Why are firms sometimes unwilling to reduce costs

This paper identifies the environments in which it does not pay for a multiproduct firm to engage in small cost reductions. Specifically, it shows that a multiproduct Bertrand firm's profits will decrease in response to a small reduction in one product's marginal cost if and only if the output share of the cost-reducing unit is below a threshold. Because cost reductions by a single-product firm or by a multiproduct Cournot firm always increase the firm's profits, this result is unique to multiproduct Bertrand firms.