question archive Each hive of bees can help to raise the value of apple output by $10
Each hive of bees can help to raise the value of apple output by $10
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Each hive of bees can help to raise the value of apple output by $10. Suppose the market value of the honey from one hive is $50 and that the beekeeper's marginal costs are given by MC=30+0.5qMC=30+0.5q, where qq is the number of hives. (1) What is the beekeeper's privately optimal number of hives? (2) What is the socially optimal number of hives the beekeeper will have? (3) What should the amount of the subsidy be in order to bring about this socially optimal level of production?
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(1) The beekeeper will produce until marginal cost equals the private marginal benefit, which is the market price of honey. Therefore, the equilibrium quantity is determined by 30+0.5q = 50, or q = 40.
(2) In the social equilibrium, the marginal cost equals marginal social benefit, which is the sum of marginal benefit from honey sales plus the marginal benefit from extra apple output = 50 + 10 = 60. Setting 30+0.5q = 60 yields the socially optimal quantity q = 60.
(3) To amount of subsidy should be equal to the value of the uncompensated externality = $10.
