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# ps3_sol - EC313-Fall 2010 Problem Set 3 solutions(Updated...

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EC313-Fall 2010 Problem Set 3 solutions (Updated 18 August 2010) Matt Turner 2. 1

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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 λ R ) to the one that the authors claim decreases by 10 - 41 if n
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ps3_sol - EC313-Fall 2010 Problem Set 3 solutions(Updated...

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