Explanation Cournot with N Firms (1)

# Explanation Cournot with N Firms (1) - a c i 2 bq i b j = N...

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First, observe that market demand is: p ( Q )= a b i = N X i =1 q i where Q = i = N X i =1 q i Each f rm i has therefore the following pro f t function: Π i = p ( Q ) q i c i q i = Ã a b i = N X i =1 q i ! q i c i q i =( a c i ) q i bq i i = N X i =1 q i =( a c i ) q i bq i q i + j = N X j =1 ,j 6 = i q j since Q = i = N X i =1 q i = q i + j = N X j =1 ,j 6 = i q j For example, if i =1 then i = N X i =1 q i = q 1 + j = N X j =2 q j Thus, f nally, the pro f to f f rm i is given by: Π i =( a c i ) q i bq 2 i bq i j = N X j =1 ,j 6 = i q j As a result, each f rm i solves the following program: max q i Π i =( a c i ) q i bq 2 i bq i j = N X j =1 ,j 6 = i q j The f rst-order condition for each f

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Unformatted text preview: a c i 2 bq i b j = N X j =1 ,j 6 = i q j = 0 1 which is equivalent to: a c i bq i bq i b j = N X j =1 ,j 6 = i q j = 0 a c i bq i b q i + j = N X j =1 ,j 6 = i q j = 0 a c i bq i bQ = 0 q i = a c i b Q 2...
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## This note was uploaded on 06/06/2010 for the course ECON 31 taught by Professor Yvez during the Fall '08 term at University of Maine Orono .

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Explanation Cournot with N Firms (1) - a c i 2 bq i b j = N...

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