WASHINGTON—U.S. homebuilding unexpectedly fell in September and permits dropped to a one-year low amid acute shortages of raw materials and labor, strengthening expectations that economic growth slowed sharply in the third quarter. The report from the Commerce Department on Tuesday also showed housing completions hitting a 13-month low. It followed on the heels of news on Monday that production at U.S. factories fell by the most in seven months in September. Strong demand as global economies emerge from the COVID-19 pandemic is running against worker shortages, straining supply chains. In the United States, every industry is experiencing shortages, fanning inflation. “Momentum in demand still appears to be positive,” said Rubeela Farooqi, chief U.S. economist at High Frequency Economics in White Plains, New York. “But supply is struggling to catch up given higher input costs and shortages that remain headwinds for builders.” Housing starts dropped 1.6 percent to a seasonally adjusted …