President Reagan says the economy has hit bottom, and most forecasters agree a recovery will begin this winter, but that does not mean an end to bad news:

The same forecasters say unemployment will continue to rise, almost certainly to 10.5 percent and conceivably to 11 percent over the next several months, and will remain high most of next year.

The end of recession will mean only that sales and production have finally stopped declining. The recovery will begin with the economy so deeply depressed that the nation will lose perhaps $250 billion to $300 billion in output this year alone. Next year's loss should be nearly as great.

As the president and Republican candidates this fall urge voters to "stay the course," they rarely mention how difficult that course is likely to be and for how long.

The president's objective remains a healthy, growing, but noninflationary economy in which entrepreneurial risk-taking is highly rewarded and lightly taxed. That sort of economy is supposed to produce jobs for those willing to take them, with incomes going up faster than prices and the standard of living rising accordingly.

But especially with the current mix of policy, virtually every forecaster now expects, at most, a modest recovery brought on by the recent decline in interest rates. And they are warning that if their forecasts prove wrong, the economy will perform worse than expected rather than better.

The unemployment rate, as President Reagan is fond of pointing out, is a lagging indicator and will continue to rise after the corner to recovery is turned.

At 10.1 percent in September, unemployment already is at its highest since the Depression gave way to World War II, and is virtually certain to go higher still; layoffs are continuing at the rate of about200,000 a month. That unemployment will hit 10.5 percent is widely assumed by forecasters, and 11 percent is not regarded as out of the question even if the recession ends as expected. Nor is unemployment apt to come down very quickly. That is partly what staying the course means.

Top administration officials and their counterparts at the Federal Reserve have said they do not want an economic rebound so powerful that it could jeopardize hard-won gains against inflation. Generally, they are pointing to a moderately paced recovery involving no more than about a 4 percent expansion in real terms in 1983 and beyond.

Yet growth no greater than that could easily leave unemployment in or very close to double digits a year from now with little if any improvement in inflation. This is explained by some simple but fundamental economic relationships.

During a recovery, labor productivity, output per man-hour, usually improves as the tempo of production rises. Employers rarely reduce their payrolls as much as they cut production because they want to make sure they do not lose workers they will need when the recovery begins.

Employers also usually seek to increase output first by keeping employes on the job longer each week to avoid some costs associated with hiring more employes, such as unemployment insurance taxes and administrative expenses.

By historical standards, a 2 percent gain in labor productivity would be modest during a recovery. Increasing the length of the average workweek by 10 minutes would raise output by one-half a percent; add 20 minutes and output would be up 1 percent.

Thus, output could rise by 2 1/2 percent to 3 percent without any additional workers being hired.

Meanwhile, the labor force will keep growing. Even during the last 12 months of recession, it has increased 1.8 percent to nearly 111 million people, with 11.3 million out of work. In a recovery, the labor force usually grows faster than normal as discouraged workers and others are drawn in by the availability of jobs.

If productivity were to grow 2 percent in 1983 and average hours worked by 1 percent, total output, the gross national product, would have to rise by 3 percent just to keep the employment level from falling. With growth no faster than that, all of the 2.2 million workers likely to come into the labor force would end up unemployed.

With 4 percent real growth, roughly 1 million of the 2.2 million would find jobs, and the unemployment rate would climb to 11 percent as the labor force increased to 113.2 million and the number of jobless reached 12.5 million.

With growth at that rate, however, productivity might go up very little and the length of the average workweek might increase negligibly, or the labor force might increase no faster than before.

The critical point is that the growth rate described as likely and appropriate by Treasury Secretary Donald T. Regan, Council of Economic Advisers Chairman Martin Feldstein and other administration officials for 1983 and beyond will mean only a slow reduction in unemployment at best. With the kind of productivity gain needed to cool inflation further, there might be no reduction -- and perhaps an increase -- in unemployment.

The outlook for inflation is much better. Wages are rising less rapidly than before the recession and neither oil nor grain prices, the two main villains in recent years, seem likely to jump in the next year or two.

But the recession has forced many companies to cut their prices faster than they have been able to cut costs, including labor costs, and that has cut their profit margins sharply. When market conditions firm up, businesses will try to return to more normal profit margins. In most cases, markets will remain much too weak for that in 1983, but it will be a factor tending to push prices up. A rebound is likely for basic commodities sold in highly competitive "auction" markets, where prices have tumbled with the recession.

Wages will continue to rise. The Labor Department's index of average hourly earnings was up 6 percent in the last 12 months, and rose at an annual rate of 4.9 percent over the last three months. Fringe benefits and other compensation are rising, too.

Since profit margins have already been squeezed so hard--profits per dollar of sales for manufacturing corporations were down to 3.6 cents in the second quarter from 4.9 cents a year earlier -- businesses will try to pass on to the consumer any increase in labor costs.

Few economists expect wages to rise less than 6 percent next year if there is a recovery. If business is getting better, labor, too, will be trying to recoup its recession losses. Still, since unemployment will be very high, the labor market will be slack and no surge in wages is expected.

But if wages plus fringes go up 6 1/2 percent or 7 percent in 1983, and labor productivity rises no more than 1 1/2 percent or 2 percent, then unit labor costs -- labor costs per unit of production, one of the most basic underlying elements of the inflation rate -- would rise roughly 5 percent. That would seem to be a floor for the inflation rate next year. Any success in rebuilding profit margins would push it higher. So would a weakening of the dollar's very strong position on foreign exchange markets, which would make imports more costly.

Most inflation forecasts show prices rising between 5 1/2 percent and 6 percent in 1983. A few are somewhat lower.

Both the administration and the Federal Reserve are determined to hold down inflation, and monetary policy in particular is still pointed in that direction.

Interest rates have stayed ex-tremely high throughout 1982, which is the major reason the recession has endured. Another is that consumers, whose spending helped offset the slump early in the year, have not stepped up their buying in the wake of the July cut in income tax withholding.

Since July, however, a drop in credit demand and aggressive action by the Federal Reserve have pushed most interest rates down 3 to 5 percentage points. Mortgage rates are falling, as are rates on consumer loans, which are usually the last to move. Interest rates eventually will drop enough to regenerate consumer spending and home sales and relieve the interest burden on businesses.

The tentative Federal Reserve target ranges for money growth in 1983 are the same as this year's: consistent with no more than about a 4 percent expansion in real GNP and that only if the Fed again aims for the upper limit of the ranges. All of the relationships involved in linking money growth to the real economy are very loose. But normally, the Fed numbers for 1983 ought to be large enough to fuel the modest economic growth it is seeking.

Staying the course in 1983 means that unemployment will remain very high, output will grow slowly and inflation will come down little if at all. It also means that federal budget deficits, already at the highest level in history in terms of both dollars and GNP, will remain high.

For the long range, the healthy economy envisaged by President Reagan requires more saving and investment than the United States has had recently. The tax cuts of the last two years have helped boost the nation's personal saving rate and spurred businesses to make investments, but the recession and high interest rates have overwhelmed the tax cuts.

For one thing, part of the lost output associated with the recession would have gone into capital investments.

For another, profits are down so sharply that most businesses do not have enough money for investments. Meanwhile, their sales have fallen so far that they are producing below capacity, hardly a situation in which a company wants to build more. Even with a recovery, business investment is expected to fall through much of next year.

The extent to which the record federal budget deficits have boosted interest rates is not clear. What is clear, as CEA Chairman Feldstein notes, is that the deficits absorb money that otherwise would be available to finance business and residential investment.

The administration will propose additional spending cuts in January when it sends its fiscal 1984 budget to Congress. Whether they will include defense cuts is uncertain. Reagan has ruled out tax increases.

Most economists hope the budget deficits can be trimmed for later years to leave room for more investment. But next year, the important policy tool remains monetary policy.

The Federal Reserve, worried about corporate and financial institutions failing and about the general impact of the lingering recession, has eased its tight policies this year and presumably will do so again if no recovery occurs. Analysts expect it to push interest rates down another notch or two after the election.

There is no sign, however, that the Federal Reserve wants a recovery any faster than that endorsed by the administration. It, too, is staying the course.