Answer to Question #287890 in Microeconomics for Johnny

Question

Given a monopoly graph: If P = 10 - 2Q

1/ Find MR

2/ Identify the break even price

3/ Identify the Profit Maximizing Price and Quantity  

4/ Identify & shade the area of the deadweight loss that is consumer surplus 

Answer 1

Solution:

1.). MR = ∂TR/∂Q

TR = P x Q

TR = (10 – 2Q) Q = 10Q – Q²

MR = 19 – 2Q

 

2.). Break-even price:

P = 10 – 2Q

10 – 2Q = 0

10 = 2Q

Q = 5

Price = 19 – 2(5) = 19 – 10 = 9

Breakeven price = 9

 

3.). Profit maximizing quantity and price is where MR = MC

MR = 19 – 2Q

MC = 0

19 – 2Q = 0

19 = 2Q

Q = 9.5

Profit maximizing quantity = 9.5

Substitute in the demand function to derive price:

P = 10 – 2Q

P = 10 – 2(9.5) = 10 – 18 = (8)

Profi maximizing piece = (8)