the nomination again.

The series of 10 broadcasts Reagan began yesterday was carried by nine radio networks which have a total of more than 3,000 affiliates, according to a White House aide. CBS was the only major network declining to carry them because of "potential fairness doctrine implications."

Many stations did carry a pre-recorded rebuttal to Reagan, however, from House Majority Leader James C. Wright Jr. (D-Tex.), who said Democrats "believe that there has to be a better way" than the Reagan economic program. Wright said Congress and the White House could not "hope to balance the budget without a serious and sober reconsideration of the one-sided tax cuts of last year," which he said mostly benefited the wealthiest taxpayers and gave "tax bonanzas" to the "nation's very largest corporations."

Wright called on Reagan to show "some flexibility, a little less rigidity, a willingness . . . to recognize the harsh realities of suffering among those nearly 10 million Americans who have been thrown out of work . . . . "

Reagan himself referred to these people in his radio address, saying, "These aren't easy times for a great many of you."

"We can . . . take some comfort from the fact that 99 1/2 million of our people are employed," he said. But he added: "I know that's no comfort to those who want to work and can't find a job."