Question

6. A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard owner 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 = HP + 10H + 10 and marginal costs MC = 10 + 2H where H is the number of hives. Each hive yields $20 worth of honey. a. How many hives would the beekeeper maintain if operating independently of the farmer? b. What is the socially efficient number of hives?

Answer 1

Answer:

A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard owner 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 = H2 +10H +10 and marginal cost

MC = 10 + 2H, where H is the number of hives. Each hive yields $20 worth of honey.

a)

How many hives would the beekeeper maintain if operating independently of the farmer?

Note that each hive yields $20 worth of honey. Hence beekeeper would equate MC = P.

10 + 2H = 20

2H = 10, H = 5

He will maintain 5 beehives independently.

b)

What is the socially efficient number of hives?

Since there is a positive externality, we would reduce the Marginal cost by subtracting MEC of $10 from MC. This gives a new MC = 10 + 2H - 10 = 2H

Hence we have 2H = 20

H = 10

This is the socially efficient number of hives.

c)

In the absence of transaction costs, what outcome do you expect to arise from bargaining between the beekeeper and the farmer?

When there are 5 beehives, farmer earns $100 from $20 per beehive but is able to earn a profit of $50 because he spends $10 per acre (or beehive) for pollination. When there are 10 beehives, he does not incurr any cost. Hence farmer can maximum pay $50 save his $50 from pollination.

The cost incurred by beekeeper from keeping 5 hives is C = (5^2) + 10*5 + 10 = $85. This cost rises to C = (10^2) + 10*10 + 10 = $210. Each beehive is costing $25 more to the beekeeper. Hence this is the minimum amount beekeeper will be willing to accept.

The bargaining price will range from $25 to $50, therefore.

d)

How high would total transaction costs have to be to erase all gains from bargaining?

Any amount greater than the gains from two parties will be the required transaction cost. Since maximum gain is $25, transaction cost greater than $25 will discourage bargaining.