There is a concerted campaign in certain quarters to reduce the second / airbnb problem of pricing out local people in the NW Wales area, and also makes claims about the loss of the Welsh language.
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But I don't think over-charging on council tax is really the way forward ...
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I've highlighted "Porthmadog" as it is an area I know fairly well. Yes, I admit that it does have some second homes, but quite a few of those are owned by people intending to retire there, plus another - somewhat overlapping - group are owned by families that volunteer for the busy narrow-gauge railways that operate there and which attract many thousands of tourists every year. The one railway is actually a significant local employer, despite using volunteers.
Note also that many second homes have been renovations of what otherwise would be derelict buildings.
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Not my Image : fair use & public education