Weighted logarithmic utility
= Weighted logarithmic utility
{title2=$\sum_rn_r\log x_r$}
The utility $\sum_rn_r\log x_r$ sums logarithmic utilities over individual flows. Its first-order condition gives <proportional fairness>. Its negative is a <strictly convex function> on active flow rates, giving uniqueness of those rates on a <convex set> of feasible allocations.