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I am really confused on how to classify low fees government nursing home services that are provided to elderly people. Is it public good or private good or quasi-public? My reasoning is that it is a private good. It is because even though it provides low fees it excludes some poor elderly people who cannot afford it. However, I really don't know how much rival it really is. If uncongested, I don't think it is rival, as someone's already admission into nursing houses doesn't reduce the quality of care I receive if get admitted to such houses. However, under congested conditions, the quality of health care received reduces significantly and hence becomes rival. So since it lies somewhere between public and private, shall we call it quasi-public? What is the line for defining a quasi-public good? Can someone explain me with examples.

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My reasoning is that it is a private good. It is because even though it provides low fees it excludes some poor elderly people who cannot afford it.

In that case it's excludable. That is sufficient to show that it's not a public good, since the standard definition of a public good is that it's both non-excludable and non-rival.

If uncongested, I don't think it is rival, as someone's already admission into nursing houses doesn't reduce the quality of care I receive if get admitted to such houses. However, under congested conditions, the quality of health care received reduces significantly and hence becomes rival.

I'm not sure that congested / uncongested is the most appropriate terminology here. A nursing home is unlikely to be run like, say, a public park. More likely it will have, at any time, a certain number of places, and the number of people admitted will not be allowed to exceed that number. So it would probably be more appropriate to consider whether demand (at the low fee) exceeds supply (places available). But with that change of terminology your logic will still apply: if demand is less than supply, it's not rival, but if demand exceeds supply, it is.

In summary, therefore, the good is excludable and, depending on circumstances, may or may not be rival. Should it then be classified as a quasi-public good? Examples commonly given of quasi-public goods are public roads and bridges (presumably those without tolls), goods which are non-excludable and often non-rival, but can sometimes become rival due to congestion. It would be stretching the meaning of the term to apply it to a good which is excludable, just because in some circumstances it is non-rival. So your initial suggestion that low fee nursing home services are a private good is valid, although it could also be argued that, when demand is less than supply, they are a club good, which has been defined as a good which is excludable but non-rival.

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