Equivalence between Cost and Production Functions by the Mizutani Cost Functons to Different Industrie Structures : What Can We Learn?

The duality between cost and production function can be a key point to explore regulation process in Agent-Principal model because the Principal observes outputs in inputs and has asymmetric information about the cost by the Agent. This paper investigates the properties of production functions related with cost functions proposed by Mizutani (2020) to different industry structures using some properties explained in cost production duality problem to linear models. The motivation to this investigation is to have more parameters to understand how to regulate network industries observing production can be used to purpose politics of separate or integrate railways structures. The results indicate that production function must have bounders as structures of the railway industry changes from the integrated to separated depending on the competition, density, scope and scale. The paper can be extended with increasing and decreasing returns of scale