Oil prices rose on Tuesday as hopes grew of a US deal to avert a “fiscal cliff” of tax hikes and spending cuts in the US — the world’s biggest consumer of crude. New York’s main contract, light sweet crude for delivery in Jan, increased by 49 cents to $87.69. Brent North Sea crude for Feb advanced 58 cents to $108.22 in London midday deals. “Crude oil prices rebounded on Tuesday amid hopes about the US budget details after the meeting between US President Obama and House Speaker John Boehner provided some optimistic signs about the US economy,” said  analyst.