A monopolist produces a good x and pollution as a by-product. The production of x units of the good generates x gross emission units (i.e. EG= x). Assume the existence of an abatement technology that can reduce emissions by an arbitrary amount 0 ? ERx (? EG). Hence, net emissions are given by E = EG - ERx.

Environmental damages are assume to be given by D(E) = 5E2. The marginal private cost function and the inverse demand function are assumed to be given by MPC(x) = 10 and P(x) = 110 - 5x. Marginal abatement cost by application of the abatement technology are given by MAC(ERx) = 5ERx.

a) Determine the socially optimal gross and net emission level EG** and E**

b) Determine the unregulated equilibrium emission level, EM

c) To induce the socially optimal emission level E**, the government considers charging an emission tax. Determine the appropriate tax level tM and the corresponding gross emission and abatement level of monopolist.