Americans are facing 10 to 15 percent higher food prices next year, and there is little that the economists who are coming to town can do about it.

The estimate, released last week by the Department of Agriculture, is based on widely accepted figures suggesting that a five-year period of plentiful grain supplies have ended and a new era of rising prices, shortages and extreme volatility in the markets have begun.

Government and private analysts say that if there are excellent harvests in 1981 the upward pressures on food prices could abate somewhat in the latter half of the year, though not enough to drop the inflation rate to this year's 8.7 percent. But if these crops fall short, the Reagan administration could face a global crisis worse than the one that led to the inflationary wave of the early 1970s.

The mood of concern is shared by private and government analysts. Schnittker Associates, a private research group in Washington, has been warning clients about a "remarkable" change in the world grain prospects. "The world and the U.S. depend heavily on near-record harvests in 1981 to prevent further significant commodity price increases," it said.

World stocks of grain -- the basic human food and the essential raw material in meat and milk production -- have been drawn down to their lowest level since the mid-1970s because of bad weather in some key growing area. By mid-1981, world stocks of rice and wheat for humans will be down to 97 million tons, a 1 1/2-month supply. Supplies of animal feeds will be even tighter. And there is no hope of replenishing these stocks until the annual grain harvest begins sweeping across the Northern Hemisphere starting next May.

To offset the upward pressure on prices, Reagan aides are banking heavily on increased production by American farmers, rather than on price controls or limits on grain exports.

Richard Lyng, who is directing the transition for President-elect Ronald Reagan at the Department of Agriculture, said the new administration probably will not require special legislation to cope with grain shortages. To illustrate his contention that American farmers will rise to the occasion, he quoted an old country adage: "When egg prices get high enough, even the rooster starts laying."

However, Lyng adknowledged that food prices could be a serious problem for the new administration's inflation fighters.

Farm prices are by no means the only factor in rising food costs. About two-thirds of overall retail food costs are tacked on after agricultural produce leaves the farm -- for labor, energy, transportation, procesing, packaging, advertising and profits. But the stability of grain and livestock prices until the middle of 1980 gave consumers a major break and helped counteract other inflationary pressures. For example, larger beef and poultry supplies held the increase in beef and pork prices below the 1979 rate.

This break to consumers is now ending. Grain and meat prices are poised for sharp upturns in the months ahead.

When beef prices last took off, in 1973, the American beef herd was of record size. But between 1975 and 1980, U.S. stockmen slashed the number of animals from 132 milliona to 111 million. With supplies thus diminished, beef prices can be expected to stay firm for the foreseeable future.

Grain prices eventually have an impact on the prices not only of grain products such as bread, noodles, spaghetti and cakes but also of milk, beef, pork, beef, poultry and eggs, which come from grain-fed animals. And the situation in the world grain markets points to higher prices.

This development stems from events over which this government has little control, regardless of its economic policy.

Last summer, hot weather and drought severely damaged the U.S. corn and soybean crops, though wheat (which is harvested earlier and which grows predominantly to the west of the stricken zones) escaped. Corn production dropped 17 percent, to 164 million tons.

At the same time, unusually wet and cloudy weather damaged Soviet crops for the second consecutive year and its harvest may now be as low as 180 million tons instead of the target of 235 million.

Adding to these pressures is the unrelenting growth in the global grain trade, an economic development that affects all Americans since the United States this year is supplying 108 million tons out of the total world trade of 185 million tons.

In the 1970s, the world feedgrain trade grew at an annual rate of 12 percent a year, compared with only 8 percent for the wheat trade. The United States, which supplies three-quarters of this corn and soybeans trade, quickly feels the impact of higher prices. This is because the United States runs an open market in grain, with foreign and domestic users competing on an equal footing for supplies. When supplies are tight they bid up prices and that eventually affects the price of grain-fed livestock, as well as cooking oil, margarines, sweeteners, starch and other products that use corn and soybeans as basic ingredients.

It is hard for economists to see how demand for these products abroad will slow down unless foreigners change their eating habits or reduce their living standards.

Finally, food prices are subject to the same pressures from rising oil and energy costs that affect other products. For most of the last five years, farmers have been absorbing the higher costs, frequently taking losses and financing their operations out of borrowings based on rising land values. However, agricultural economists have been saying that this cannot go on forever -- that at some point farm prices will have to reflect the higher costs.

Given these pressures, some are eying government controls over exports. Outgoing Assistant Secretary of Agriculture Dale E. Hathaway said last week some restraints might be necessary, to protect U.S. food supplies. And yesterday, the economic policy council of the United Nations Association of the U.S.A. proposed a U.S. "initiative toward world food security" that would encourage other countries to establish their own permanent food reserves.

The panel, chaired by former secretary of agriculture Orville L. Freeman, departed from traditional policy favoring a comprehensive international agreement. Instead, it suggested that the United States work out arrangements with individual countries, or groups of countries, and possibly grant priority access to U.S. grain markets to nations that establish their own emergency food reserves.

At present, only the United States, India and possibly the Soviet Union set aside grain.And the United States has bilateral supply agreements with only the Soviet Union, China and Mexico.

Freeman said last week that efforts to work out a binding international agreement to stabilize grain prices have failed. As a result, he said, individual countries should work out their own agreements, "based on their own national interests." Freeman said that stabilizing world grain markets is in the U.S. interest because of the inflation threat, and he added that "we sit in the catbird seat." He suggested that this nation use its advantage to put pressures on other countries to join the food security system. a

Freeman said a copy of the proposal had been sent to President-elect Reagan, we well as to the Department of Agriculture, but thus far there had been no response.