Homework Answers
a) Profit is given by πA = revenue - cost
πA = (100 - 2qA - 2qB)qA - 10qA
= 90qA - 2qA^2 - 2qAqB
Use the best response function of B
πA = 90qA - 2qA^2 - 2qA(20 - 0.5qA)
= 50qA - qA^2
b) Profit is maximum when π'(qA) = 0
50 - 2qA = 0
qA = 25 units and qB = 20 - 0.5*25 = 7.5 units
Market price P = 100 - 2*25 - 2*7.5 = $35 per unit
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