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Unformatted text preview: EC313Fall 2010 Problem Set 3 solutions (Updated 18 August 2010) Matt Turner 2. 1 1. 3 2. From equation 2 on page 170, the value of a marginal species is: v ( n ) = V ( n + 1 ) V ( n ) = [ pR c ]( 1 p ) n So there are two ways that a change in n can affect the marginal value of a species. A direct effect on the exponent, and an indirect effect on the value of p (if we continue to take p as being optimal). If we ignore the indirect effect which is probably reasonable p is an exogenous parameter, then an increase in the number of species from n 1 to n 2 leads to a decrease in v on the order of ( 1 p ) n 2 n 1 . If we take p = 0.00012, the optimal value when n = 250,000 and ask what happens when n increases from 250,000 to 1.4 million, we see a decrease in the value of a marginal species on the order of ( 1 0.000012 ) 1400000 250000 = 1.0155 10 6 If n increases to 10 million, we see a decrease on the order of ( 1 0.000012 ) 10000000 250000 = 1.539 10 51 . Even though the equation I started with is identical (up to a factor of R ) to the one that the authors claim decreases by 10 41 if n goes to 10 million, I am getting a decrease that is 10 orders of...
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This note was uploaded on 11/04/2010 for the course ESC 313 taught by Professor M during the Fall '10 term at University of Toronto Toronto.
 Fall '10
 M

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