Hello, could you solve
Question3 - Part 3 (the third question) please, Thank you very
much!
Homework Answers
3) From part 2) we have a demand function P = 53 - (Q1 + Q2)
Profit for firm 1 = π1 = Revenue - costs = PQ1 - 5Q1
π1 = (53 - Q1 - Q2)Q1 - 5Q1
= 53Q1 - Q1^2 - Q1Q2 - 5Q1
π1 = 48Q1 - Q1^2 - Q1Q2
Now profit is maximum when marginal profit is 0
π1 '(Q1) = 0
48 - 2Q1 - Q2 = 0
Q1 = 24 - 0.5Q2
This is the reaction function for firm 1
Similarly we have
Profit for firm 2 = π2 = Revenue - costs = PQ2 - 5Q2
π2 = (53 - Q1 - Q2)Q2 - 5Q2
= 53Q2 - Q1Q2 - Q2^2 - 5Q2
π2 = 48Q2 - Q2^2 - Q1Q2
Now profit is maximum when marginal profit is 0
π2 '(Q2) = 0
48 - 2Q2 - Q1 = 0
Q2 = 24 - 0.5Q1
This is the reaction function for firm 2
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