Resource shadow price calculation under long-term and short-term production

Shadow price has important guiding significance for resource allocation. However, the definition of shadow price is usually associated with short-term production. while the adjustments of multiple resource elements in the long-term production have always been ignored. In this article, the author consider the total revenue function as a piecewise linear function of resource combination, and use the directional derivative to calculate the shadow price in view of short-term production and long-term production respectively. This method is not only suitable for the calculation of shadow price under a single resource element adjustment, but also multiple resource elements adjustments.