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Public Provision of Private Goods

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Public Provision of Private Goods
1. Background Information
The traditional wisdom among economists states that only public goods (i.e. non-rival and non-excludable) should be publicly provided and cash transfers dominate in-kind transfers because recipients’ decisions are unconstrained. This is puzzling given the fact that most governments provide a large amount of goods that are private in nature (i.e. rival and excludable), for example, health care, education and public housing. Since the eighties, there has been a growing literature dedicated to study the public provision of private goods, with a focus on the rationale. A few decades have passed, although models have been proposed, consensus has not been reached.
2. Introduction
The objective of this essay is to analyze the public provision of private goods through basic microeconomic approaches. First, based on some related academic work, a simplified basic model is presented. After deriving and concluding the optimal situation in the model and a variation with the presence of mimickers, I discuss a few aspects of the basic model, which interest me the most, including (4.1) the meaning of price in the model, (4.2) positive externalities, (4.3) market provision, (4.4) inefficient provision and (4.5) an extreme scenario when only high-income group finances the public provision with only low-income group consuming. A brief conclusion is drawn at the end.
3. A Basic Model and Mimickers
As is mentioned in the background information, a body of literature has modeled the public provision of private goods (to name a few, Blackorby and Donaldson, 1988; Besley and Coate, 1991; Currie and Gahvari, 2008). I have simplified the models and proposed a basic version for convenience of discussions in this

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