A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard owner

Question

since the bees pollinate the apple trees: one beehive pollinates one acre of orchard. Unfortunately, there are not enough bees next door to pollinate the whole orchard and pollination costs are $10 per acre. The
beekeeper has total costs of TC = H
2 + 10 × H + 10 and marginal costs MC = 10 + 2 × H where H is the
number of hives. Each hive yields $20 worth of honey. (In the space below, draw a graph with H on the
horizontal axis and cost/benefit on the vertical axis.)
1. How many hives would the beekeeper maintain if operating independently of the farmer?
2. What is the socially efficient number of hives?
3. In the absence of transaction costs, what outcomes do you expect to arise from bargaining between
the beekeeper and the farmer?

Answer 1

1. If the beekeeper operates independently of the farmer, they will maintain a number of hives that maximize their profit. We can find the profit-maximizing level of production by setting the marginal cost (MC) equal to the marginal revenue (MR). The beekeeper's revenue per hive is $20 worth of honey, so MR = 20.

MC = 10 + 2 × H
20 = 10 + 2 × H
10 = 2 × H

Therefore, H = 5 hives.

2. The socially efficient number of hives would take into account the pollination benefits to the farmer. Given that pollination costs for the farmer are $10 per acre and each hive pollinates one acre of orchard, the farmer benefits by $10 for each additional hive. The marginal external benefit (MEB) is $10. The marginal social benefit (MSB) is the sum of MR and MEB, so MSB = 20 + 10 = 30.

We can find the socially efficient number of hives by setting MSB equal to MC:

30 = 10 + 2 × H
20 = 2 × H

Therefore, H = 10 hives.

3. In the absence of transaction costs, we would expect the beekeeper and the farmer to reach a mutually beneficial agreement through bargaining. The beekeeper would likely increase the number of hives to the socially efficient level of 10, as the farmer would be willing to pay for the additional pollination benefits provided by the extra hives. This would lead to an agreement in which the farmer compensates the beekeeper for the additional costs associated with maintaining more hives, while both parties benefit from the increased pollination of the orchard and production of honey.