Abstract
This paper provides the smallest upper bound or the critical level for a Cournot firm's market share below which its cost reduction reduces welfare. It shows that a firm's cost reduction increases social welfare with nonlinear demand and nonlinear costs if and only if its market share is above the critical level, which is equal to a weighted sum of the other firms' market shares. The paper also reports similar results for technological spill-overs within any given set of firms.
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