Show graphically and explain why the private provision of a public good will not result in an allocatively efficient outcome. As part of your answer you must provide a full explanation of what allocative efficiency is and from where it derives.
Private provision of public good doesn't result in allocative efficient outcome.
First of all, understanding what allocative efficiency is.
Allocative efficiency is a state of the economy in which production represents consumer preferences; in particular, every good or service is produced up to the point where the last unit provides a marginal benefit to consumers equal to the marginal cost of producing.
To understand why private provision of public good would cause allocative efficiency, let us take the example of education.
Education improves an individual's earning potential, but at the same time it may facilitate basic research, creating non-rival and non-excludable knowledge (which are the properties of public goods) that benefits others in the community. It also creates a more cultural environment and also leads to improved decision making of the voters.
(Consider the graph below)
So, the demand curve of education (individual) is shown as Dp. It represents the private benefits that students believe they will enjoy by procuring education.
As discussed above, education has some external social benefits as well, so E indicates the value of external benefits to others in the community.
As establishede education is a public good, so adding vertically the values of E to the private demand Dp gives the Marginal Social Benefit line (MSB). This shows that there are positive social benefits of education over and above the private benefits which the market would not properly internalize.
It is clear from the graph that the private demand at price OP is only OQp (where D=MC) and that is less than the socially optimal output OQs (i.e. the point at which the MSB of education is equal to the MC of education).
Hence, if education was provided by private sector there would be allocative inefficiency and Qs-Qp output would not have been provided.
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