You get old, get sick, and die, though some unfortunate people skip the first step.
In the sickness before your death, you consume a lot of society's resources, without producing much. (Note that calculating value is very tricky: you may be producing value as a beloved grandparent without directly producing visible economic output. The value is reflected in the output of those who love you.)
After you die one can counterfactually figure out when was the socially optimal point in time you should have taken euthanasia. Repeat the calculation with many lives and deaths and find a pattern.
If there is a pattern, and the answer isn't "never" (it could be), consider encouraging euthanasia at the optimal point.
However, this is likely a bad idea, for necessity drives invention, inventions to reduce the cost, or even cure, an illness, ultimately to produce longer, healthier lives. Euthanasia decreases that necessity.
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