Answer to Question #273116 in Microeconomics for Malithi pabasara

Question #273116

Following information shows that a firm offering a good at different prices to groups of consumers with different levels of willingness to pay.







Inverse Demand for movies: P1 = 20 – 4Q1







Inverse Demand for students: P2 = 10 – Q2







MC = 4Q LKR /ticket







(a) What price and quantity and maximizes profits if the firm charges each market?







(b) Demonstrate that charging different prices for the two groups results in higher profits than charging the same price for everyone.

1
Expert's answer
2021-11-29T10:40:45-0500

Solution:

a.). A firm maximizes profits at the point where: MC = MR

Market 1 - Movies:

Inverse Demand for movies: P1 = 20 – 4Q1

Derive MR1:

TR1 = P "\\times" Q1

TR1 = (20 – 4Q1) "\\times" Q1 = 20Q – 4Q12

MR1 = "\\frac{\\partial TR_{1} } {\\partial Q_{1} }" = 20 – 8Q1

MR1 = 20 – 8Q1

MC1 = 4

MR1 = MC1

4 = 20 – 8Q1

8Q1 = 20 – 4

8Q1 = 16

Q1 = 2

Market 1 quantity = 2


Substitute in the demand function to derive price:

P1 = 20 – 4Q1

P1 = 20 – 4(2) = 20 – 8 = 12

Market 1 price = 12

Market 2 - Students:

Inverse Demand for students: P2 = 10 – Q2

Derive MR2:

TR2 = P "\\times" Q2

TR2 = (10 – Q2) "\\times" Q2 = 10Q2 – Q22

MR2 = "\\frac{\\partial TR_{2} } {\\partial Q_{2} }" = 10 – 2Q2

MR2 = 10 – 2Q2

MC2 = 4

MR2 = MC2

4 = 10 – 2Q2

2Q2 = 10 – 4

2Q2 = 6

Q2 = 3

Market 2 quantity = 3

Substitute in the demand function to derive price:

P2 = 10 – Q2

P2 = 10 – 3 = 7

Market 2 price = 7

 

b.). Profits in terms of revenue:

TR – Market 1 = 12 "\\times" 2 = 24

TR – Market 2 = 7 "\\times" 3 = 21

This means that market 1 will generate more revenues than market 2, signifying that charging different prices will generate more revenue for the firm.


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