Bee keepers in your state have been complaining that the che

Bee keepers in your state have been complaining that the cherry orchard owners are killing bees when they spray cherry trees for pests. you estimate that the private marginal benefit your residents enjoy from cherry consumption is PMB=306-4Q and the private marginal cost of cherry production is PMC=4Q where Q is pounds of cherries. Using data from the bee keepers, you calculate that the marginal external damage to their livelihood associated with cherry production is MD=20+2Q.

1) what tax T should you set to achieve the social optimum?

Please include an explination with your answer. Thanks!

Solution

The economically efficient quantity is the quantity at which private marginal benefit is equal to the private marginal cost

PMB = PMC

306-4Q = 4Q

8Q = 306

Q = 38.25 units

The tax T that should be set to achieve the social optimum should be equal to the marginal external damage

MD = 20+2Q

MD = 20 + 2 X 38.25

Tax = $ 96.50