PS7sol - Econ 100B Problem Set 7 Externalities Open Access...

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Econ 100B Problem Set 7: Externalities, Open Access, and Public Goods 1. Consider the example of the upstream &rm producing X and downstream &rm produc- ing Y that we solved in class, except now P Y =50 X = f ( L X ) = L 1 = 2 X ;Y = g ( L ; X ) = 4 L 1 = 2 Y & 0 : 1 X 2 ;P X = 400 ;w = 10 (a) Find the employment and output in the two industries under competition. X = P X X wL X = 400 L 1 = 2 X 10 L X @ X @L X = 400 ± (1 = 2) L 1 = 2 X 10 = 0 L X = 400 ;X = 400 1 = 2 = 20 Y = P Y Y wL Y = 50(4 L 1 = 2 Y & 0 : 1 X 2 ) 10 L Y @ Y @L Y = 50 ± 4 ± (1 = 2) L 1 = 2 Y 10 = 0 L Y = 100 ;Y = 4 ± 100 1 = 2 & 0 : 1 ± 20 2 = 0 marginal products of labor are equated. P X X wL X + P Y Y wL Y = 400 L 1 = 2 X 10 L X +50(4 L 1 = 2 Y & 0 : 1 X 2 ) 10 L Y = 400 L 1 = 2 X 10 L X + 50(4 L 1 = 2 Y & 0 : 1 L X ) 10 L Y @ @L X = 400 ± (1 = 2) L 1 = 2 X 10 50 ± 0 : 1 = 0 L X = 1600 = 9 ;X = 40 = 3 @ @L Y = 50 ± 4
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This note was uploaded on 04/07/2008 for the course ECON 100B taught by Professor Rauch during the Fall '07 term at UCSD.

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PS7sol - Econ 100B Problem Set 7 Externalities Open Access...

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