Karol Grzywa was appointed director of the July Manifesto Coal Mine here as a result of the great miners' strike last summer. He is ambitious, popular, and at, 38, the youngest mine director in Poland. He is also a very worried man.

During his 10 months as director of the mine, production of coal has dropped by the incredible figure of 40 percent. The average working week of his miners has gone from 60 hours to 37 1/2, and the average wage has risen 20 percent to about $500 a month.

The mine provides a good illustration of Poland's current economic problems. The miners have little interest in increasing production when there is nothing to buy in the shops with the extra money they earn. Mistruct of the communist authorities still runs deep, and the workers are wary about being "tricked" again. They are waiting, they say, for concrete guarantees of the government's commitment to reform.

But there is a danger that while each side waits the other out, the economy might slide into total chaos. Present economic trends in Poland resemble what one Western economist in Warsaw described as "a vicious circle stuck onto a downward spiral." Less coal means less raw materials for the rest of Polish industry and therefore less production.

That, in turn, means a lower national income and less in the shops for miners, among others, to buy.

The July Manifesto mine, named after the first wartime declaration of Poland's provisional communist government, has a special significance. It was here that labor unrest first erupted in Silesia, the industrial region of southern Poland traditionally considered loyal to the former Communist Party leader, Edward Gierek. Here too, on Sept. 3, an agreement was signed between the authorities and Poland's 350,000 miners.

The document, modeled on the factory workers' agreement signed in Gdansk four days earlier, amounted to a miners' bill of rights. They had considered themselves overworked and underpaid, and they won a five-day week and the right to set up their own independent unions. The hated four-brigade system, which ensured a continuous operation at the coal face, was abolished. Perhaps most important, miners won back their pride and self-respect.

All this Grzywa accepts as positive achievements of the landmark Jastrzembie agreement. Viewed solely in the short-term economic context, however, he believes it was "a disaster."

When the minister for mines signed that agreement, "he lost 50 million tons of coal," Grzywa said.

Coal, as Premier Wojciech Jaruzelski said in a recent speech, is "the oxygen" of the Polish economy. It is a vital energy source for industry and domestic heating. As Poland's principal export, it also provides much of the hard currency needed to import needed raw materials, machinery and spare parts.

In 1979, according to official statistics, Poland produced about 220 million tons of coal. Of this, 45 million tons went abroad, making Poland the world's second biggest coal exporter after the United States. This year, most officials believe total production will barely scrape 180 million tons -- and exports 15 to 20 million tons.

From his vantage point, Grzywa regards even these reduced estimates as optimistic. He suggests that 160 million tons would be a more realistic figure. On the basis of this calculation, Poland will be fortunate if it remains a net exporter of coal.

The drop in production at the July Manifesto mine has been particularly marked, although it is still representative of the country's overall economic problems. Partly as a result of last summer's strike, the miners here are more radical than elsewhere and less willing to work overtime. The mine is also bedeviled by technical problems and lack of spare parts.

In some Polish factories, notably the Lenin Shipyard in Gdansk, labor productivity has increased as a result of last summer's agreement. Relations between workers and management have improved, and the new Solidarity trade union federation has helped root out inefficiency. The increase in productivity, however, must be set against the lack of materials and shorter working week.

In the mining industry the reduction in working hours has been the most catastrophic for the economy.

The miners complain that under Gierek, a former miner, they were forced to work inhumanely long hours. Production, they say, was raised to artificially high levels to disguise the deep cracks already appearing in the economy. Most galling, the miners were regarded by other workers as "Gierek's children."

"Miners with Gierek" was one of the favorite slogans of Communist Party propagandists during the 1970s.

The fantasy of the Gierek mythmakers had to burst somewhere, and it was no accident that it happened here in Jastrzembie. Snuggling up close to the Czechoslovak border in the rolling Silesian countryside, the July Manifesto mine is a new one. The work force is predominantly young and gathered from all over Poland, but particularly from coastal towns such as Gdansk, which had already been infected by working-class militancy in 1970. a

Grzywa's predecessor as mine director was particularly unpopular, the miners say, because of his arrogance and brusqueness. In an attempt to win the favor of local party chiefs, he agreed to start mining operations at a depth that enabled maximum coal extraction during the first two years, but reportedly is creating enormous technical difficulties now.

All mining experts knew that the decision was ludicrous, according to Grzywa, but nobody dared criticize it.

After the strike, the director was fired at the miners' insistence and Grzywa appointed.Grzywa's relations with the men are good and he is on easy terms with local Solidarity leaders, but he complains of poor work discipline and lack of concern for Poland's economic well-being.

Solidarity officials do not contest Grzywa's figures. They put more emphasis than he does on the technical reasons for the drop in coal production, including the lack of spare parts, but agree that the cut in the work week is the major factor. They insist, however, that the government is to blame for failing to come agreement with the workers on overtime.

Earlier this year, when the five-day week was introduced in mining, the authorities attempted to persuade miners to work overtime by offering them special food rations. This only fueled the suspicions of Solidarity members who claimed that if they got more food, other workers would get less. They pressured the government into withdrawing the plan, and coal production dropped further.

Josef Blaut, a Solidarity leader at the mine, said he appreciated the need for raising production. But he added: "We must get something in return. There's no sense us working harder unless we know what use is being made of the coal we produce. In the past, they tricked us" into working to prop up an inefficient economy.

It is a crisis of confidence. Miners are not yet convinced of the government's sincerity. They also point to the tremendous wastage of coal as a result of its low domestic price.

Exported, high quality coal can bring as much as $100 a ton. In Poland, the price is 500 zlotys a ton ($18 at the artificially low official rate of exchange). One miner remarked bitterly that this means that 3 1/2 tons of coal can be bought for the black market price of a single turkey. The cost of producing a ton of coal is three times higher than its sale price.

Economic reform offers a glimmer of hope that Poland might find a solution to its problem. All Polish economists agree that the pricing system is in need of an overhaul as is the huge central planning apparatus.

But all these proposed reforms come against bureaucratic inertia and the threatening prostect of an unemployment and inflation.

As Grzywa remarked, "To tell you the truth, I can't see any way out. I expect the crisis to deepen."