Question

Adams and Braun own lots A and B, respectively, of Section 236, bordering on State Route 116. The Adams lot (236A) is adjacent to the state road and the Braun lot (236B) is immediately behind it. Access to 236B is provided for in an easement under which the owner of 236A must allow free passage to occupants of all inned lots.

Adams already has a house on lot A and has resided there for five years. Upon construction of the house, Adams also caused a road to be prepared, running from Route 116 to the back border of his lot. The road is not hard-surfaced, but is a type of "oiled gravel" surface common to private roads and driveways in rural areas. This kind of surface is subject to erosion and general deterioration over time. However, Pitts Gravel will come and provide any number of "doses" of road repair at a price of $25 per dose.

[The concept of a "dose" of an input is a pedagogical simplification that will be utilized a number of times below. It is used to collapse a heterogeneous, multidimensional package of possible adjustments to a single dimension. Hence "road repair" could be a mix of many different services in varying proportions, but no useful purpose is served by explicitly considering multidimensional adjustments. Through the simplification of road repaid into "dose" we can focus on a straightforward quantitative adjustment]

*Note: the cost of each individual dose is $25, so 2 doses would cost in total $50, 3 doses cost $75, etc.

Fortunately, we just happen to be in possession of Adams' true subjective evaluations of how much different levels of road repair are "worth" to him. Column 2 of the Table below shows his total value of the services received from the road, assuming different levels of maintenance, i.e., different quantities of doses. Note that these values are "gross" of any costs incurred in purchasing the maintenance.

Table: Benefits of Road Repairs

Number of "Doses"	Total Benefits to Adams	Marginal Benefit to Adams	Marginal Benefit to Adams andBraun
0	$50	-NA-	-NA-
1	$90
2	$120
3	$140
4	$150
5	$150

1. Copy the table above and fill in the marginal benefits to Adams column. [Strictly speaking, the word “marginal” refers to infinitesimal rates of change, but it is commonly used loosely to refer to discrete changes, as in the present case.]^*
2. If only Adams is on the scene, what level of road repair would he choose? Explain in terms of marginal benefits and marginal costs.
3. Suppose Braun now builds a house on Lot B. Braun, coincidentally, has the same preferences about road repair as Adams. Fill in the marginal benefit to Adams and Braun.
4. What is the efficient amount of road repair? Explain how you determine this.
5. Suppose that Adams and Braun choose the amount of road repair to pay for as a simultaneous move game. Write out the strategic grid, with the strategies of each player being how many doses they contribute (E.g., 1 dose, 2 doses, 3 doses, 4 doses…). Fill in the payoffs to the strategic grid.
6. How much road repair will be purchased? Use the concept of Nash equilibrium to make this prediction. Is the equilibrium efficient? Briefly explain why or why not.
7. Suppose more people enter the scene, Cherkas, Donatella, Eglin, all with the same preferences. Is it any more likely the efficient solution will be reached? Explain.
8. In what sense might the parties prefer to be “coerced” to contribute? Explain specifically how everyone can be made better off through being forced to contribute to repairs through a contract or taxes.
9. Is there a defect in the property rights (ownership) of the road? What characteristics of the ownership of the road lend to the problem?

Answer 1