A lone shepherd can graze 10 sheep per year in a meadow. Each additional shepher

Question

A lone shepherd can graze 10 sheep per year in a meadow. Each additional shepherd who uses the meadow reduces the number of sheep that can be maintained by one per shepherd. If a person would rather stay home than graze fewer than four sheep (i. e., the opportunity cost of going to the meadow is four sheep), how many shepherds will lead their flocks to the meadow every year? What are the net benefits to society of this outcome? What is the efficient number of shepherds at the meadow? Is the meadow a public good?

Explanation / Answer

Let each shepard lead the minimum number of sheep to medow each year. Then, total number of shepard that can graze the field is 10/4=2.5. Therefore, 2 sheperd can lead their flock of sheep to field. Each shepard can take 5 sheep to the fields.

The net benefit to the society is total benefit per shepard minus opportunity cost. That is opportunity cost of grazing is 4 sheep. Each shepard will lead 5 sheep to the medow. Then net benefit per shepard is 1 sheep. The total social benefit is 2 sheep.

If one shepard lead his flock to medow his benefit is equal to the social benefit. The maximum number of sheep one can graze is 10. Opppertunity cost is 4 sheep. Net social benefit is 6 sheep. Therefore, the social benefit will maximized if only 1 shepard lead his flock to medow. The efficient number of shepard is 1.

Here as maximum number of shepard uses the resource the benefit of the resource will decrese. This problem is commonly known as the Tragedy of Commons. The tragedy of commons is a special type of externality that arises when everyone use one common resource unlimitedly. A common resource is exhaustive and non-excludable. This means that if everyone use it unlimitedly the resource or the benefit of the resource will decrease, but it is not possible or costly to stop someone from using the resource. A common example of common resource is gazing fields.

The medow is a common resource.  A common resource is exhaustive and non-excludable. The public goods can be defined as the goods that can be consumed by anyone without reducing the amount of consumption of others and without keeping anyone from consuming them. The public good have two unique properties; that is non-rivalry and non-excludability. Therefore, medow is not a public good.

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