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

Author

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  • Rodrigo Peñaloza

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.

Suggested Citation

  • Rodrigo Peñaloza, 2017. "Hotelling's product differentiation: an infinite-dimensional linear programming approach," Economics and Politics Working Paper Series 72/2017, Economics and Politics Research Group (EPRG), University of Brasília.
    • Handle: RePEc:gvn:eprgwp:722017
    DOI: 10.5281/zenodo.23594446
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality

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