Ec383 - Problem set 3
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Ec383 - Problem set 3
Consider a spatially differentiated pollution problem as in section 5.8 of Perman et al.
Assume that there are two pollution sources (N=2) and two receptors (J=2).
Let the D matrix of transfer coefficients be
D = 
, = . 3(2)
2(4) , :
a. Write an expression for the total pollution concentration at receptor 1 (A1 ) and one for the total pollution concentration at receptor 2 (A2 ).
Assume that the pollution damage function Dj (Aj ) is the same for the two receptors and is given by
Dj (Aj ) = 
for j = 1; 2:
Assume that the pollution benefit function Bi (Mi ) is the same for the two sources and is equal to
Bi (Mi ) = 344Mi 一 
Mi2 for i = 1; 2:
b. Using the above assumptions on Dj (Aj ) and Bi (Mi ) ; write an ex- pression for the total net benefits function that a social planner wants to maximize.
c. Using the expressions for (A1 ) and (A2 ) calculated in part (a), rewrite the net benefit function as a function of M1 and M2 :
d. Write an expression for the marginal pollution damage for each re- ceptor, D
(Aj ) ; and one for the marginal pollution benefit at each source, B
(Mi ).
e. Write the two marginal conditions for an e¢ cient solution (expression 5.13 in the textbook) using all the above assumptions.
Calculate the efficient level of emissions at each source and the corre-
sponding level of pollution at each receptor..
2022-12-03