Recently, the paper Identifying and computing shadow prices in case of multiple Lagrange multipliers, co-authored by Tao Jie and Gao Yan in the business school of USST, was published in the Journal of Management Science in China (JMSC). The JMSC is recognized as an authoritative journal in management science in China, and it is also a Class A journal among the TOP journals of the business school.
The notion of the shadow price, which was proposed independently by Tinbergen and Kantorovich in 1930s, is a common tool for pricing of public goods. The shadow price can be computed by the Lagrange multiplier when the latter is unique. However, the equivalence of shadow prices and multipliers fails to hold when the Lagrange multipliers are multiple, which causes difficulty to compute shadow prices. In this paper, we provide a method to identify shadow prices in the multiple Lagrange multipliers’ case, and propose a gradient descent type algorithm to compute shadow prices. The findings can be applied as a guidance for public goods pricing in the area of economics and management.
