Hotelling's product differentiation: an infinite-dimensional linear programming approach

Rodrigo Peñaloza

No 72/2017, Economics and Politics Working Paper Series from Economics and Politics Research Group (EPRG), University of Brasília

Abstract: We show that Hotelling's (1929) linear city model of product horizontal differentiation can be rewritten as an infinite-dimensional linear programming problem as in Kantorovich (1942). This reformulation of the Hotelling's model allows us to characterize its optimal allocation through duality theory and to characterize total costs in terms of the marginal contributions of the agents, that is, their shadow-prices. We analyse an industry with uniformly distributed firms and an industry where firms are concentrated and show how the total cost in each case is related to the Hirschmann-Herfindahl index.

Keywords: mass transportation problem; shadow-prices (search for similar items in EconPapers)
JEL-codes: C61 D61 L11 L15 (search for similar items in EconPapers)
Date: 2017-07-19
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Persistent link: https://EconPapers.repec.org/RePEc:gvn:eprgwp:722017

DOI: 10.5281/zenodo.23594446

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