This paper deals with a category of concavifiable functions that can be used to model inelastic traffic in the network. Such class of functions can be concavified within an interval of interest using a quadratic pricing term so that we obtain as a result a concave objective function. We use a game- theoretical framework as well as a centralized optimization approach to discuss the heterogeneous network with nonlinear quadratic pricing. We point out the equivalence between these two frameworks and use a Stackelberg player as an extra degree of freedom to design pricing policy for the network. In the end, we propose an auction-like iterative algorithm and illustrate it with a numerical example.