The Hotelling locational model and its adaptations to a circular city provide a core framework for research in industrial organization. The present paper expands the explanatory power of this model by incorporating a continuum of consumers with constant-elasticity demand functions along with stores that have constant marginal costs of production. The stores are evenly spaced in equilibrium. The model generates a simple formula in which the markup of price over marginal cost depends on the spacing between stores and a transportation-cost parameter but is independent of the elasticity of demand. This result reflects pricing decisions by stores that factor in the threat of losing business entirely at the borders with neighboring stores. The free-entry solutions for the number of stores and their spacing approximate socially optimal values but quantities of goods consumed are inefficiently low.
Authors
- Acknowledgements & Disclosure
- I have no sources of funding to disclose. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research.
- DOI
- https://doi.org/10.3386/w32660
- Pages
- 21
- Published in
- United States of America
Table of Contents
- NBER WORKING PAPER SERIES 1
- MARKUPS AND ENTRY IN A CIRCULAR HOTELLING MODEL 1
- Robert J. Barro 1
- Working Paper 32660 httpwww.nber.orgpapersw32660 1
- NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge MA 02138 July 2024 1
- I have no sources of funding to disclose. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. 1
- Markups and Entry in a Circular Hotelling Model Robert J. Barro NBER Working Paper No. 32660 July 2024 JEL No. L1L12L13 2
- Robert J. Barro Department of Economics Littauer Center 218 Harvard University Cambridge MA 02138 and NBER rbarroharvard.edu 2
- I. Circular Hotelling Model 3
- H H 3
- N j 3
- N N 4
- P j 5
- P P 5
- ๐๐ ๐ง๐ง ๐๐ ๐ก๐ก 5
- ๐๐๐ง๐ง ๐ด๐ด ๐๐ ๐ง๐ง 5
- ๐๐๐ง๐ง. 6
- ๐๐ ๐๐๐ง๐ง๐๐๐ง๐ง 6
- ๐๐ ๐๐ ๐ก๐กโ 6
- P Q 6
- ๐๐ 1 ๐ก๐ก 6
- ๐๐ ๐ก๐กโ 6
- ๐๐ ๐๐ ๐๐๐๐ ๐ท๐ท 6
- ๐ท๐ท 0 ฮฆ 6
- ๐๐ ๐๐ ๐๐ 7
- ๐๐ ๐๐ ๐ก๐กโ ๐๐ ๐๐๐๐ ๐๐ ๐ก๐กโ 7
- P Pz 7
- P tz 7
- ๐ก๐กโ ๐๐ 7
- ๐๐ ๐๐ 7
- P ฮท1 7
- II. Hotelling Effect at the Borders 8
- 1 ๐ก๐ก 8
- ๐๐ ๐๐ ๐ก๐กโ ๐๐ ๐๐๐๐ 9
- ๐๐ ๐๐ ๐ก๐กโ 9
- Q P 9
- X N 10
- 2h. 10
- III. Free-Entry Condition 11
- P Q 11
- ๐๐ ๐ก๐กโ 11
- ๐๐ 2โ๐ด๐ด๐๐ ๐ก๐กโ 11
- ๐๐ 2๐ก๐ก๐ด๐ดโ ๐๐ ๐ก๐กโ ๐ท๐ท 11
- ๐๐ 0 11
- ๐๐ 0 11
- N N 11
- ๐๐ 0 11
- ๐ด๐ด๐๐ 12
- N H 12
- ๐ด๐ด๐๐ 12
- ๐๐ ๐๐ 12
- ๐ท๐ท ๐ด๐ด๐๐ 12
- ๐ด๐ด๐๐ 13
- IV. Socially-Optimal Entry 13
- 2h N 13
- P ctz 13
- 2h qz 14
- 2h N 15
- P ctz 15
- Pctzth th 15
- V. Summary 15
- H N 15
- PPtz P 15
- N H H 16
- References 17
- Econometrica 17
- Quarterly Journal of Economics 17
- Journal of Political Economy 17
- Contestable Markets and the 17
- Theory of Industrial Structure 17
- Journal of 17
- Political Economy 17
- Economic Journal American Economic 17
- Review 17
- Review of Economic Studies 17
- Rand Journal of Economics 17
- Bell Journal of 17
- Economics 17
- Bell 17
- Journal of Economics 17
- Capitalism Socialism and Democracy 17
- Journal of Political 17
- Economy 17
- Review of Economic Studies 17
- The Theory of Industrial Organization Microstatics 18
- Appendix 19
- Social-Planner Problem 19
- ๐๐๐ง๐ง ๐ด๐ด ๐๐ ๐ก๐ก๐ง๐ง ๐บ๐บ๐ง๐ง 19
- ๐บ๐บ๐ง๐ง 19
- ๐๐ ๐ก๐ก๐ง๐ง ๐๐๐๐ 19
- ๐บ๐บ๐ง๐ง 19
- ๐บ๐บ 2 19
- ๐๐๐ง๐ง 19
- ๐๐ ๐๐ ๐ก๐กโ . 19
- NH2h 20
- Nฮฆ h 20
- ๐๐๐๐๐ก๐ก ๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐ ๐ ๐ ๐ ๐๐๐๐ 20
- ๐๐ ๐๐ ๐ก๐กโ 20
- ๐๐ ๐๐ ๐ก๐กโ 20
- ๐๐ ๐ก๐กโ 20
- ๐ด๐ด๐ก๐กโ ๐๐ 20
- Figure 1 21
- Salop-Hotelling Circular City 21
- H N 2h. h 21
