= Discounted infinite-horizon utility integrability
{title2=$b>0,\ L\leq U\leq R\ \Longrightarrow\ \int_0^\infty e^{-bt}|U(c_t)|dt<\infty$}
Finite lower and upper utility bounds together with a positive discount rate bound the absolute time integral by $\max(|L|,|R|)/b$. This justifies <expectation> and integration in marginal-utility verification. Bounded utility alone on an undiscounted infinite horizon does not prevent both positive and negative parts from having infinite integral.
Back to article page
