We consider the problem of pricing multiple differentiated products
with the nested logit model and, as a special case, the multinomial
logit model. We prove that concavity of the total profit function
with respect to market share holds even when price sensitivity may
vary with products. We use this result to analytically compare the
optimal monopoly solution to oligopolistic equilibrium solutions.
To demonstrate further applications of the concavity result, we consider
several multiperiod dynamic models that incorporate the pricing of
multiple products in the context of inventory control and revenue
management, and establish structural results of the optimal policies.
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