After Yuri Andropov's first month in office, the Soviets clearly are looking to the new Soviet Communist Party leader with a certain hopefulness.

Perhaps the change itself has brought about a new sense of expectation. One discovers a measure of hazy optimism in conversations with Muscovites who only a few months ago professed to be on the verge of despair.

For all the continued frustrations and shortages, restrictions and oppressiveness, there is something compelling about the current public mood, suggesting that a decisive attempt already is under way to move this vast and diverse country in a somewhat new direction.

While the change seems to have been accepted with general approval, some skeptics worry that the enormous bureaucratic edifice that is the Soviet state eventually may frustrate Andropov's broadly hinted designs to institute changes to make the society and economy work again. But this is a minority view at the moment.

People know precious little about the 68-year-old man who stepped out of an impressive but not widely publicized 15-year career as head of the Soviet KGB secret police to inherit the leadership of the Soviet Communist Party from Leonid Brezhnev.

In spite of public relations work on Andropov's image, only a few tantalizing hints are available about his personality.

The generally positive public response to Andropov is based largely on his Nov. 22 inaugural speech, which was extraordinary by Soviet standards. For once in many decades, the leader announced publicly what the people knew and could say only in private -- that the system is in a crisis, that the economy is doing poorly and that he, the leader, had no "recipe" to solve the problems.

Andropov also held out the hope that the problems can be resolved by joint efforts, that the country should learn from others how to cope with them and that, in short, some changes in the economy are going to be made.

The precise and straightforward tone of Andropov's pronouncement was accompanied by his display of physical vigor and decisiveness. This was in sharp visual contrast to Brezhnev, whose physical infirmities had been painfully obvious during the last years of his life and tarnished his image as a vigorous leader.

If one thing is certain in the transfer of power from Brezhnev to Andropov, it is that the style of the new leadership would be different.

Russians traditionally look for a strong leadership at the top -- the hozyayin or nachalnik, the boss who wields real power whatever his title. There is a finely tuned instinct at the popular level to detect which boss had better be obeyed.

The change in style is an important indicator here of the intentions of the new ruler. Within a few days Andropov's actions and words wiped out the more theatrical memories of the Brezhnev rule. As one taxi driver put it, "We now have someone who can straighten out this place."

The remark provides an insight into a curious public reaction to one of the paradoxical features of the Brezhnev years. Brezhnev had let various institutions and regions run their own affairs as long as they did not interfere with Kremlin politics. As a result, his years were marked by democratization of public life in the sense that special interest groups developed and operated within the system.

Although all the components remained intermeshed, the central authorities found it increasingly difficult to impose order. During the past few years, however, the economy has been plagued by falling industrial growth rates, a series of agricultural disasters, widespread corruption and inefficiency and a demoralized work force.

Amid signs of an approaching crisis, the Brezhnev leadership appeared unwilling to risk any radical steps to deal with the problems. There was a sense of drift or stagnation as the country waited for the end of the Brezhnev era.

The public mood now is for efforts to restore economic discipline, to end corruption and to institute changes to promote economic performance.

Perhaps the most significant reflection of this new mood is the tone of public discussion. The press has changed considerably during the past month. There is a renewed interest in government affairs.

The most interesting newspaper these days is the stodgy Communist Party daily Pravda. On its front page last week there was an extraordinary admission that people with their "honestly earned money cannot always buy elementary necessities."

A mechanic from the Stavropol region published an article in another issue of Pravda complaining about food shortages and the chronic agricultural failures.

"These," he said, "are being ascribed to objective conditions -- either the land is poor or the weather conditions are bad -- but I believe that worse than any drought or other natural calamities is the incompetence of the authorities."

In another front-page editorial, Pravda attacked the authorities for simply ignoring public opinion and called this a case of "administrative deafness."

Yet another Pravda article compared Soviet industry to that of West Germany and the United States. The article said that the average Soviet metal-working plant employed 1,600 workers, while its West German equivalent employed 250. It said the average Soviet machine tool factory had 38 percent of its work force in auxiliary jobs -- maintenance, transport, packing and so on -- while its equivalent in the United States had 11 percent in such positions.

The appearance of the articles, written with refreshing simplicity and without any ideological window dressing, suggests that the new government is preparing to consider entirely new methods to revive the economy.

That the debate involves basic aspects of the command economy became clear this week when two economists publicly assailed the sacred practice of "socialist" labor. This involves a system of moral incentives known as "socialist emulation" and the dispatch of millions of people to "voluntary" projects such as the annual harvest or security duties.

The two economists argued that it makes no sense to dispatch engineers and highly trained specialists to "clear snow" or collect potatoes and that the society suffers greater losses than benefits from such centrally organized endeavors. "We need to have measure of economic character" to deal with problems, they said. They said they prepared their article on the basis of conversations with industrial and agricultural managers who revealed "the depressing but accurate statistics under the conditions that they or their enterprises not be mentioned in the press."

On the question of so-called voluntary security service, the economists said that the longstanding practice results in the annual loss to the state of at least "140 million rubles" -- more than $200 million. The volunteers, the druzhiniki, are office or industrial workers deputized to act as policemen. The problem of security, the economists said, "is primarily the responsibility of the Ministry of Internal Affairs."

The tone of public discussions apparently reflects internal pressures for reforms. It is still too early to assess how far the debate will go, particularly before an important holiday such as the 60th anniversary of unification of the Soviet republics next week. Prior to major anniversaries, the Soviets tend to emphasize the achievements of their system rather than its shortcomings.

Whether by accident or design, more food is available now in shops, although restrictions on quantity of individual purchases remain in force.

A dairy products shop on Gorki Street this week featured substantial quantities of goods that have not been available for some time, such as butter and cheese. This time there were six types of cheese available, including Dutch and Swiss imports.

"You see," said an elderly lady in the line for cheese, "things are already improving."

There are rumors here of major personnel changes in the new year and of a possible shift in the official attitude toward various aspects of social life. A recent debate among artists focused on the rumor that Andropov has developed tastes for modern painting and Western music. One school of thought holds that he was going to be "good for the arts," while the other assumes the wait-and-see attitude.

Rumors in this traditionally secretive capital often acquire a life of their own.

For instance, it is said that the new leader is tough, incorruptible and always at his desk before 9 a.m.

Andropov's KGB reputation has intimidated the uniformed police, who are famous for their corruption.

Foreigners noted this year that the time-honored tradition of giving bottles of vodka to neighborhood policemen at the Nov. 10 Soviet militia day has been broken. Brezhnev died on Nov. 10, and many foreigners decided a few days later to deliver their due to their friendly policemen.

At least one policeman who reminded people before Nov. 10 that he expected a bottle or two of vodka would not touch the presents a few days later.