Exercise1Answers

Exercise1Answers - EXCERCISES: EXTERNALITIES Here are the...

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EXCERCISES: EXTERNALITIES Here are the solutions to the first exercise. 1. Negative externality. Demand for Q is given by: P = 120-Q The total cost (TC) of producing Q is given by: TC = ½Q 2 Finally, there is a negative externality associated with the production of Q. The value of the total damage (TD) done by the pollution is give by: TD = ¼Q 2 Total surplus is equal to consumer surplus (CS) plus producer surplus (PS) less the total damage to the environment (TD). Consumer surplus Consumer surplus is equal to the area under the demand curve up to the amount of Q consumed (Q) minus the amount paid for Q. The area under the demand curve is given by integrating the demand curve, from zero to Q: P(Q)dQ = 120Q - ½Q 2 The amount paid for Q equals P*Q = (120-Q)*Q = 120Q-Q 2 So consumer surplus is given by: CS = 120Q- ½Q 2 – (120Q-Q 2 ) = ½Q 2 Producer surplus Producer surplus equals total revenues, less the cost of production. Total revenues of producing Q equals P*Q, or: TR = (120-Q)*Q 1
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The total cost is given by TC, above. So producer surplus is given by: PS = 120Q – Q 2 – ½Q 2 = 120Q - 1½Q 2 Total damage Total damage is given by TD, above: TD = ¼Q 2 Total surplus Total surplus equals consumer surplus + producer surplus – total damage: TS = ½Q 2 + 120Q – 1½Q 2 – ¼Q 2 = 120Q – 1¼Q 2 1.a. What is the optimal outcome? The optimal outcome maximizes total surplus. To maximize total surplus, we take the derivative of TS with respect to Q, and set it equal to zero: dTS/dQ = 120 – 2½Q = 0 Q = 48 Thus, the optimal quantity is equal to 48. Price is equal to 120-Q = 120-48 = 72. Plugging 48 into the equation for TS above gives us the total welfare at the optimal
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This note was uploaded on 10/30/2008 for the course ECON 103 taught by Professor Sandrablack during the Fall '07 term at UCLA.

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Exercise1Answers - EXCERCISES: EXTERNALITIES Here are the...

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