Question

Suppose a beekeeper, who produces honey. Its marginal cost of producing honey is constant, c>0 while its marginal profit decreases with the amount of honey produced - a reflection of a market price that must fall in order for a larger quantity of honey to flow. In addition, the production of honey generates an external benefit for an apple grower, next door to the beekeeper, because of pollination of his orchard. The external marginal profit, b > 0, is also assumed to be constant.

a) Describe and graphically represent the situation described above. In doing so, take care to contrast the balance of the market with the social optimum and explain why they differ from each other.

b) Suppose the two neighbours, the beekeeper and the apple grower, negotiate to jointly determine honey production. The status quo (in the absence of a negotiated agreement) is the market balance found in a) and the negotiating costs are zero. What would then be the minimum payment to be paid to the beekeeper by the apple grower to encourage him to produce the optimum amount of honey? And what would be the maximum amount that could be paid by the apple grower? Represent your answer graphically and detail your reasoning.