Class+14+Partial+Equilbrium+IV+_Pollution%2C+Public+Good_bw

Class+14+Partial+Equilbrium+IV+_Pollution%2C+Public+Good_bw...

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Partial Equilibrium IV: Pollution Taxation and Pollution, Taxation and Public Goods
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Administration Thank you for your participation in the feedback Thank you for your participation in the feedback. After spring-break: General Equilibrium (Edgeworth Box) You should prepare yourself by reading: Perloff, Section 10.2, 10.3 (Trading between two people, pp 330-340 and/or Varian, Chapter 31 (Ctools/general information). There is little time after the spring break and before the ne t midterm Take o r time to read There is little time after the spring break and before the next midterm. Take your time to read the chapters. Administration
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Pollution
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Pollution (Negative Externalities) The consumer is directly affected by the output of the firm: Example Economy Y=10 U( D S ) 5 ! D 0 5 S U (m, q d , q s ) = m + v(q d ) – e (q s ) ! If firm produces q s limes, consumer utility ( ) U(m,q ,q ) = m + 5 q - 0.5q c(q S )= (q S ) 2 Externality: e (q s ) = 0 5q s is reduced by e (q s ) . Negative Externality: Externality: e (q ) 0.5q What is the competitive allocation? Is the competitive allocation Pareto efficient? The utility of one agent (consumer) depends not only on his own consumption/production choice but also on the consumption/production choice of others consumption/production choice of others. Pollution
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! " 5 2 D P q q # ! " S P q ! " ! " ' S P q e q $ Price p* q * quantity Deadweight Loss Competitive Allocation Just as before: In a competitive market, the quantity traded is q* 1 16 Competitive Allocation with Pollution: Same as before: A price p* such that D(p*)=S(p*) Th t k th i * d s i traded is q*=1.16 Allocation: A*= [1.16, 1.16, 1.35 ,7.31] The consumer takes the price p* and q as given and maximizes utility by choosing the optimal q d : max U (m, q d , q s ) s.t. Y " m + pq d Th fi t k th i d d i d The firm takes the price and q as given and maximizes profits by choosing the optimal q s : max ! = pq s – c (q s ) Pollution: Graphical
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Competitive Allocation: Efficient? The competitive allocation is not efficient: Competitive Allocation: A*= [1.16, 1.16, 1.35 ,7.31] Alternative Allocation: A’= [1, 1, 1.35 , 7.65 ] A’ Pareto Dominates A*: (i) A’ is feasible: S D - q =q (everything that is consumed, is produced) - Y – c(q) = m + ! because 10 – (1) 2 = 7.65 + 1.35 = 9 (ii) No one is worse off and the consumer is strictly better off: Additional Utility: 0.04 Profit of the firm is the same: In both cases, ! = $1.35 ! " ! " ! " ! " ! " ! " * 7.31,1.16 7.31 5 1.16 0.5 1.16 12.115 ' 7.65,1 7.65 5 1 0.5 1 12.15 U A U U A U # # $ % # # # $ % # Utility of the consumer: Pollution: Pareto Improvement
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