Necessary And Sufficient Conditions for Uniqueness of a Cournot Equilibrium
Necessary And Sufficient Conditions for Uniqueness of a Cournot Equilibrium
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Then a unique Cournot equilibrium exists if and only if for all equilibria, q*, |-J„(h, q*)| > 0.
B It would be desirable to relax the pseudoconcavity of profit assumption. However, without pseudoconcavity, solutions to CP need not be equilibria although all equilibria must solve CP (lemma 1). When we relax pseudoconcavity, we lose existence but not uniqueness.
Corollary 2. 2 : Assume 2 N i) cost and inverse demand are C over R ; and ii) industry output is bounded.
Then if at all q* satisfying ...profit stationarity condition (3), |jD(h, q*)| > 0, then there is at most one Cournot equilibrium. B IV. ECONOMIC INTERPRETATION What is lacking from Theorem 2 and its corollaries is an explicit indication of how the shape of cost and demand functions translate into conditions on existence and uniqueness. In this section we provide that bridge as well as an intuitive interpretation of our results.
2 Theorem 3: With cost and inverse demand function C, then P'(0*) + q*P"(Q*) . , ^ |J (h, q*)| = {1 - Z [ J ]} E [C.
What to read after Necessary And Sufficient Conditions for Uniqueness of a Cournot Equilibrium?
You can find similar books in the "Read Also" column, or choose other free books by Charles D Kolstad to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Then a unique Cournot equilibrium exists if and only if for all equilibria, q*, |-J„(h, q*)| > 0.
B It would be desirable to relax the pseudoconcavity of profit assumption. However, without pseudoconcavity, solutions to CP need not be equilibria although all equilibria must solve CP (lemma 1). When we relax pseudoconcavity, we lose existence but not uniqueness.
Corollary 2. 2 : Assume 2 N i) cost and inverse demand are C over R ; and ii) industry output is bounded.
Then if at all q* satisfying ...profit stationarity condition (3), |jD(h, q*)| > 0, then there is at most one Cournot equilibrium. B IV. ECONOMIC INTERPRETATION What is lacking from Theorem 2 and its corollaries is an explicit indication of how the shape of cost and demand functions translate into conditions on existence and uniqueness. In this section we provide that bridge as well as an intuitive interpretation of our results.
2 Theorem 3: With cost and inverse demand function C, then P'(0*) + q*P"(Q*) . , ^ |J (h, q*)| = {1 - Z [ J ]} E [C.
What to read after Necessary And Sufficient Conditions for Uniqueness of a Cournot Equilibrium?
You can find similar books in the "Read Also" column, or choose other free books by Charles D Kolstad to read onlineMoreLess
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