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ADDITIVE‐INTERACTION MODELS OF SPATIAL AGGLOMERATION *
Author(s) -
Fujita Masahisa,
Smith Tony E.
Publication year - 1990
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.1467-9787.1990.tb00080.x
Subject(s) - variety (cybernetics) , conjugacy class , economies of agglomeration , series (stratigraphy) , mathematics , computer science , mathematical economics , pure mathematics , economics , artificial intelligence , microeconomics , paleontology , biology
A wide variety of existing models of spatial agglomeration postulate additive‐interaction effects among agents. In this paper, a synthesis of such models is achieved by establishing certain mathematical equivalences between them. In particular, it is shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one‐to‐one correspondence between three classes of existing models, here designated as spatial‐accessibility models, endogenous‐contact models, and fixed‐contact models. These correspondences not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model. A series of examples are drawn from the literature to illustrate these results.