Each hive of bees can help to raise the value of apple output by $10. Suppose the

Question:

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 cost are given by MC = 30 + 0.5q, where q is the number of hives.
(1) What is the beekeeper's privately optimal number of hives?
(2) What is socially optimal number of hives the beekeeper will have?
(3) What should the amount of subsidy be in order to bring about this socially optimal level of production?