Problem:

(Coase Theorem) 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 the marginal pollination cost to the orchard owner is (14-H) dollars per acre, where H is the number of beehives that the beekeeper maintain. The beekeeper has total costs of TC = H2 +10H +10 and the marginal costs MC = 10+2H. Each hive yields $20 worth of honey.

Requirement:

a)  In the absence of transaction cost, could private negotiation achieve socially efficient outcome when there is positive externality? What is the price that the farmer will pay to the beekeeper on a per beehive basis for each additional beehive up to H∗? Show that both the farmer and the beekeeper will be better off after negotiation.

b) There are other potential negotiation mechanisms in addition to negotiating on the per unit price for each additional beehive. One possibility is that the farmer pays a lump-sum fee to the beekeeper for all of the additional beehives (H∗ - H0). What is the minimum lump-sum fee so that that the beekeeper is interested in negotiating? What is the maximum lump-sum fee so that that the farmer is interested in negotiating. 

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