The bees and the orchardA beekeeper lives adjacent to an apple orchard. The orchard owner benefitsfrom the bees because each hive pollinates about one acre of apple trees. The orchard owner pays nothingfor this service, however, because the bees come to the orchard without his having to do anything. Becausethere are not enough bees to pollinate the entire orchard, the orchard owner must complete the pollinationby artificial means, at a cost of $10 per acre of trees. Beekeeping has a marginal costMC = 10 + 5Q, where Q is the number of beehives. Each hive yields $40 worth of honey. a. How many beehives will the beekeeper maintain?
The beekeeper keeps beehives up to the point where the marginal revenue from a the last beehive ($40) equals its marginal cost (10 + 5Q). This is Q such that 10 + 5Q = 40. Solving, we get Q = 6. So 6 beehives are maintained.
b. Is this the economically efficient number of hives? Explain. The economically efficient number of hives would be where marginal social benefit of the beehives equals marginal cost. Since pollination by artificial means costs $10 an acre and a beehive pollinates an acre, the additional benefit of a beehive to the orchard owner is $10. This is the marginal external benefit of beehives. Marginal social benefit equals marginal revenue plus marginal external benefit. So MSB equals 10 + 40 = 50. Setting this equal to MC, we get 10 + 5Q = 50, and Q = 8.
Intuitively, the beekeeper doesn’t maintain the economically efficient number of beehives because he doesn’t take into account the benefit the beehives give to the orchard owner.
c. What changes would lead to a more efficient operation?
The orchard owner could offer to pay the beekeeper $10 each for two extra beehives. Then the beekeeper would get a marginal revenue of $50 from each of the last two hives, and would keep 8 hives. Another possibility is for the two firms to merge.