An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry.The marginal social cost production can be expressed as MSC = 2Q + 30.The consultants calculate the marginal private cost production to be MPC = Q+30.The market demand curve can be expressed as If the consultants have accurately measured the impact of the pollution externality,the change in social surplus from moving to the social optimum (rather than at the private optimum) is

Question

An environmental economic consulting firm is hired to measure the negative externalities associated with the pollution from an industry.The marginal social cost production can be expressed as MSC = 2Q + 30.The consultants calculate the marginal private cost production to be MPC = Q+30.The market demand curve can be expressed as  If the consultants have accurately measured the impact of the pollution externality,the change in social surplus from moving to the social optimum (rather than at the private optimum) is

Quizplus · Accepted Answer

At the private optimum, the marginal private cost (MPC) equals the marginal private benefit (MPB). Thus, Qp +30 = 55 - 5ep (solve for Qp), which gives Qp = 25 - 0.2ep.
At the social optimum, the marginal social cost (MSC) equals the marginal social benefit (MSB). MSC = MSB = 55 - 5ep.
Setting MSC = MSB, we get 2Q + 30 = 55 - 5ep, which gives Qs = 12.5 - 0.5ep.
The change in Q from Qp to Qs is -12.5 + 0.3ep.
The change in social surplus is the difference between the social surplus at Qs and the social surplus at Qp. 
At Qp, social surplus = (55 - 5ep)(Qp/2) = (55 - 5ep)(12.5 - 0.1ep).
At Qs, social surplus = (55 - 5ep)(Qs/2) - (1/2)(2(Qs)^2 - Qp^2) = (55 - 5ep)(6.25 - 0.025ep) - ((2.5 - 0.1ep)^2 - (25 - 0.04ep^2))/2.
Taking the difference, we get the change in social surplus as $37.5.

An Environmental Economic Consulting Firm Is Hired to Measure the Negative