Consider a beekeeper that is deciding how much honey to produce. The beekeeper gains a benefit from producing honey, represented by the marginal benefit function and which is given by:

MB= 300 - 6Q

Where Q is barrels of honey.

In addition, she has a marginal cost function, which reflects her cost of producing honey; this is given by:

MC= 40 + 4Q

The beekeeper’s total profit function is given by:

Profit= 360Q + Q^2

The more honey the beekeeper produces, the more bees there are to pollinate a neighboring apple orchard. Thus, in addition to the private benefit accruing to the beekeeper herself, there is also a marginal external benefit to the apple orchard, which is given by:

MEB= 100 - 2Q

And a total external benefit to the apple orchard given by:

TEB= 100Q - Q^2

a. Find an expression for the social marginal benefit (SMB) in this case, defined as you think appropriate. Calculate the level of honey production that will arise if the beekeeper acts in her self-interest only. Calculate the socially efficient level of honey production as well.

b. Suppose that the beekeeper and the owner of the apple orchard enter into negotiations. The orchard owner wants to offer a payment to the beekeeper to change honey production from her self-interested production level to the socially efficient level (all at once). What is the maximum total payment that the orchard owner would be willing to pay for this overall change? What is the minimum total payment that the beekeeper would require before making this overall change?

c. Assume that, if a deal is reached, each party must pay $35 in legal fees to finalize it. If there are no additional transaction costs, will the socially efficient quantity be reached? Explain.

d. Irrespective of your answer to part c, assume that the beekeeper and the orchard owner come to a private agreement to set honey production at the socially efficient quantity. However, now suppose that a policymaker reads somewhere that honey production provides a positive externality to apple orchards, and therefore decides that the beekeeper should be provided with a production subsidy for each unit of honey that the beekeeper is willing to produce. With this subsidy in place, the beekeeper decides to increase production by an additional 5 barrels. Calculate the associated efficiency loss.