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A beekeeper and the owner of an orange orchard have a synergistic relationship. The beekeeper benefits from putting his beehives in the orchard since his bees make honey from the orange blossom pollen. The orchard owner benefits from having the beehives in his orchard since the bees pollinate his trees. There is a reciprocal positive externality. The table below gives the profit of the beekeeper and the orchard owner as a function of the number of beehives that the beekeeper places in the orchard, before any transfer between them.
0 1 2 3 4 5 6 7
Beekeeper 0 4 8 11 10.5 7 3 -1
Orchard 0 1 2 3 4 5 6 7
Sum 0 5 10 14 14.5 12 9 6
a) What is the efficient number of beehives to have in the orchard? Assume that the above table is common knowledge to both the orchard and beekeeper, that bargaining is costless, and that there are no other orchards or beehive owners.
b) Suppose that the orchard owner has property rights to his orchard, so that the beekeeper has to obtain the orchard owner’s permission to put his beehives in the orchard. What is the equilibrium number of beehives in the orchard? How much will the orchard owner charge to have the beehives in his orchard? Is the equilibrium efficient?
c) Suppose that the beekeeper has the property right to place his beehives in the orchard. What is the equilibrium number of beehives in the orchard? How much will the orchard owner pay the beekeeper? Is the equilibrium efficient?
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