# Answer to Question #51662 in Microeconomics for Dipankar sonowal

Question #51662

Assume that there are four firms supplying a homogenous product.They have identical cost function given by C(Q)=40Q.If the demand curve for the insdustry is given by U=100-Q,find the equlibrium insdutry output if the producers are cournot copetitors.What would be the result market price?What are the profits of each firm?

Expert's answer

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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