Chapter 9 pollution p level of pollution dp damage

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Chapter 9 Pollution P : level of pollution D(p): damage resulting from pollution MD(p): damage resulting from an additional unit of p Additional pollution harmful for residents, but benefits factories ($ made from cleaning pollution) See figure 9.2 Marginal Damage Curve Increasing function of pollution D(p) X-axis is P, Y-axis is $ Area under MD curve up to pollution level P’ is total damage attributable to that level of pollution Area is D’(p) Marginal benefit function (MB(P)) See figure 9.3 Pollution abatement (cleaning up pollution) costs the factory Reducing pollution from P(bar) to the left to p’ costs A under the MB(P) line to the firm -Allowing pollution to increase from 0 to p’ benefits space B under the MB(P) line Under MB(p) negative sloped line: (Area B is left of P’, Area A is right of P’) Total cleanup from P(bar) to 0 equals A+B See figure 9.4 The socially optimal level of pollution At P(bar), no money is spent on pollution abatement (where MB curve reaches 0 on P horizontal axis) Total damage equals C + E + F (total area under MD curve, positive sloping from 0,0 up to P(bar)) Socially optimal level found by interest of residents and firm MB curve must be higher than MD from society’s desired pollution level Where MB and MD curves intersect is P*, the socially optimal level of pollution F: loss in social surplus (above MB and Below MD curve) A: social surplus is maximum (above MD curve and below MB curve) Achieving social optimum P* cannot be achieved without government intervention, two forms of it 1. Pollution standard (maximum allowable level) equal to P*, firm would choose this maximum a. Gov must know P*, must know MB and MD curve i. Requires medical experts to compute health damage by pollution ii. Hire engineers to compute abatement costs required to achieve levels of P iii. Gov derives two curves to find P* 2. Pigouvian Tax(Arthur Pigou) a. Firm charged tax (t) per unit of pollution, so pollution would generate tax liability of (tP) b. Set t equal to the height of the social optimum level ($ or Y-axis equilibrium of MD and MB) c. Benefit is lower since t must be paid on each unit d. Marginal Benefit of pollution is MB(P) - t at pollution level P. now MB - t = 0, means MB = t e. See figure 9.5
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f. Another method: total tax liability at each level of P; tax liability = D(p) g. Firm’s MB from additional unit of pollution, net of tax, is MB-MD i. Firm increases this pollution until MB=MD ii. Firm choose p* h. Gov only needs MD curve i. Firm pay area under MD curve behind p*(C), gain from not cleaning up above MD curve behind p*(A) Clean factory’s MB curve is lower than Dirty factory’s MB curve. MBc is clean, MBd is dirty (for MB curves) A different P* exists for each factory, dirty or clean MB and MD curves needed for Pigouvian taxes (t c and t d ) Non-pigouvian tax, only MD curve needed to be known Another approach: set different pollution standards for clean and dirty factories New pollution standard for both factories = p**, between Pc* and Pd* See figure 9.6 Surplus loss would be H+J, J= area under MD curve and above MBc curve between Pc* and P**
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