# A rancher and a farmer are located next to each other. Here are the facts of their situation

November 24, 2016

Question1 [8]:

A rancher and a farmer are located next to each other. Here are the facts of their situation:

There is no fence between the ranch and the farm
The cattle enter the farmer’s fields and destroy \$300 worth of corn each year.
The rancher’s business is worth \$1000 annually (not taking into account any crop damage).
The farmer’s business is worth \$800 before the cattle trample the corn
It would cost the rancher \$100 to build a fence that would keep the cattle on his property.
It would cost the farmer \$400 to build a fence that would keep the cattle out of her property.
Assume that it costs the rancher and the farmer nothing to negotiate with each other.
Suppose the rancher has to compensate the farmer for any crop damage. Will a fence get built? If so, who will build it and who will pay for it? How much better off do you think the farmer will be as the result of the fence? The rancher? Explain your answer.
Suppose the farmer has to absorb (pay for) the crop damage herself. Will a fence get built? If so, who will build it and who will pay for it? How much better off do you think the farmer will as the result of the fence? The rancher? Explain your answer.
Question2 [6]

The demand for trips across a river is Q = 1000 – 100P, where Q is the number of trips

per WORK day (assume 250 workdays per year). If the interest rate is 6% determine

which of the following options you would recommend to the government:

They can build a ferry for \$350,000. It takes one year to build the ferry and it will run for three years. They would charge a price of \$2 per ride, which would just cover the operating costs.
They can build a bridge for a cost of \$20 million. The bridge would last forever and it would be free.
Question 3[8]:

Assume that we have fixed supply of 30 units of a depletable resource to allocate between two

periods. Assume first that demand is constant in the two periods; the marginal willingness to pay is given by P= 9 – 0.3q. Also assume that marginal cost is constant at \$0 per unit and discount

rate is 10%.

What would be the dynamically efficient allocation?

c) Due to population growth, demand is higher in the second period. Thus the marginal willingness to pay is given by P-0.3qin later period. What would be the dynamically efficient allocation? (Use 10% discount rate). Compare your answer to the one from part a).

d) In addition to part c) also marginal cost is higher in the second period than in the first, due to the reserve depletions. The new marginal cost is given by MC= q.

What would be the dynamically efficient allocation in this case? Compare your answer with the one from part c).

Question4 [6]

What are marketable permits?
Suppose there are two firms in an area, each emitting tons of sulphur. The government decides on a target level of 200 tons of sulphur, and gives each firm a permit to emit 100 tons of sulphur. Suppose Firm A is very efficient and can reduce pollution by 100 tons with an abatement cost of \$500. Firm B has an older plant, so it will cost Firm B \$1,000 to reduce emissions by 100 tons. What will occur with marketable permits?

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