ABERDEEN, Scotland—When he was laid off in December, Sean Murphy thought he would easily find a new job with his 30 years of experience as a supervisor on oil rigs all over Europe’s North Sea. Five months and more than 200 résumés later, Mr. Murphy has lost confidence.

So, too, has this once-buoyant city. Often called Europe’s energy capital for the high number of oil-and-gas firms operating here, Aberdeen is a victim of the sharp drop in oil prices since last year.

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