Two firms compete in selling homogeneousgoods. They choose their output levels q1and q2 simultaneously and face demandcurve P=80-6Q, where Q=q1+q2.The total cost function of firm 1 is C1=8q1and the total cost function of firm 2 isC2=32q2+2/3.a) Find and draw the reaction curves of thetwo firms.b) Compute equilibrium quantities, priceand profits.Suppose now that firm 2, thanks to atechnological innovation, becomes moreefficient. The new total cost function offirm 2 is C2=8q2c) Compute the new equilibrium quantities,price and profits.

Answered: Two firms compete in selling…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two firms compete in selling homogeneous
goods. They choose their output levels q1
and q2 simultaneously and face demand
curve P=80-6Q, where Q=q1+q2.
The total cost function of firm 1 is C1=8q1
and the total cost function of firm 2 is
C2=32q2+2/3.
a) Find and draw the reaction curves of the
two firms.
b) Compute equilibrium quantities, price
and profits.
Suppose now that firm 2, thanks to a
technological innovation, becomes more
efficient. The new total cost function of
firm 2 is C2=8q2
c) Compute the new equilibrium quantities,
price and profits.

Expert Solution

Given

We are given:

$P = 80 - 6 Q (D e m a n d f u n c t i o n) w h e r e Q = q 1 + q 2 C 1 = 8 q 1, C 2 = 32 q 2 + 2 / 3 M C 1 = \frac{\partial C 1}{\partial q 1} = 8 M C 2 = \frac{\partial C 2}{\partial q 2} = 32 T R 1 = P * q 1 = (80 - 6 Q) * q 1 = > (80 - 6 q 1 - 6 q 2) * q 1 M R 1 = \frac{\partial T R 1}{\partial q 1} = (80 - 6 q 1 - 6 q 2) + q 1 (- 6) = 80 - 12 q 1 - 6 q 2 T R 2 = P * q 2 = (80 - 6 Q) * q 2 = > (80 - 6 q 1 - 6 q 2) * q 2 M R 2 = \frac{\partial T R 2}{\partial q 2} = (80 - 6 q 1 - 6 q 2) + q 2 (- 6) = 80 - 6 q 1 - 12 q 2 P r o f i t m a x i m i z a t i o n f o r f i r m_1 : = > M R 1 = M C 1 = > 80 - 12 q 1 - 6 q 2 = 8 = > q 1 = 6 - 0.5 q 2 (R e a c t i o n c u r v e f o r f i r m 1) P r o f i t m a x i m i z a t i o n f o r f i r m_2 : = > M R 2 = M C 2 = > 80 - 6 q 1 - 12 q 2 = 32 = > q 2 = 4 - 0.5 q 1 (R e a c t i o n c u r v e f o r f i r m 2)$

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