Multiple Lagrange multipliers in nonlinear programming usually lead to incorrect computation of shadow price of resources. This paper proves that the minimum Euclidean norm Lagrange multiplier is the shadow price. Moreover, an unconstrained optimization model is proposed to model the minimum Euclidean norm Lagrange multiplier. Finally, asubgradient-based algorithm is proposed to compute the shadow price. This algorithm is sub-linearly convergent, and the computational time grows linearly with the number of constraints and variables.