The rising cost of business borrowing jumped another notch yesterday when most commercial banks raised their prime lending rates one-half percentage point to 13 1/2 percent, their highest level in four months.

The prime is the rate banks charge on short-term loans to their best-risk corporate customers. Smaller and less-creditworthy businesses usually pay at least one percentage point above the prime for their loans.

The prime does not apply to consumser loans, but its recent increases have paralleled rises in rates for home mortgages and auto loans. Some economists say those increases are delaying the economy's recovery from recession.

Chase Manhattan Bank often a trendsetter for the prime rate, led the latest rate increase. Other major banks across the country quickly followed suit, marking the seventh rate jump in as many weeks. The prime is now at its highest point since May, when it stood at 14 percent.

Among the other major banks to raise their rates were Bank of America in San Francisco, First National Bank of Chicago, and Morgan Guaranty Trust Co. and Chemical Bank in New York.

Meanwhile, the Commerce Department said construction spending nationwide dipped slightly in August, largely because federal, state and local governments cut back on their building expenditures.

The department also announced separately that new orders for manufactured goods, spurred by stronger demand for steel and electrical machinery, increased by 0.3 percent in August.

The department said construction spending fell 0.6 percent from a seasonally adjusted annual rate of $214.2 billion in July to $212.9 billion in August. In July, spending had fallen 0.4 percent.

August's drop was the seventh straight monthly decline and left construction spending 8.1 percent below where it was a year ago.

However, government economists cautioned that the decline in building expenditures does not necessarily signal an end to the housing recovery which is still in its infant stages.

They noted that during the worst of the recession, spending on private residential construction dropped dramatically. But the experts said most of August's decline was due to a 6 percent drop in construction expenditures by federal, state and local governments.

Private construction rose 1.3 perecent in August, from $158.9 billion to $160.9 billion. However, it was still down 12 percent from August a year ago.

Within this category, private residential spending rose 5.9 percent from $75 billion to $79.4 billion, and private nonresidential expenditures slipped 4.5 percent from $49.4 billion to $47.2 billion.

New orders for manufactured goods totaled a seasonally adjusted $147.4 billion during the month. In July orders increased for the first time since January, by a revised 6 percent. That was the biggest jump in a decade.

Orders for duable goods -- those expected to last three years or more -- fell 1.5 percent in August to $72.9 billion, while orders for nondurables were up 1.2 percent to $74.5 billion.

The decline in durable goods followed a revised July increase of 11.3 percent. Just as a great deal of the July imnprovement was a result of an 18 percent increase in orders for aircraft and parts, much of the August decline was caused by a 41 percent drop in those orders.

Manufacturers' shipments in August were up 1.2 percent to $147.2 billion, with primary metals leading the way, increasing 4.7 percent to $10.7 billion. Shipments of durable goods were up 0.7 percent to $72.8 billion, while non-durables shipments rose 1.8 percent to $74.4 billion.

Manufacturers reported backlogs of orders totalling $282.6 billion, virtually the same as in July. Backlogs rose an average of 1.3 percent a month in 1979 but only 0.1 percent a month during the first eight months of 1980.

Inventories of U.S. manufacturers dropped 0.2 percent in August to $243.6 billion -- the first decline since December 1975.