A monopolistic seller sells the same good in 2 markets. The demands in the two m
ID: 1201999 • Letter: A
Question
A monopolistic seller sells the same good in 2 markets. The demands in the two markets areQ1= 100-p1. Q2=60-(1/2)p2 Assume marginal cost is 10
A) find the profit maximizing price and output in the two markets. What is total profit? A monopolistic seller sells the same good in 2 markets. The demands in the two markets are
Q1= 100-p1. Q2=60-(1/2)p2 Assume marginal cost is 10
A) find the profit maximizing price and output in the two markets. What is total profit?
Q1= 100-p1. Q2=60-(1/2)p2 Assume marginal cost is 10
A) find the profit maximizing price and output in the two markets. What is total profit?
Explanation / Answer
1st market:
Q1 = 100 – P1
P1 = 100 – Q1
TR = P1Q1 = 100Q1 – (Q1)^2
MR = Derivative of TR with respect to Q1
= 100 – 2Q1
The equilibrium condition is MR = MC
100 – 2Q1 = 10
2Q1 = 90
Q1 = 45
Putting Q1 = 45 in P1 = 100 – Q1 = 100 – 45 = 55
Answer: Profit maximizing price is $55 and quantity is 45 units.
2nd market:
Q2 = 60 – 0.5P2
0.5P2 = 60 – Q2
P2 = 120 – 2Q2
TR = P2Q2 = 120Q2 – 2(Q2)^2
MR = Derivative of TR with respect to Q2
= 120 – 4Q2
The equilibrium condition is MR = MC
120 – 4Q2 = 10
4Q2 = 110
Q2 = 27.5
Putting Q2 = 27.5 in P2 = 120 – 2Q2 = 120 – 55 = 65
Answer: Profit maximizing price is $65 and quantity is 27.5 units.
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