(Recasts, updates yields) By Karen Pierog CHICAGO, Aug 12 (Reuters) - U.S. Treasury yields on the longer end of the curve hovered near the unchanged mark on Thursday after struggling to maintain higher levels reached in the wake of a 30-year bond auction, while cash flowing into to an overnight Federal Reserve facility set a new record. The 30-year yield, which hit a session high of 2.035% following the early-afternoon auction, was last at 2.0048%. The benchmark 10-year yield rose as high as 1.379% after the auction and was last at 1.3607%. The $27 billion of 30-year bonds were sold at a high yield of 2.040% and with a bid-to-cover ratio, a gauge of demand, of 2.21. "You had a really pretty normal result relative to average so I think the market looked through the auction results and just kind of kept on doing what it was doing," said Tom Simons, a money market economist at Jefferies in New York. He added that a really weak or really strong auction would have had the potential to move rates more. Yields, meanwhile, continued to inch higher ahead of an expected announcement by the Fed on tapering its asset purchases and with the latest inflation readings, Simons said. U.S. producer prices increased more than expected in July, suggesting inflation could remain high as strong demand fueled by the economic recovery from the coronavirus pandemic continues to press supply chains. The producer price report on Thursday from the Labor Department followed data on Wednesday that showed U.S. consumer price increases slowed in July even as they remained at a 13-year high on a yearly basis amid tentative signs inflation has peaked as supply-chain disruptions caused by the pandemic work their way through the economy. Inflation expectations have risen this week, with the breakeven inflation rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) climbing as high as 2.616% on Thursday. It was 2.552% on Monday. The Labor Department also reported on Thursday that initial claims for state unemployment benefits fell 12,000 to a seasonally adjusted 375,000 for the week ended Aug. 7. "It"s the third decline in a row, so that"s giving people more optimism that the next jobs figures will be reasonably strong," said Kathy Jones, chief fixed income strategist at the Schwab Center for Financial Research in New York. The U.S. Treasury also announced auctions for $27 billion of 20-year bonds next Wednesday and $8 billion of 30-year TIPS on Aug. 19. Auctions earlier this week were solid, with Wednesday"s 10-year note auction the strongest since 2012, possibly as a result of foreign demand, Citi analysts said in a research report. The amount of cash pouring into the Fed"s overnight reverse repurchase agreement facility set a record high of $1.087 trillion on Thursday, topping the previous record of $1.039 trillion set on July 30. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last 2.29 basis points steeper at 113.60 basis points. August 12 Thursday 3:42PM New York / 1942 GMT Price Current Net Yield % Change (bps) Three-month bills 0.05 0.0507 0.000 Six-month bills 0.05 0.0507 -0.002 Two-year note 99-207/256 0.2227 0.002 Three-year note 99-194/256 0.4565 0.005 Five-year note 99-8/256 0.8245 0.013 Seven-year note 99-32/256 1.131 0.012 10-year note 98-248/256 1.3607 0.002 20-year bond 105-136/256 1.9124 0.004 30-year bond 108-68/256 2.0048 0.001 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 9.00 0.50 spread U.S. 3-year dollar swap 9.75 0.75 spread U.S. 5-year dollar swap 8.50 0.00 spread U.S. 10-year dollar swap 0.25 -0.75 spread U.S. 30-year dollar swap -29.25 0.50 spread (Reporting by Karen Pierog; editing by Jonathan Oatis and Chizu Nomiyama)