Question

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?

b)What 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?

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

Answer 1

The cost of pollination is $10 per acre, price of hives yield and the MC of beekeeping is 10 + 2H. Therefore, the amount of hives that beekeeper would maintain by operating independently is determined at a point where P = MC. That is, 20 = 10 + 2H which means Hives = 5 units.

(b) the socially efficient number of hives is 10.

(c) When P = 20, Profit = Price * Quantity of Hives - TC of hives; that is, 20 * 5 - (5^2 + 10 * 5 + 10) which is $15.

(d) When P = 30, Profit = Price * Quantity of Hives - TC of hives; that is, 30 * 10 - (10^2 + 10 * 10 + 10) which is $90.