Answer to Question #51157 in Economics of Enterprise for s math

Question

four firm supplying homogeneous product have identical cost function given by C(Q)=40Q. if demand curve for the industry is given by m=100-Q. find the equilibrium output if they are cournot competitors what would be the resultant market price? what are the profit of the each firm ?

Answer 1

Each firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a monopoly.
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.