Chase Manhattan Bank, the nation's third largest, cut its prime lending rate by one-half percentage point yesterday to 20 percent, the first drop in the prime since early July.

First National Bank of Chicago was the only other major bank to follow Chase's lead immediately, and financial analysts said bankers could be slow to lower their rates. Expectations of lower interest rates have been dashed repeatedly this year as the demand for credit has clashed with the tight-money policy of the Federal Reserve.

Murray Weidenbaum, chairman of the Council of Economic Advisers, asked by reporters if the economy can continue to tolerate such high interest rates, replied, "Yes, it can stand it, but . . . it would inhibit a stronger economy and make recovery slower than expected."

A number of private economic forecasters believe high interest rates will mean a string of quarterly declines in economic activity that will last until some time in 1982.

Neither Chase's action nor the general drop in short-term interest rates that preceded it seemed to impress the stock market yesterday. It closed with the Dow Jones industrial average down 10 3/4 points at 881.47, and the New York Stock Exchange Index off 0.77 point at 71.20.

Chase Manhattan's cost of acquiring funds had dropped significantly in recent days, allowing it to trim the rates charged commercial borrowers, according to Fraser Seitel, a spokesman. "This clearly is a reflection of market conditions," he said.

The drop in short-term rates was sparked at week's end by a report from the Federal Reserve that the money supply measure known as M1-B fell by $3.7 billion in the week ended Aug. 19. Despite warnings from the Fed that the weekly money supply numbers are highly volatile and frequently revised, markets react swiftly to them. In this case, the decline was interpreted as indicating the Fed might be able to supply more funds to the banking system without exceeding its targets for money growth, a process that could lead to lower short-term rates.

Meanwhile, high interest rates and reductions in public works programs combined to reduce the value of new construction contracts by 10 percent from June's level to $13.7 billion in July, McGraw-Hill Information Systems Co. reported. The company's index of construction contracts, which has fallen by one-fourth since last November, reached its lowest point of the year.

McGraw-Hill economist George A. Christie said the "monetary and budgetary disciplines of the Reagan economic program are choking off essential support of the construction industry. The mounting probability of a $20 billion overrun in 1982's projected budget deficit means still more trouble ahead for the building business in the form of added interest rate pressure from government borrowing, or further budget cuts, or both."

But Christie cautioned that even a drop in interest rates may not bring a new surge in construction spending. "For the short run . . . commercial and industrial building may be temporarily disrupted by excess capacity that is developing in the manufacturing sector and by a tendency toward overbuilding in the booming office market," he said.

Separately, the Agriculture Department reported that prices received by farmers declined 2.1 percent between July and August. The department said most of the drop in August was due to lower prices paid for corn, cattle, soybeans, peanuts and cotton. With the decline, average farm prices were 2.1 percent below August 1980 levels.