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2008_02_28_Solutoins

# 2008_02_28_Solutoins - One can maximize net beneﬁts of...

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Unformatted text preview: One can maximize net beneﬁts of pollution or net benefits of abatement, for same result If maximizigg net benefits of mllution M, B(M) is the surplus gain from being allowed to polute more. E.g. increased PS from reduced production costs and possibly increased PS and CS from increased goods output. . For clarity, we often assume goods output is constant, so B(M) is just cost savings from reduced emission control costs. In this case we call it S(M). C(M) (or “D(M)”) is the damages from pollution A If maximizing net benefits of abatement Z = ﬂu - M, B(Z) is the beneﬁts of abatement in the form of reduced damages from pollution. C(Z) is the loss in PS and possibly CS from having to change production to curtail pollution. 4' , \$ 64/3 45"] Whywewill MS: MAC ‘“ (13 K Lagrange multiplier method for constrained optimization " 0 with equality constraint ‘ , . Ex: Maximi e area of rectan Wig} F(X,Y) H” a. H Subject to G(X,Y) = K 5.1. 8H! s to K-Gllsﬂ:0 Step 1: Form Lagrangian L=|i§XY)+A K—czgxy B-HI’ADO-vaj o J I )Y) . u + 1' K" Step 2: Take derivative with ”J. 3.. H ,, g) g Q respect to each control H: & , )3 g 0 variable and A (lambda). This A: 26- 5- H - 0 gives you system of ' simultaneous equations. H g A § g , A / Step 3: Solve that system for H: 3 each control variables: 20., 3- (B) 3 0 ’ f 20 = 25 Step 4 (if desired): Solve for A .: H : 5 9- l0 lambda. It is rate at which 1,"? Imme \$31., 2 maximized value of F(X,Y) M“ 3+ H = 22 increases, ifKincreases. A". s M‘” = ’2’ V3. I60 Kahuna-ell! 2 r a. ’ - 9x1 6% IN ...
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