Answer to Question #51002 in Microeconomics for jemkhomang lotjem
have identical cost
functions given by C (Q) = 40 Q. If the demand curve for the industr
y is given by
= 100 – Q,
find the equilibrium industry output if the producers are Cournot competitor
s. What would be
the resultant market price? What are the profits of each firm?
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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