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.

A). Use the TV and TC functions and solve for the open access outcome in terms of number of heads. (Hint: I gave you the MC function. If you do not first get the TC function before solving this, then all of your answers to this problem will be incorrect!)

B). What is the net benefit of the grassland to the society under the open-access outcome?

C). The slope of the TV equals 10000 – 12H. The slope of TC = 1000. We know the socially optimal number of heads is where these slopes are equal. Find the socially optimal number of heads.

D). Solve for the optimal grazing tax by finding the variable, t, such that TV = TC + tH* where H* is the number of heads your solved for in part C. 

E). Calculate the tax revenue raised from ranching under the optimal grazing tax.

F). Calculate the net benefits from ranching under the socially optimal outcome.

G). Solve for the optimal number of permits, where each permit allows a rancher to graze 10 heads of cattle.

H). Suppose the government is under pressure from ranching lobbyists, and allows not only an open-access outcome, but in addition gives subsidies with the amount of $600 for each additional head they graze. Calculate the number of heads in this open-access, subsidized scenario.

I). Calculate the net benefit to the society under which the government gives out $600 to each head. (Hint: The society will have to pay for the subsidy to the ranchers in addition to what is generated from the grassland.)