by **Jeroen** » Fri Feb 02, 2018 9:25 am

Nice cartoon!

But I would disagree with the statement "Utility remains constant" given the graph. It would seem "Desire to help", Y, is negatively correlated with "Ability to help", X. So Y = A - B*X. When you define utility as the product of "Desire to help" and "Ability to help", it follows that utility = Y * X = A*X - B * X^2. This formula has a local maximum when the derivative equals zero, so at A - 2*B*X = 0. It follows that utility of children grows until the age where ability to help equals A /(2*B) , after which it decreases again. So maybe if we can quantify the parameters of this system, we can find a way to trap our children forever in the state where utility is maximised?

Nice cartoon!

But I would disagree with the statement "Utility remains constant" given the graph. It would seem "Desire to help", Y, is negatively correlated with "Ability to help", X. So Y = A - B*X. When you define utility as the product of "Desire to help" and "Ability to help", it follows that utility = Y * X = A*X - B * X^2. This formula has a local maximum when the derivative equals zero, so at A - 2*B*X = 0. It follows that utility of children grows until the age where ability to help equals A /(2*B) , after which it decreases again. So maybe if we can quantify the parameters of this system, we can find a way to trap our children forever in the state where utility is maximised?