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b/CurrentWriting/sections/03_SurvivalAnalysis.tex index c98b806..10d8307 100644 --- a/CurrentWriting/sections/03_SurvivalAnalysis.tex +++ b/CurrentWriting/sections/03_SurvivalAnalysis.tex @@ -31,8 +31,8 @@ The marginal survival rates when a given constellation $i$ changes size are: =& \sum_{i=1}^N \left[ \frac{R_i}{S_t} \right] - \frac{R}{S_t} +\sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{} \label{EQ:i} \end{align} -Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival rate- -across constellation operators. +Note that $ \sum_{i=1}^N \frac{ s^i_t}{ S_t} \parder{R_i}{s^i_t}{}$ is the weighted, average marginal survival +rate across constellation operators. The derivation of \cref{EQ:i} is in Appendix \ref{APX:Derivations:SurvivalRates}. Direct comparison between the marginal survival rates of an individual operator and the social planner's fleet cannot proceed further without specifying the functional loss forms $l^i(\cdot)$

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