Copper may also get a boost from standing on the shoulders of other downtrodden commodities, the report said.
"Cheaper oil is here to stay and the prices of many agricultural commodities will remain subdued, too. But the resulting downward pressure on inflation should help the recovery in the global economy, boosting the prices of industrial metals," it said.
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Capital Economics, whose end-2015 and end-2016 forecasts are for copper to rise to $7,200 and $8,000 a metric ton, respectively, isn't alone in taking a positive view on copper.
"Despite the negativity around China's growth prospects, China's apparent consumption remains in positive territory, with export market strength a likely aid source," Morgan Stanley said in a note Monday.
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Market forecasts for supply increases might also have been overly bullish, Morgan Stanley noted, citing Chinese miner MMG's announcement last week that the start of operations at its large-scale Las Bambas copper mine in Peru will be delayed until the first quarter of 2016. That news followed an announcement that a mine in Mongolia would also miss its production guidance, it noted.
"The supply/demand balance this year will post a fifth straight year of supply shortage, a plague that will also spill into next year," Morgan Stanley said. "Consensus is too bearish if current market conditions are sustained."
It expects copper prices to average $7,055 a metric ton this year and $7,175 a metric ton next year.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1