Topics in matrix analysis
Investigating Dynamic Multifirm Market Interactions in Price and Advertising
Management Science
Management Science
Competition in Service Industries
Operations Research
Strategic Technology Choice and Capacity Investment Under Demand Uncertainty
Management Science
Profit loss in differentiated oligopolies
Operations Research Letters
Manufacturing & Service Operations Management
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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.