BEIJING, Jan 6 (Reuters) - Activity in China"s services sector expanded at a faster pace in December amid higher demand and easing inflationary pressure but continuing small-scale COVID-19 outbreaks weighed on the outlook, a private sector survey showed on Thursday. The Caixin/Markit services Purchasing Managers" Index (PMI) rose to 53.1 in December from 52.1 in November, remaining above the 50-point mark that separates growth from contraction on a monthly basis. The survey, which focuses more on small firms in coastal regions, tallied with those of an official survey, which also showed the expansion in the services sector sped up. read more Analysts say the services sector, which has been slower to recover from the pandemic than manufacturing, is more vulnerable to sporadic COVID-19 outbreaks and anti-virus measures, with leisure and tourism businesses hurt the most. Most of China"s recent local cases have been in the northwestern province of Shaanxi, where the capital city Xian has been on lockdown to control the spread of the disease. read more Firms" input prices rose for the 18th month in a row, but at a slower pace, the survey showed. A sub-index for employment rose at the fastest pace since May, and a gauge of new business accelerated. "Supply and demand both improved. As new products helped lift the market sentiment, business activity and total new business both expanded for the fourth consecutive month. But surveyed enterprises were concerned about the disruptions caused by scattered COVID-19 flare-ups," said Wang Zhe, senior economist at Caixin Insight Group, in a note accompanying the data. "Although the measure for business expectations remained in positive territory, it fell to the lowest since September 2020 and was remarkably lower than the long-term average." Caixin"s December composite PMI, which includes both manufacturing and services activity, rose to 53.0 from 51.2 the previous month.