(20 points) The City of Smartsville is deciding how much money "E" to spend on public education.

(5 points) Diagram and briefly explain the private market failure for education, that is, why education would be underprovided if financed exclusively by private contributions.

(5 points) As a result of the analysis in (a), the City decides to provide some level of public education ("E"). Three levels of provision are considered: Low (L), Medium (M), and High (H). The expense "E" will be financed through a lump-sum tax on each household. There are three types of households (A,B,C) with heterogeneous preferences over spending on education. There are an equal number of each household. Household preferences over each level of spending are given:

Households A have preferences: L > M > H

Households B have preferences: L > H > M

Households C have preferences: H > M > L

Would pair-wise voting result in a stable (consistent) outcome E* (cite a relevant concept from the course)? If so, determine provision level E* and demonstrate that this outcome is indeed stable (consistent).

(5 points) Suppose that pair-wise voting results in a stable (consistent) outcome E* Is this level of provision of E necessarily socially optimal? Explain.

(5 points) Suppose that in the United States, there are many cities, and each city independently determines its own level of local spending on public education. Explain why each city may establish the (locally) socially optimal level of provision? Discuss two plausible reasons why this may not occur.