Answer to Question #210104 in Microeconomics for alem

Question #210104

1.     Assume the following for price discriminating monopolist aimed at maximizing profit. Total demand for the product of the monopolist is Q = 50-5P (P = 100-2Q) (10 Marks)

·        Demand in Market one is Q1= 32-0.4P1(P1= 80-2.5Q1)

·        Demand in Market two is Q2= 18-0.1P2(P2= 180-10Q2)

·        Cost function is C = 50+40Q (where Q = Q1+ Q2)



1
Expert's answer
2021-06-27T18:43:04-0400

a.

Total revenue in market 1

"= 80Q_1 - 2.5 Q_1^2"

Marginal revenue in market 1

"=\\frac{ \u2206TR}{ \u2206 Q_1}\\\\\n\n = 80 - 5 Q_1 \\\\\n\nMC = 40 \\\\\n\n80 - 5 Q_1 = 40 \\\\\n\n40 = 5 Q_1 \\\\\n\nQ_1 = 8"


Total revenue 2

"= P \u00d7 Q = 180Q_2 - 10 Q_2^2"

Marginal revenue 2

 "= 180 - 20 Q_2 \\\\\n\nMC = 40 \\\\\n\nEquating \\space MR = MC \\\\\n\n180 - 20 Q_2 = 40 \\\\\n\n140 = 20 Q2 \n\nQ_2 = 7 \\\\"


b.

"P_1 = 80 - 2.5 (8) = 60\\\\\n\nP_2 = 180-10Q_2 = 110"


c.

"Profit = TR_ 1 + TR_ 2 - TC \\\\\n\n = 8(60) + 7(110) - 50 - 40(15) \\\\\n\n = 480 + 770 - 50 - 600\\\\ \n\n = 600"


d.

"Q_1= 32-0.4P_1 \\\\\n\n\\frac{\u2206Q_1}{\u2206P_1 }= - 0.4 \\\\\n\ne = \\frac{\u2206Q_1 }{ \u2206 P_1} \\times \\frac{ P\n_1 }{Q _1}\\\\\n\ne = -0.4 \\times (\\frac{60 \n\n\n\n\n\n\n}{ 8}) = - 3\\\\\n\nQ_2= 18-0.1P_2 \\\\\n\n\\frac{\u2206Q2}{ \u2206 P_2 }= -0.1 \\\\\n\ne =\\frac{ \u2206Q2 }{\u2206 P_2 }\\times \\frac{P_2 }{Q _2}= -0.1(\\frac{110}{7}) = -1.57"


Good 2 is less price elastic. 

A higher price is charged to the low elasticity segment and a lower price is charged to the high elasticity segment.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS