(Variant on exercise 8.1 in Phaneuf and Requate) Consider a pollution problem with two sources and two recipient regions. Abatement cost functions are given by Cj(ej)=(ajbjej)2/2bj for j=1,2. The diffusion matrix is given by H=(h11h21h12h22) and the damage function for receptor m is Dm(Am)=dmAm2/2. a. Set up each firm's first order condition under optimal policy and solve for optimal e1 and e2 as a function of the diffusion coefficients hjm, the pollution levels in each recipient region Am,dm,a, and b. b. What are the pollution levels in each recipient region as a function of the diffusion coefficients hjm and emissions from each source, ej ? c. Without doing the algebra, explain in words the steps describing how you could use the results you derived in parts a and b to calculate the optimal emissions level in each recipient region, Am Consider the special case where h11=h22=0. d. Derive the optimal emissions in each recipient region, Am, for this special case e. Interpret the meaning of h11=h22=0 in terms of emissions transport between sources and recipient regions. How does this simplify the regulator's problem of setting optimal policy? (Variant on exercise 8.1 in Phaneuf and Requate) Consider a pollution problem with two sources and two recipient regions. Abatement cost functions are given by Cj(ej)=(ajbjej)2/2bj for j=1,2. The diffusion matrix is given by H=(h11h21h12h22) and the damage function for receptor m is Dm(Am)=dmAm2/2. a. Set up each firm's first order condition under optimal policy and solve for optimal e1 and e2 as a function of the diffusion coefficients hjm, the pollution levels in each recipient region Am,dm,a, and b. b. What are the pollution levels in each recipient region as a function of the diffusion coefficients hjm and emissions from each source, ej ? c. Without doing the algebra, explain in words the steps describing how you could use the results you derived in parts a and b to calculate the optimal emissions level in each recipient region, Am Consider the special case where h11=h22=0. d. Derive the optimal emissions in each recipient region, Am, for this special case e. Interpret the meaning of h11=h22=0 in terms of emissions transport between sources and recipient regions. How does this simplify the regulator's problem of setting optimal policy