Why Are Firms Sometimes Unwilling to Reduce Costs?

This paper establishes three new results for multiproduct oligopolies: 1) it presents the first explicit expression of Nash equilibria for asymmetric multiproduct oligopolies; 2) it shows that reducing a multiproduct firms cost in Bertrand oligopolies will reduce its profits if the cost-reducing unit is sufficiently small; and 3) it demonstrates that a multiproduct firm has no incentive to eliminate a product whose sales are zero. Because a single-product firm whose sales are zero is indifferent between exiting and staying, and its cost reductions always increase its profits, our results are unique to the multiproduct firm, and they suggest that extending oligopoly studies from a single product to multi-products could be as significant as the extension of calculus from a single variable to multi-variables.