New factory orders dropped by 0.9 percent from August to September and construction fell by 0.4 percent, according to separate Commerce Department reports released yesterday.

The reports added to the evidence that the economy is in recession. They came as the nation's major banks dropped their prime lending rates by one-half percentage point to 17 1/2 percent, following the lead set last week by Continental Illinois of Chicago.

Riggs Bank in Washington will lower its prime to 17 1/2 percent this morning. Citibank and Chase Manhattan of New York and Bank of America in California were among banks reducing the prime rate yesterday and many analysts predict there may be further reductions in the prime rate soon, perhaps even this week, as the recession eases pressures on financial markets by curbing the private-sectors' demands for credit.

In further economic news, the administration forecast yesterday that retail food prices will rise by between 5 percent and 9 percent in 1982. The rise will come largely because of increased marketing and processing costs, the Agriculture Department said. This estimate is slightly lower than the previous forecast of a 7 percent to 10 percent rise.

Food prices this year are now expected to rise by 8.4 percent. Early estimates from the Agriculture Department last year were for increases from 10 percent to 15 percent. In 1980 retail prices were up by 8.6 percent. Although forecasting farm income is "highly tentative," Deputy Assistant Secretary Dawson Ahalt said, "there is little evidence at this time for predicting a good year for farm income in 1982."

High interest rates and tight money have been the main cause of the present recession, which has been felt most heavily in the housing industry. The 0.4 percent drop in construction in September to a seasonally adjusted annual rate of $231.8 billion included a 1 1/2 percent decline in private construction. A drop of 6.4 percent in new housing units pushed down private construction.

The 0.4 percent drop was the seventh in eight months, but much smaller than the 0.9 percent fall recorded in August. New construction contracting rose by 2 percent in September, the F. W. Dodge Division of McGraw Hill Informations Systems Co. reported yesterday, but analysts said that the rise had "little significance" because the level is still far below that at the beginning of the year.

The recession is spreading more widely. The September drop in new factory orders was the second consecutive monthly fall reported by the Commerce Department. The overall drop was smaller than the 1 1/2 percent decline in August. But it would have been considerably sharper than reported--at about 1.6 percent--without an 18.1 percent runup in defense orders, the department said.

At the same time, there was a 1.1 percent jump in manufacturers' inventories to a seasonally adjusted $276.4 billion. This was the biggest inventory rise since February. As sales fall off in recession, manufacturers typically are left with bigger inventories than they intended to carry. In turn, they then cut back on production and employment, adding to the recessionary influences.

A survey of top financial executives by the Conference Board showed they expect inflation to fall in the next two years but interest rates to stay relatively high despite the drop in inflation, and the economy to have only sluggish growth.

Forecasters, including those in the administration, generally are revising downwards their view of how strongly the economy will perform next year.