# PS2_Answers - Environmental Economics(AEM 4510/ECON 4090...

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Environmental Economics (AEM 4510/ECON 4090) Solutions to Assignment #2 1. (a) ( 3 points ) See figure 1 below. Notice the aggregate marginal savings curve. Its derivation and an explanation follows in part (c). (b) ( 1 point ) See figure 1 below. Figure 1: Firm Level and Aggregate MS and MD (c) ( 3 points ) Since pollution is non-rival, aggregate damage is the vertical sum of the individual marginal damage functions: MD T = MD 1 + MD 2 = e + e = 2 e Industry aggregate marginal savings is slightly more complicated. How much is saved between the two firms for a given level of total emissions? This will require a horizontal summation of marginal savings curves, and the answer to this question depends on how emissions are distributed among the firms. Efficiency would sug- gest that this distribution take place as to maximize total savings. The necessary condition for this is the equimarginal principle: marginal savings should be equated across firms to maximize savings from pollution (minimize total cost of abatement). This is imposed here in deriving the aggregate marginal savings function: e 1 = 5 - MS 1 1

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2 e 2 = 8 - MS 2 e 2 = 4 - 1 2 MS 2 Equimarginal principle: MS 1 = MS 2 = MS e 1 + e 2 = e T = 5 - MS + 4 - 1 2 MS e T = 9 - 3 2 MS MS = 6 - 2 3 e T This is the effective aggregate level marginal savings function when emissions are dis- tributed cost effectively. The optimal level of emissions is found where this marginal savings function equals aggregate marginal damage: 6 - 2 3 e = 2 e 6 = 8 3 e e * = 2 . 25 The Pigouvian fee that supports this optimum level of emissions is equal to the level of marginal savings (and marginal damage) at the optimum: fee * = 6 - 2 3 2 1 4 4 . 5
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