Product Design and Utility Function

Abstract

We theoretically propose new theoretical consistent formulation to unify product design and utility function in the market. As the first step, we introduce the Fermi-Dirac entropy for modularity matrix in product design from statistical mechanics, and show that the entropy for modularity matrix is the number of possible product design to be realized by satisfying both functional requirements and constraints. Next, from information theory, we confirm that the Fermi-Dirac entropy in product design is one of Shannon entropy in information theory even if discretized. As the second step, the entropy for modularity matrix in product design is connected to the market by extended Lancaster’s consumption technology matrix from functional requirements in product design to customer needs in the market. As the third step, the Shannon entropy in product design is identified as one kind of expected utility function as preference in the market, and also the Fermi-Dirac entropy in product design is shown to be equivalent to quasi-linear utility function in economics.