Excerpt from Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium Our result is that if at all equilibria the determinant of the Jacobian of the marginal profit functions is positive (subject to some conditions), then there is exactly one equilibrium. Conversely, if there is exactly one equilibrium, the determinant must be non negative. If one rules out the case of a zero determinant, then posi tivity of the Jacobian at all equilibria is necessary and sufficient for uniqueness. This condition on the ...
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Excerpt from Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium Our result is that if at all equilibria the determinant of the Jacobian of the marginal profit functions is positive (subject to some conditions), then there is exactly one equilibrium. Conversely, if there is exactly one equilibrium, the determinant must be non negative. If one rules out the case of a zero determinant, then posi tivity of the Jacobian at all equilibria is necessary and sufficient for uniqueness. This condition on the Jacobian can be interpreted in terms of a firm's marginal profit function. At equilibria, the effect of a small change in a firm's output on its own marginal profits must be greater than the effect on its marginal profits from a similar out put change on the part of all other competitors. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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