期刊
OPERATIONS RESEARCH LETTERS
卷 38, 期 4, 页码 280-286出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.orl.2010.04.006
关键词
Differentiated products; Bertrand competition; Linear demand
资金
- National Science Foundation [0758061-CMII, 0824674-CMII, EFRI-0735905]
- Singapore MIT Alliance
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0758061] Funding Source: National Science Foundation
We derive a nonnegative extension of the affine demand function for differentiated substitute products from the optimization problem facing a representative consumer whose utility function is quadratic. We show that the extended demand function reduces to a linear program. The linear program has a simple intuitive interpretation in terms of a shifted price vector. We prove the existence and uniqueness of the Bertrand equilibrium in oligopolies consisting of multiproduct firms under the proposed demand function. The equilibrium, available in closed form, coincides with that obtained when allowing negative demands. (C) 2010 Elsevier B.V. All rights reserved.
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