A beekeeper lives adjacent to an apple orchard. The orchard owner benefits from

Question

A beekeeper lives adjacent to an apple orchard. The orchard owner benefits from the bees because each hive pollinates about one acre of apple trees. The orchard owner pays nothing for this service, however, because the bees come to the orchard without his having to do anything Because there are not enough bees to pollinate the entire orchard, the orchard owner must complete the pollination by artificial means, at a cost of £10 per acre of trees.
Beekeeping has a marginal cost
MC = 10 + 5Q,
where Q is the number of beehives. Each hive yields £50 worth of honey.
a) assuming the beekeeper wishes to maxmise his profits, how many beehives will the beekeeper maintain?
b) what is the socially effiecient number of hives?

Explanation / Answer

The beekeeper will maintain hives where marginal cost equals marginal revenue. So 10 +5q= 50 5q=40, q=8 hives. Since there is an external benefit to the orchard owner from the bees pollinating his orchard, the socially efficient number of hives is more than 8. However the problem does not give us enough information to determine what that number is.

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