Interpretation of Lagrange multipliers in nonlinear pricing problem

We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization problem more efficiently. We also find that the multipliers satisfy a conservation law for each node in the digraph, and the non-uniqueness of the multipliers are connected to the stability of the solution structure.