An industry demand curve faced by firms in a duopoly is P = 69 - Q, where Q = Q1 + Q2. MC for each firm is 0. How many units should each firm produce? How much money will each firm make?
What will be an ideal response?
First the anticipated demand curves for each firm are derived:
For firm 1: P = (69 - Q2) - Q1.
For firm 2: P = (69 - Q1) - Q2.
Now the MR curves for each firm are derived:
For firm 1: MR1 = (69 - Q2) - 2Q1
For firm 2: MR2 = (69 - Q1) - 2Q2
Set MR = MC for both firms and solve for the quantities:
(69 - Q2) - 2Q1 = (69 - Q1) - 2Q2
or Q1 = Q2,
which means (69 - Q1) - 2Q1 = 0
or 69 - 3Q1 = 0
or Q1 = 23 units = Q2.
Therefore, Q = Q1 + Q2 = 46 units,
and so P = 69 - 46 = $23.
So each firm's TR = $23 x 23 = $529.
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