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- b(q, + 92 +...+ qy)-c)q, - 9N)-c- bq, =0 + 9N)-c %3D lim n→∞ \n + 1, 1 = 0 lim n→∞

- b(q, + 92 +...+ qy)-c)q, - 9N)-c- bq, =0 + 9N)-c %3D lim n→∞ \n + 1, 1 = 0 lim n→∞

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 16E
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The Chinese government has created a fund worth more than 20 trillion won to foster the semiconductor
industry. Although there is a large technological difference between memory semiconductors, system
semiconductors can be developed in a short period of time. The number of companies producing
homogeneous quality products has increased.
￭Question (a) In the Cournot game, when the number of firms increases from 2 to n, compare the output,
total output, and profit of each firm with N.E. in the Cournot model. 
￭Question (b) If the number of companies participating in the semiconductor market increases to infinity,
that is, in a perfectly competitive market, what will be the equilibrium point?

In the case of n22, firms: MaxII, (q,..g) = (a - b(q, + 92 + ...+ qy)-c)q, FOC: a – b(q, + q, +...+q,)- c - bq, = 0 а -b(q, +...+ 9N) -с 2b If all firms are symmetric: 4 = 92 = ... = AN = 9 • When n becomes infinity: 1 n lim lim n→∞ \n + 1 lim n→0 \n + 1 = 0 = 0 = 1
Transcribed Image Text:In the case of n22, firms: MaxII, (q,..g) = (a - b(q, + 92 + ...+ qy)-c)q, FOC: a – b(q, + q, +...+q,)- c - bq, = 0 а -b(q, +...+ 9N) -с 2b If all firms are symmetric: 4 = 92 = ... = AN = 9 • When n becomes infinity: 1 n lim lim n→∞ \n + 1 lim n→0 \n + 1 = 0 = 0 = 1
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