PS14+homework - Intermediate Microeconomics 2010 Problem...

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Intermediate Microeconomics, 2010 Problem Set 14: Homework Due Mon/Tues March 8/9 1. Negative externalities. Consider the following quasilinear economy: A rm can produce metal at costs c ( q s ) = 1 4 ( q s ) 2 . Metal production leads to gunk: For each unit of metal, the rm also releases e ( q s ) = 2 q s units of gunk. A consumer has preferences over metal, money, and gunk: U m; q d ; q s = m + v q d e ( q s ) = m + 10 q d 1 4 q d 2 2 q s : The initial income of the consumer is Y = 0 (Recall: Negative m is ok and will happen here.) (Also recall: You have actually seen part of this economy before. On problem set 12 we looked at a version of this economy without the externality.) (a) Find the demand and supply functions, D ( p ) and S ( p ). Derive the compet- itive allocation x . What is the surplus in the competitve allocation? (The surplus with an externality is S ( q ) = v ( q ) c ( q ) e ( q )).
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