The market demand is p=50-Q. There are two firms who behave as Cournot duopolist
ID: 1201984 • Letter: T
Question
The market demand is p=50-Q. There are two firms who behave as Cournot duopolists. For simplicity assume the marginal cost is zeroA) solve for the equilibrium price and output
B) compare results with monopoly price and output The market demand is p=50-Q. There are two firms who behave as Cournot duopolists. For simplicity assume the marginal cost is zero
A) solve for the equilibrium price and output
B) compare results with monopoly price and output
A) solve for the equilibrium price and output
B) compare results with monopoly price and output
Explanation / Answer
A. Cournot duopoly:
P = 50 – Q
P = 50 – (q1 + q2)
TR = Pq1 = 50q1 – (q1)^2 – q1q2
MR = Derivative of TR with respect to q1
= 50 – 2q1 – q2
MC = 0
The equilibrium condition is MR = MC
50 – 2q1 – q2 = 0
2q1 + q2 = 50 ……………………..(i)
Again, TR = Pq2 = 50q2 – q1q2 – (q2)^2
MR = Derivative of TR with respect to q2
= 50 – 2q2 – q1
MC = 0
The equilibrium condition is MR = MC
50 – 2q2 – q1 = 0
2q2 + q1 = 50 ……………………..(ii)
Solving equation (i) and (ii), q1 = 50/3 and q2 = 50/3
Putting q1 = 50/3 and q2 = 50/3 in the price function
P = 50 – (q1 + q2)
= 50 – (50/3+ 50/3)
= 50 – 100/3
= 50/3
Answer: Equilibrium price (P) is 50/3. Equilibrium output (q1) is 50/3 and (q2) is 50/3.
B. Monopoly:
P = 50 – Q
TR = PQ = 50Q – Q^2
MR = Derivative of TR with respect to Q
= 50 – 2Q
The equilibrium condition is MR = MC
50 – 2Q = 0
2Q = 50
Q = 25
Putting Q = 25 in the price function, P = 50 – Q = 50 – 25 = 25
Answer: Equilibrium price (P) is 25. Equilibrium output (Q) is 25.
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