In exercise 27.3, we considered some ways in which we can differentiate between goods that lie in between the extremes of pure private and pure public goods.
A: Consider the case where there is a (recurring) fixed cost FC to producing the public good quantity y —and the marginal cost of producing the same level of y is increasing in the group size N because of crowding.
(a) Consider again a graph with N —the group size—on the horizontal and dollars on the vertical. Then graph the average and marginal cost of providing a given level of y as N increases.
(b) Suppose that the lowest point of the average curve you have drawn occurs at N∗, with N∗ greater than 1 but significantly less than the population size. If the good is excludable, what would you expect the admissions price to be in long run competitive equilibrium if firms (or clubs) that provide the good can freely enter or exit?
(c) You have so far considered the case of firms producing a given level of y. Suppose next that firms could choose lower levels of y (smaller swimming pools, schools with larger class sizes, etc.) that carry lower recurring fixed costs. If people have different demands for y, what would you expect to happen in equilibrium as firms compete?
(d) Suppose instead that the public good is not excludable in the usual sense — but rather that it is a good which can be consumed only by those who live within a certain distance of where the good is produced. (Consider, for instance, a public school.) How does the shape of the average cost curve you have drawn determine the optimal community size (where communities provide the public good)?
(e) Local communities often use property taxes to finance their public good production. If households of different types are free to buy houses of different size (and value), why might higher income households (who buy larger homes) be worried about lower income households “free riding”?
(f) Many communities impose zoning regulations that require houses and land plots to be of some minimum size. Can you explain the motivation for such “exclusionary zoning” in light of the concern over free riding?
(g) If local public goods are such that optimal group size is sufficiently small to result in a very competitive environment (in which communities compete for residents), how might the practice of exclusionary zoning result in very homogeneous communities— i.e. in communities where households are very similar to one another and live in very similar types of houses?
(h) Suppose that a court rules (as real world courts have) that even wealthy communities must set aside some fraction of their land for “low income housing”. How would you expect the prices of “low income houses” in relatively wealthy communities (that provide high levels of local public goods) to compare to the prices of identical houses in low income communities? How would you expect the average income of those residing in identical low income housing to compare across these different communities?
(i) True or False: The insights above suggest that local community competition might result in efficient provision of local public goods, but it also raises the “equity” concern that the poor will have less access to certain local public goods (such as good public schools).
B: Consider again the cost function c (N) = FC +αNβ with α > 0 and β ≥ 0 (as we did in exercise 27.3).
(a) In the case of competitive firms providing this excludable public good, calculate the long run equilibrium admission price you would expect to emerge.
(b) Consider a town in which, at any given time, 23,500 people are interested in going to the movies. Suppose the per auditorium/screen costs of a movie theater are characterized by the functions in this problem, with FC = 900, α = 0.5, and β = 1.5. Determine the optimal auditorium capacity N∗, the equilibrium price per ticket p∗ and the equilibrium number of movie screens.
(c) Suppose instead that a spatially constrained public good is provided by local communities that fund the public good production through a property tax. Economic theorists have shown that, if we assume it is relatively easy to move from one community to another, equilibrium may not exist unless communities find a way of excluding those who might attempt to free ride. Can you explain the intuition for this?
(d) Would the (unconstitutional) practice of being able to set a minimum income level for community members establish a way for an equilibrium to emerge? How does the practice of exclusionary zoning (as defined in part A of the exercise) accomplish the same thing?
(e) In the extreme, a model with exclusionary zoning might result in complete self-selection of household types into communities — with everyone within a community being identical to everyone else. How does the property tax in this case mimic a per-capita user fee for the public good?
(f) Can you argue that, in light of your answer to a (g), the same might be true if zoning regulations are not uniformly the same within a community?