> As another commentor says, it simply can't be that marginal productivity drops to zero.
It can even fall below zero. Imagine the totally overworked surgeon killing his patient because of fatigue and total exhaustion. His net productivity has fallen, reducing the outcome of the last 12 hours.
No, that's 'just' a bad outcome of his productivity.
His contribution to 'product' is providing the service of surgery; he has done that.
But yes, overworked and tired surgeons are more likely to kill patients; killing patients bad; overworking surgeons bad. (It's just not a 'productivity' issue.)
It can even fall below zero. Imagine the totally overworked surgeon killing his patient because of fatigue and total exhaustion. His net productivity has fallen, reducing the outcome of the last 12 hours.