SILVER SPRING, Md. — The rate of expansion in the U.S. services sector, where most Americans work, hit a record high in October as demand remained strong even as supply chain problems persisted.

The Institute for Supply Management reported Wednesday that its monthly survey of service industries — which includes restaurants and bars, trucking companies, hotels and many other businesses — jumped to a reading of 66.7 from September’s reading of 61.9.

Although business activity, new orders, supplier deliveries and backlog of orders all surpassed previous records, sticky issues that have plagued almost every kind of economic activity since infections began to ease in the U.S. continued: labor shortages, supply chain bottlenecks and higher prices.

“The broad picture painted by this report is that the economy is overheating,” said Stephen Stanley, chief economist for Amherst Pierpont Securities. “Demand is overwhelmingly strong at the same time that supply is constrained. Still, I am not sure that even a fully-functioning supply side, with more labor and a resolution of snags would be able to handle the pace of demand right now.”

The reading for employment grew for the fourth straight month in October, but dipped slightly from September, creeping closer to contraction at 51.6. Respondents to the survey, which include purchasing and supply executives, said they are still having trouble filling positions.

The labor shortages, along with the difficulties in getting parts and products due to supply chain issues, led to a record reading of 67.3 in the backlog of orders category. Businesses have also had trouble stocking up on goods, with the inventories index declining for the fifth straight month, to 42.2.

All of these problems, along with strong demand, have led to higher prices for just about everything. The prices index rose 5.4 percentage points from September, registering 82.9 in October. That’s the highest reading since 2005, when it hit an all-time high of 83.5.