TY - JOUR
T1 - A nonnegative extension of the affine demand function and equilibrium analysis for multiproduct price competition
AU - Farahat, Amr
AU - Perakis, Georgia
PY - 2010/7
Y1 - 2010/7
N2 - 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.
AB - 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.
KW - Bertrand competition
KW - Differentiated products
KW - Linear demand
UR - https://www.scopus.com/pages/publications/77955666440
U2 - 10.1016/j.orl.2010.04.006
DO - 10.1016/j.orl.2010.04.006
M3 - Article
AN - SCOPUS:77955666440
SN - 0167-6377
VL - 38
SP - 280
EP - 286
JO - Operations Research Letters
JF - Operations Research Letters
IS - 4
ER -