f the monopolist cannot maintain the separation between the two markets, calculate the optimal output level and determine the price will this be sold?

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Hello! I just want to ask for help whether the answers in the given pictures are correct. If it's not, please help me recheck and resolve it. Please refer to the given pictures below for the answers.

 

After verifying the given answers shown in the subsequent picture, PLEASE ANSWER LETTER D.

 

SITUATION/PROBLEM:

Consider a price discriminating monopolist facing two markets for its good. The demand equations faced by the monopolist and its cost function are:

 

Market 1: Q1 = 55 - P1

Market 2: Q2 = 70 - 2P2

Cost Function: TC(Q) = 100 + 5Q, where Q = Q1 + Q2.

 

a. If the monopolist can maintain the separation between the two markets, calculate the optimal output level that the firm should produce for each market to maximize profits.

 

b. Determine the prices the monopoly should charge in each market, and calculate the profit of the monopoly.

 

c. Construct a graph to represent your findings in item # 3.a and #3.b.

 

d. If the monopolist cannot maintain the separation between the two markets, calculate the optimal output level and determine the price will this be sold?

 

NOTE: Type only your answers. Please do not handwritten your answers.

Step 3
*A
Profit maximization condition:
MR=MC
For market 1
MC=MR15=55-2Q
2Q1=50
Ql=25
For market 2
MC=MR2
5=35-Q2
Q2=30
So the optimal level of output level that the firm should produce for market lis 25 and for market 2 is 30.
Step 4
В
Putting Q1=25 in equation 4
P1=55-25=30
Putting Q2=30 in equation 6
P2=35-0.5×30P2=20
Monopoly should charge $30 for each unit of the good in market 1 and 20 for each unit of the good in market 2.
Monopolist profit:
Profit=R1+R2-TC
Profit=25x30+30×20-(100+5(25+30))
Profit=975
Step 5
*C
50
Price
Q1=55-P1
MR1
40
P1 3G
P2 20-
Q2=70-2P2
10-
(30, 5)
MC=5
(25, 5)
10
20
30
40
50
60
70
Q1
Q2
Quantity
Transcribed Image Text:Step 3 *A Profit maximization condition: MR=MC For market 1 MC=MR15=55-2Q 2Q1=50 Ql=25 For market 2 MC=MR2 5=35-Q2 Q2=30 So the optimal level of output level that the firm should produce for market lis 25 and for market 2 is 30. Step 4 В Putting Q1=25 in equation 4 P1=55-25=30 Putting Q2=30 in equation 6 P2=35-0.5×30P2=20 Monopoly should charge $30 for each unit of the good in market 1 and 20 for each unit of the good in market 2. Monopolist profit: Profit=R1+R2-TC Profit=25x30+30×20-(100+5(25+30)) Profit=975 Step 5 *C 50 Price Q1=55-P1 MR1 40 P1 3G P2 20- Q2=70-2P2 10- (30, 5) MC=5 (25, 5) 10 20 30 40 50 60 70 Q1 Q2 Quantity
*Answer:
Given
Market demand:
Market 1: Q1 = 55 – P1
%3D
(1)
Market 2: Q2 = 70 – 2P2
(2)
-
Cost function of the monopolist: TC(Q)=100+5Q
(3)
Where Q=Q1+Q2
Since you have posted multiple subparts question, as per the answering guideline, we will solve the first three subparts. Thanks
Step 2
MC=DTCDQ=5
The marginal cost of the firm is constant and equal to 5.
Inverse demand function in market 1:
P1=55-Q1
(4)
Revenue function of market 1:
R1=P1Q1
R1=55Q1-Q1?
And marginal revenue in market 1:
MR1=55-2Q1
(5)
Similarly:
Inverse demand function in market 2:
P2=35-0.5Q2
Revenue function of market 2:
R2=P2Q2
R2=35Q2-0.5Q2²
And marginal revenue in market 1:
MR2=35-Q2
(7)
Transcribed Image Text:*Answer: Given Market demand: Market 1: Q1 = 55 – P1 %3D (1) Market 2: Q2 = 70 – 2P2 (2) - Cost function of the monopolist: TC(Q)=100+5Q (3) Where Q=Q1+Q2 Since you have posted multiple subparts question, as per the answering guideline, we will solve the first three subparts. Thanks Step 2 MC=DTCDQ=5 The marginal cost of the firm is constant and equal to 5. Inverse demand function in market 1: P1=55-Q1 (4) Revenue function of market 1: R1=P1Q1 R1=55Q1-Q1? And marginal revenue in market 1: MR1=55-2Q1 (5) Similarly: Inverse demand function in market 2: P2=35-0.5Q2 Revenue function of market 2: R2=P2Q2 R2=35Q2-0.5Q2² And marginal revenue in market 1: MR2=35-Q2 (7)
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