The Open Access Problem

The US Bureau of Land Reclamation (BLM) manages grazing on public lands in the Western U.S. Suppose that for a certain grassland grazing generates a total value of 10,000H 6H², where H is the number of heads of cattle grazed on the land. Ranchers also have a marginal cost of MC=1000 for each head they graze.

1. Calculate the net benefits from ranching under the socially optimal outcome.
2. Solve for the optimal number of permits, where each permit allows a rancher to graze 10 heads of cattle. (Hint: the government want to issue permits to the ranchers in order to achieve the socially optimal outcome)
3. Suppose we are at the open access outcome and a government under pressure from ranching lobbyists gives subsidies to each rancher in the amount of 600H, where H is number of heads. Calculate the new open access outcome under this. (Hint: You can consider subsidy as a way to lower the total costs of ranchers)
4. Calculate the net benefit to the society under which the government gives out 600H to each rancher. (Hint: The society will have to pay for the subsidy to the ranchers in addition to what is generated from the grassland, so the subsidies that are handed out to the farmers are net losses to the society.)