The Stray Cow Problem

Rancher Roy has his ranch next to the farm of farmer Fern. Cattle tend to roam and sometimes stray onto Fern's land and damage her crops. Roy can choose the size of his herd. His revenues are $6 for each cow he raises. The schedules of his marginal cost of production (MCP) and the damage each additional cow creates (marginal cow damage, or MCD) are given.

Farmer Fern can choose either to farm or not to farm. Her cost of production is $10, and her revenue is $12 when there are no cattle roaming loose. For each additional cow, her revenue is reduced by the amount in the MCD column. To answer the following questions, you need to figure out four things: the profit maximizing number of cows for Roy to own, his profits, whether Fern will farm, and what her profits will be. Remember that efficient outcomes maximize the net monetary benefits to both parties; in other words, total ranching plus farming profits. Finally, a diagram won't help for this problem.

a. What will be the outcome if there is no liability (Roy does not pay for any damages caused)?

b. What will be the outcome if Roy is liable for damages?

c. What is the efficient outcome (the outcome that maximizes total profits)?

d. Suppose it is possible to build a fence to enclose the ranch for a cost of $9. Is building the fence efficient?

e. Suppose the farmer can build a fence around her crops for a cost of $1. Is building this fence efficient?