A way of thinking about saving vs improving lives
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I think there's an error in your math. You're using log base 10 consistently in your article and the linked spreadsheet, but then you say the derivative of the function log(c)+k is 1/c. If you're using log base 10 throughout, the derivate is 1/(ln(10)*c). If you use log base e throughout, then each value you got for log_10(x) should be multiplied by ln(10) to get the value of ln(x). In either case, we end up with dollar amounts a bit over 2.3 times higher than your calculated values for the value of a marginal life in a pure aggregate utilitarian framework.
Also, nit: the Carl Shulman link is broken. You left off the http:// in the original link on your blog, so it was interpreted as a relative link, which was then copied over here.