The Dzerzhinski collective farm occupies more than 9,000 acres at the edge of the vast Ukrainian steppes about 30 miles northeast of this Black Sea port city.

It is the kind of place to be shown to foreigners, prosperous looking with freshly painted peasant houses. Dropping in on Ludmilla Shelengovskaya, whose well-appointed home is more spacious and comfortable than the homes of mid-level officials in Moscow, one is served good food and exquisite local wine, which the local Communist Party secretary hailed as cerkovnoe, or wine fit for the gods.

The farmers have planted some poplars along the roads, and the only landmarks upon the horizon are occasional high voltage relay stations that look like gigantic mosquitoes in the distance.

To hear collective farm leaders tell it almost smugly, there is more than enough food and money to go around among the 1,814 members of the farm, which last year made a profit of more than $3 million (and paid only 9 percent in various state taxes). It has built a new school, a new medical station and all sorts of other things.

At the Dzerzhinski farm one does not have the impression that its members are aware that the country has gone through four successive bad harvests and that food shortages are officially described as the country's main economic and political problem.

A somewhat different picture emerges from a conversation with the party's first secretary for the Odessa oblast, Nikolai Kirichenko.

Odessa is one of the 25 administrative regions in the Ukraine, a Soviet republic roughly the size of France and its main grain-producing area. Odessa ranks first among the 25 regions in meeting its food production plans.

Kirichenko conceded in a conversation with visiting foreign journalists, however, that Odessa's grain production has been sliding, from 1.4 million tons in 1978 to about 1 million tons in 1982.

Low farm production along with slow technological changes, low labor productivity and the rigidities of centralized planning are the main headaches Yuri Andropov inherited when he replaced Leonid Brezhnev as Soviet Communist Party leader on Nov. 12.

Andropov had hinted broadly that the new leadership would move decisively to end years of economic inertia and introduce reforms to stimulate the Soviet economy, which is second in size, complexity and strength to America's. It has become obvious here that the system is now in danger of choking on its own cumbersomeness and that changes are overdue.

The annual growth rate for Soviet industry had fallen from around 7.5 percent in the early 1970s to 2.7 percent for the first 10 months of 1982.

Although it is too early to predict what direction the changes will take, the government has moved to institute fiscal incentives and has called for greater internal and economic discipline.

One hint as to the direction Soviet agriculture may move comes in a film shown in December. The movie, "Hopes and Support," features a young agronomist who returns to his native village to bury his mother. He is persuaded by an old friend, who happens to be party secretary in the village, to remain there and take over the local collective farm.

The hero accepts the challenge. He had visited Hungary and muses about the "wealth and cleanliness" of Hungarian villages compared with the "grayness" of his poor village. He proposes that his collective farm should emulate the Hungarians and sets about organizing production by ignoring instructions from the central authorities in Moscow.

The movie ends with the hero symbolically halting the wasteful practices of the past and holding out the hope of a more efficient and prosperous life in the village.

The specific mention of Hungary, whose government has instituted cautious reforms introducing an element of market economy in the formerly Soviet-style system, is particularly telling. Andropov was the Soviet ambassador there at the time Soviet tanks crushed the 1956 Hungarian rebellion, but he is generally credited with having subsequently supported Hungarian reforms in the high Kremlin councils.

In Hungary, most of the land is run by cooperatives that have become very profitable because of financial incentives for productivity and the establishment of what amounts to two markets--one state, the other free. The country not only produces enough food for its own needs but also exports about $2 billion worth of food products annually.

To fully appreciate the scope of Moscow's agricultural predicament, one has to keep in mind that agriculture has swallowed 27 percent of all Soviet investment during the past 10 years, yet the need to import food has increased dramatically. Food imports in 1970 cost $700 million, while a decade later the Russians had to pay 10 times more, or $7.2 billion.

The Soviet Union has been using earnings from its vast energy and raw material resources to import food and technology. Its hard currency comes from exports of gold, platinum, diamonds, timber, furs, crude oil and gas.

Occupying nearly one-sixth of the world's land surface, the Soviet Union is the largest producer of oil, platinum metals and probably diamonds, the second largest miner of gold, and a key source of strategic metals such as manganese and titanium.

In platinum metals, which are important in the electronics and motor industries, Soviet exports run an estimated 2.5 million ounces each for platinum and paladium, and 150,000 ounces for rhodium.

Figures on diamond and gold production are secret here. According to Western estimates of the Soviet gold industry, the Russians produce up to 400 tons annually, compared with South Africa's production of 658 tons in 1981. The gold mine at Muruntau, Uzhbekistan, is believed to be the world's biggest, with an estimated annual production of 80 tons.

According to Western figures, the Russians accounted for nearly 20 percent of the supply of gold to the Western private sector during 1971-81, with sales of 2,700 tons. According to U.S. estimates, the Russians are believed to mine about 17 million carats of diamonds annually, more than South Africa.

Soviet oil production accounts for 22 percent of world output, but most of it is consumed domestically or sold to Soviet client states at discount prices. About half of the 1.1 billion barrels of exported oil is sold to Western European nations.

It has become clear, however, that Soviet mineral production is moving increasingly into the inhospitable Siberian wastes. Oil production is expected to level off in this decade, and new Siberian oil is more expensive than that produced in the European part of the country.

Mines such as the one producing platinum at Norilsk, the world's northernmost city, become uneconomical in a sagging world platinum market.

The new gas pipeline complex that includes the controversial export trunk from Siberia to Western Europe is designed to offset anticipated declines in oil production. The export pipeline is expected to bring in about $8 billion annually. Also, while gold and platinum prices have fallen during the past two years, the Russians are reported to have increased their diamond exports.

Despite their nation's vast natural wealth, the Russian leadership seems to be aware that energy and mineral exports have made the country chronically dependent on Western food and technology imports and have delayed meaningful efforts to restructure its manufacturing and, especially, agricultural sectors.

It is also clear here, by all indications, that the new leadership believes that the pattern of extensive growth that served the country well during its industrial buildup is now no longer possible. To exploit its human resources fully, the Kremlin must resort to innovation and reform.

What this means in practice is that the new leadership may be faced with the necessity of abandoning or seriously adjusting some of the time-honored practices in this society, such as the social "equalizing" factors that have been in force for nearly six decades, and of introducing competition, financial incentives and other economic tools.