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, whereQis the number of beehives. Each hive yields \)40 worth of honey.

a. How many beehives will the beekeeper maintain?

b. Is this the economically efficient number of hives?

c. What changes would lead to a more efficient operation?

Short answer

1. The beekeeper would be able to maintain 6 beehives.

2. 6 beehives is not the efficient number of hives.

3. The merger of both the business of a beekeeper and orchard will lead to a more efficient outcome.

Step-by-step solution

Explanation for part (a)

The revenue of the beekeeper will be maximized where marginal cost is equal to the marginal benefit.

The marginal benefit is $40 since that is the worth of honey produced by the hives, and the marginal cost is given, therefore:

$$\begin{gathered} 40=10+5Q \\ Q=6 \end{gathered}$$

The beekeeper will maintain 6 beehives.

Explanation for part (b)

If there are too few bees to pollinate the orchard, the farmer, in that case, must pay $10 per acre for artificial pollination. Therefore, the farmer would pay up to $10 to the beekeeper to maintain each additional hive, which is the external cost. Thus,the marginal social benefit, $50, is greater than the marginal private benefit of $40.

Equating the marginal social benefit to marginal social cost:

$$\begin{gathered} 50=10+5Q \\ Q=8 \end{gathered}$$

Therefore the economically efficient number would be 8.

Explanation for part (c)

If both the farmers merge their businesses, the farmer would be willing to pay $10 to the beekeeper. Therefore, this will always produce the most efficient outcome where the marginal social cost equals marginal social benefits.