Homework Answers
a) Profit function for firm A is given by πA = (400 - 5QA - 5QB)QA - 30QA
πA = 370QA - 5QA^2 - 5QAQB
Similarly, profit function for firm B is given by πB = (400 - 5QA - 5QB)QB - 40QB
πB = 360QB - 5QB^2 - 5QAQB
For reaction functions, find πA'(0) = 0 and πB'(0) = 0
This gives 370 - 10QA - 5QB = 0 or 360 - 10QB - 5QA = 0
The reaction functions are therefore
QA = 37 - 0.5QB for firm A and QB = 36 - 0.5QA for firm B
b) Find the equilibrium using the reaction functions
QA = 37 - 0.5*(36 - 0.5QA)
QA = 25.33 and so QB = 23.33
Equilibrium price P = 400-5*(25.33+23.33) = $156.67
c) Profit πA = (156.67 - 30)*25.33 = 3208.88 and πB = (156.67 - 40)*23.33 = 2722.22
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