Question
Hello, could you solve Question3 - Part 3 (the third question) please, Thank you very much!...
Hello, could you solve Question3 - Part 3 (the third question) please, Thank you very much!
Question 3 A monopolist can produce at a constant average and marginal cost of ATC- MC demand demand curve given by Q-53-P. $5. It faces a market 1. Calculate the profit maximizing price and quantity for this monopolist. Also calculte its profits. 2. Suppose a secod firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1Q2 53 - P. Assuming that this second firm has the same costs as the first one, write the profits of each firm as functions of Q1 and Q2 3. Suppose (as in the Cournot model) that each firm chooses its profit maximizing level of output on the assumption that its competitior's output is fixed. Find each firm's "reaction function"
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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