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A rancher and a farmer are located next to each other

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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.

a. 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.

b. 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.