Answer to Question #54583 in Microeconomics for kitto

Question

assume that there are four firms suppying a homogeneous product.they have identical cost functions given by C(Q)=40Q.
IF THE demand curve for the industry is given by U=100-Q
find the equilibrium industry output if the producers are cournot competitors.
what would be the resultant market price?what are the profits of each firm?

Answer 1

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.