(Collusive Duopoly Model) There are two firmsproducing widgets. It costs the first firm q1 dollars to produceq1 widgets and the second firm 0.5q2 2 dollars to produce q2widgets. If a total of q widgets are produced, consumerswill pay $200  q for each widget. If the two manufacturerswant to collude in an attempt to maximize the sum of theirprofits, how many widgets should each company produce?

Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Oligopoly
Section: Chapter Questions
Problem 1CQQ
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(Collusive Duopoly Model) There are two firms
producing widgets. It costs the first firm q1 dollars to produce
q1 widgets and the second firm 0.5q2
2 dollars to produce q2
widgets. If a total of q widgets are produced, consumers
will pay $200  q for each widget. If the two manufacturers
want to collude in an attempt to maximize the sum of their
profits, how many widgets should each company produce?
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