A public good has two main characteristics they are non-rivalrous and they are not excludable. That means they can be used by many people at the same time and we can't exclude anyone from using it. A lighthouse fits both the criteria. Many ships can benefit from a lighthouse at the same time and no one can exclude anyone from using the lighthouse. So, it is a public good.
It doesn't matter if it benefits the ships going to a port nearby. The lighthouse is still doing its function of guiding ships in the sea and it is fulfilling both the criteria of a public good.
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