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if the price of a minivan is 40,000 find the price and quantity of a passenger...

if the price of a minivan is 40,000 find the price and quantity of a passenger car that maximizes revenue when the demand for a passenger car is characterized by the following question

Qd= 20,000 - 4P1+ 2P2

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Homework Answers

Answer #1

Q = 20000 - 4P1 + 2P2

P2 = price of minivan = 40000

P1 = price of passenger car

Q = 20000 - 4P1 + 2(40000)

Q = 20000 - 4P1 + 80000

= 100000 -  4P1

R = QP1

= (100000 -  4P1 )P1

= 100000P1 - 4P12

dR/dP1 = 100000 - 8P1

put dR/dP1 = 0

100000 - 8P1 = 0  

100000 = 8P1

P1   = 100000/8

= 12500

d2R/dP12 = - 8 < 0

so  P1 = 12500 is the revenue maximizing price

Q = 100000 - 4P1

= 100000 - 4(12500)

= 100000 - 50000

= 50000

Thus revenue maximizing price and quantity of passenger car are 12500 and 50000 respectively.

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