Continuing with the example of wilderness area to be preserved by the residents of the village of Taugswater...

Immediate following their return to Taugswater, the Herbert family is informed of the wilderness preservation proposal. As George, the grandfather and patriarch, is a walker of the bush, the other village residents assumed that the Herberts would want to participate (and contribute).

George recognizes that his family will obtain benefits from wilderness preservation and protection, irrespective of the amount of land protected from the loggers. He notes that his neighbours in Taugswater seem determined to have some area of the wilderness set aside and protected from logging, so there will be some land protected whether the Herbert family wants this or not.

George then chooses to tell the other Taugwater residents that the Herbert family does not care whether or not any of the wilderness area is protected or preserved. By making this claim, George exempts the Herberts from having to contribute any money toward the cost of wilderness preservation.

Recall that the cost of preserving "H" hectares of wilderness is

TC(H) = 100H + H²

Suppose that the marginal benefit of preserved wilderness to the Herbert family truly is described by the (typical) willingness-to-pay (MB) function:

P(H)[MB(H)] = 500 - 2H.

The Herbert family receives one amount of net benefit from the wilderness area's preservation if the family is dishonest and 'free-rides."

The family receives another amount of net benefit from the wilderness area's preservation if the family reveals (states) its willingness-to-pay honestly.

What is theincreasein net benefit to the Herbert family from making dishonest claims (what is the dollar amount of benefit from free-riding)?