Midterm Exam Worksheets With Answers - Prof. James Peck - The Ohio State University, Department Of Economics - 2010 Page 6
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6the price is zero and the payoff function is a downward sloping line instead of a
parabola. In this case, reducing q
to 6 also leads to a higher payoff for firm 1.]
1
(c) To find the Nash equilibrium, simultaneously solve the two best response
equations for the two outputs. By substituting, we have
q
6 −
1
2
q
= 6 −
,
1
2
q
1
2q
= 12 − (6 −
),
1
2
4q
= 24 − 12 + q
,
1
1
q
= 4.
1
Given that q
= 4, substituting into firm 2’s best-response function gives q
= 4.
1
2
Thus, the NE is (4, 4).
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