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Optimal Product Differentiation in a Circular Model

32 Pages Posted: 6 May 2010 Last revised: 3 May 2016

Qiang Gong

Peking University

Qihong Liu

University of Oklahoma - Department of Economics

Yi Zhang

University of Wisconsin - Madison - Department of Economics

Date Written: April 29, 2016

Abstract

Since circular model was introduced in Salop (1979), it has been the workhorse for analyzing spatial competition among differentiated firms. A common assumption in this literature is that firms are evenly spaced on the circle, even when entry is allowed. We characterize conditions for even spacing to be an equilibrium, using a two-stage (location-then-price) circular model with general transport cost function. Under duopoly competition, we characterize a mild sufficient condition -- the first derivative of transport cost is concave (together with an assumption governing the transport cost difference to the two firms). If one only considers pure strategy equilibrium in prices, this sufficient condition is weakened to the first derivative of transport cost being -1-concave. These conditions ensure that firms' profits are concave in their prices when firms are evenly spaced and that even spacing maximizes profits. Under oligopoly competition (N>= 2 firms), we characterize a necessary condition for even spacing to be an equilibrium. This necessary condition requires a firm's profit to be concave in location at the symmetric location. It involves the third derivative of transport cost function, so having convex transport cost in general is neither necessary nor sufficient to determine equilibrium location choice. Our results have implications for studies employing circular models, especially in terms of welfare analysis which depends on firms' location choices.

Keywords: Product differentiation, Circular model, Location choice, rho-concavity

JEL Classification: D43, L13

Suggested Citation

Gong, Qiang and Liu, Qihong and Zhang, Yi, Optimal Product Differentiation in a Circular Model (April 29, 2016). Journal of Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1600931 or http://dx.doi.org/10.2139/ssrn.1600931

Qiang Gong

Peking University ( email )

School of International Studies
Beijing, 100871
China

Qihong Liu (Contact Author)

University of Oklahoma - Department of Economics ( email )

Norman, OK 73019-2103
United States
405-325-5846 (Phone)

HOME PAGE: http://qliu.oucreate.com

Yi Zhang

University of Wisconsin - Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706
United States
6086093218 (Phone)

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