Answer to Question #51157 in Economics of Enterprise for s math
If the firms have identical cost functions given by C (Q) = 40 Q, so every firm produce the quantity, for which MR = MC.
MC = C' = 40
MR = TR' = (P*Q)' = ((100 - Q)*Q)' = 100 - 2Q
So, 100 - 2Q = 40,
Q = 30
So, the equilibrium industry output if the producers are Cournot competitors is 30*4 = 120 units.
The market price is P = 100 - 30 = $70.
Total profits of each firm are: TP = TR - TC = P*Q - TC = 70*30 - 40*30 = $900.
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