Homework Answers
Answer ) d) 50 units
MC1 = MC2 = 10
q1 - quantity by firm 1
q2 - quantiy by firm 2
Demand :
P = 110 - 0.5q
Profit of firm 2 = P x q2 - 10q2 = (110 -0.5q1 -0.5q2) x q2 - 10q2
Differenting with respect to q2 and equate to 0
110 -0.5q1 -q2 - 10 = 0
100 -0.5q1 - q2 = 0
q2 = 100 -0.5q1 (equation 1)
Profit of firm 1 = P x q1 - 10q1 = (110 - 0.5q1 -0.5q2) q1 -10q1
Profit = [110 - 0.5q1 - 0.5(100 -0.5q1) ] q1 - 10q1 = ( 60 - 0.25q1) x q1 -10q1
Differentiating with respect to q1 and equate to 0
60 - 0.5q1 - 10 = 0
q1 = 100
Put this in equation 1
q2 = 100 -0.5( 100) = 100 - 50 = 50
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