Some residents of the village of Taugswater have proposed purchasing logging permits relating to a nearby wilderness area. The majority of residents agree that the purchase of permits, to be set aside and not used, is the most effective means of preventing commercial forest-product firms from clear-cutting the land.
Taugswater is a very small village; only five families have permanent homes there. Four of these five families were represented at a village meeting to discuss the logging-prevention (permit acquisition) proposal; the entire Herbert family were in New York visiting relatives that season, so could not attend.
At the meeting, a representative of the Provincial Government pointed out that, in addition to paying the standard fees for logging permits, the residents of Taugswater also must pay for enforcement services. to ensure that their exclusive claim to wilderness land is honoured.
The Provincial Government representative estimates that the cost of keeping logging firms out of the wilderness area depends on the amount of wilderness to be protected. The cost of preserving "H" hectares of wilderness is TC(H) = 100H + H2
Each of the four families are represented at the meeting by honest and forthright individuals, who reveal that each family's valuation of a hectare of wilderness can be described by the following (surprisingly identical) willingness-to-pay function: P(H) [≡MB(H)] = 500 - 2H
If only four families' preferences (willingness-to-pay amounts) are used when deciding how much wilderness to preserve, AND if the cost of preservation is shared equally among all four families, what is the surplus-maximizing amount of wilderness land to be preserved?